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Flemington-Raritan Regional School District Flemington, New Jersey

Mathematics Curriculum Grades 7-8

Gregory Nolan, Superintendent Daniel Bland, Assistant Superintendent Sandra Pollock, Mathematics Supervisor

Jennifer Bajorek Kristen Campbell David Hallinan Kim Holthaus Susan Hubert

Sherry Kodidek Patricia Machusak Melissa McAnlis

David Plichta Elizabeth Roll

Council of Instruction Review Date: May 9, 2012 BOE Curriculum Committee Review Date: June 7, 2012Board of Education Approval Date: June 18, 2012

Flemington-Raritan Regional Schools Mathematics Curriculum

Grades 7-8 Table of Contents

Mission Statement 1

Philosophy 2

2004 New Jersey Core Curriculum Content Standards 4

Program Description 5

Calculator Philosophy 7

Grade 7 Curriculum 9

7th Grade Interdisciplinary Connections 10

7th Grade Math Curriculum 18

7th Grade Algebra IA Curriculum 65

7th Grade Algebra IB Curriculum 110

Grade 8 Curriculum 154

8th Grade Interdisciplinary Connections 155

8th Grade Pre-Algebra Curriculum 164

8th Grade Algebra IB Curriculum 215

8th Grade Advanced Algebra Curriculum 258

8th Grade Algebra II Curriculum 304

Flemington-Raritan Regional Schools

Mathematics Curriculum

Grades 7-8

District Mission Statement

The Flemington-Raritan Regional School District provides our

students with an exceptional education, empowering them to

become problem solvers, collaborators and critical thinkers. The

district creates a culture in which students act responsibly and

communicate effectively in preparing to become productive citizens

in a changing, global society.

It is the expectation of the Flemington-Raritan School District that

all pupils achieve the New Jersey Core Curriculum Content

Standards at all grade levels.

1



Grades 7-8

Philosophy

The Grades 7-8 Mathematics Curriculum is based on the belief that all

students can learn mathematics. The mathematics program develops each

child’s mathematical reasoning in understanding the big ideas (concepts) of

mathematics. The program sets high benchmarks and expectations for

students to effectively express mathematical content, process, and skills

through verbal and written communication.

The use of technological tools is a vital component of the program, not only to

enhance the understanding of concepts, but an important tool used in the

adult world to access and analyze real world data.

In accordance with the above beliefs, the program includes a comprehensive

range of content in a variety of contexts. The program integrates skills,

concepts, and applications based on the 2004 New Jersey Core Curriculum

Content Standards for Mathematics, providing each student the opportunity to

become an active participant in his/her mathematical education. Students

explore the beauty of mathematics with confidence, with the aim to become a

generation of mathematically literate adults.

The grades 7-8 mathematics program is built on developmentally appropriate

practice for middle school students:

All students can learn and understand mathematics;

Students construct their own meaning based on prior experience;

Learning occurs in social situations;

Learning is tied to contextual, real-world situations;

Learning involves numerous strategies involving higher order thinking

skills. Students continually reflect on the following question: “Does this

make sense?”

2



Grades 7-8

The 21st Century Learning and Thinking Skills are an integral part of the 7-8

mathematics program including:

Critical Thinking and Problem Solving Skills

Communication Skills

Creativity and Innovation Skills

Collaboration Skills

Information and Media Literacy Skills

Contextual Learning Skills

3



Grades 7-8

2004 New Jersey Core Curriculum Content Standards – Mathematics

The 2004 New Jersey Core Curriculum Content Standards contain Specific

Cumulative Progress Indicators for each grade and the Mathematics

Curriculum for grades 7 and 8 reflects the relevant cumulative progress

indicators for grades 7, 8 and, where appropriate, grade 12. There are five

standards altogether, each of which has a number of lettered strands. These

standards and their associated strands, are enumerated below:

4.1 Number and Numerical Operations

A. Number Sense

B. Numerical Operations

C. Estimation

4.2 Geometry and Measurement

A. Geometric Properties

B. Transforming Shapes

C. Coordinate Geometry

D. Units of Measure

E. Measuring Geometric Objects

4.3 Patterns and Algebra

A. Patterns

B. Functions and Relationships

C. Modeling

D. Procedures

4.4 Data Analysis, Probability, and Discrete Mathematics

A. Data Analysis (Statistics)

B. Probability

C. Discrete Mathematics -- Systematic Listing and Counting

D. Discrete Mathematics -- Vertex-Edge Graphs and Algorithms

4.5 Mathematical Processes

A. Problem Solving

B. Communication

C. Connections

D. Reasoning

E. Representation

F. Technology

4



Grades 7-8

Program Description

The curriculum emphasizes a balance between hands-on, inquiry-based

problem solving, and traditional mathematical computation and arithmetic.

Teachers focus on making connections between facts and fostering new

understanding in students, and tailor their teaching strategies to student

responses, encouraging students to analyze, interpret, and predict information.

Teachers also rely heavily on open-ended questions and promote extensive

dialogue among students through cooperative learning strategies.

Assessments consist of teacher-created quizzes, tests, teacher observations,

student responses, student projects, student daily work, district wide and state

wide testing as well as the Hunterdon Central High School placement exams.

In practice, assessment is ongoing and serves to provide feedback to students

and to inform instruction. Teachers use a variety of assessment techniques,

both quantitative and qualitative, to assess student development in the areas of

mathematical conceptual understanding, mathematical procedures, and

mathematical process. Multiple choice, short answer, and open-ended

responses requiring written explanations are all components of the ongoing

assessments in the classroom.

In grades 7 and 8, all students are grouped homogeneously by ability and

achievement in mathematics. Various district wide tests, teacher

recommendation, and student performance are considered when placing

students for mathematics. Mathematics textbooks, support materials, and

teacher instruction are modified according to the different needs of students in

order for students to meet the New Jersey Core Curriculum Standards for each

grade level. Continual assessment and reflection upon student work and

achievement drives instruction. All student data, performance and

achievement are constantly monitored in order to move students forward to

their fullest mathematical potential. Placements procedures include not only

student ability and achievement in concepts and computation, but also the

ability to work independently at an accelerated pace.

5



Grades 7-8

The following textbooks are used in grades 7 and 8 mathematics classes at

J.P. Case Middle School:

Level Textbook

Grade 7

7th Grade Math McDougal Littell Course 2

Holt Course 2 (Special Education)

Algebra IA Larson Algebra 1 (first half)

Algebra IB Larson Algebra 1 (second half)

Grade 8

Pre-Algebra McDougal Littell Course 3

Holt Course 3 (Special Education)

Algebra IB Larson Algebra 1 (second half)

Advanced Algebra Larson Algebra 2

Algebra II Larson Algebra 2

6



Grades 7-8

Calculator Philosophy

The J.P. Case Middle School mathematics program believes that calculators are

a vital component of the mathematics program.

The following rationale from Texas Instruments covers many of the advantages

of using calculators, as outlined by the NCTM and the 2004 New Jersey Core

Curriculum Standards.

Calculators are valuable educational tools that allow students to reach a higher

level of mathematical power and understanding. By reducing the time that, in

the past, was spent on performing tedious paper-and-pencil arithmetic and

algebraic algorithms, calculator use today allows students and teachers to

spend more time developing mathematical understanding, reasoning, number

sense, and applications. They afford students learning tools that complement,

but do not replace, mental and paper-and-pencil skills, and they expand

students’ ability to solve problems by providing multiple solution techniques.

Calculator technology allows students who would ordinarily be frustrated or

bored by tedious manipulations to have access to the real mathematics itself,

thus gaining a higher level of mathematical understanding, rather than giving

up. The fact is, calculators are better tools to do some of the computations and

manipulations that were once done with paper and pencil. In the past, paper

and pencil were the only tools available. Appropriate use of technology and

associated pedagogy will get more students thinking and reasoning

mathematically. Thus more students will develop useful mathematical

understanding and mathematical power.

Despite all of their benefits and capabilities, calculators will never be able to

replace the human mind when it comes to knowing how to read and

understand a problem situation, writing an appropriate equation for the

problem, choosing which operations to use to solve the problem, correctly

interpreting the solution displayed on the calculator, and determining the

appropriateness of the answer. Calculators are only as effective as the

information students enter into them. Calculators, in conjunction with mental,

paper-and-pencil, and estimation skills when appropriate, comprise the tools to

7

help students work through the computations and manipulations necessary for

solving problems. Calculators are like computer word processors to English

students. Computer word processors do not “create” essays but they do

facilitate the creation of an essay. Calculators do not “understand”

mathematics but they do facilitate the understanding of mathematics. Despite

all of their capabilities, however, they will never replace the important, complex

thought processes of which only humans are capable.

8

7th Grade Curriculum

9

4.2.A.2. Understand and apply the concept of similarity:

Using proportions to find missing measures; Scale

drawings; Models of 3D objects.

Art

Social Studies

Scale Drawings, Polygon Project

Reading a map, identifying landmarks on a

map

4.1.B. 1. Use and explain procedures for performing

calculations with integers and all number types named

above with: Pencil-and-paper; Mental math;

Calculator.

Science Labs throughout the year

4.1.C.1. Use equivalent representations of numbers such

as fractions, decimals, and percents to facilitate

estimation.

All Disciplines Discussions, labs all year long

4.1.A.2. Demonstrate a sense of the relative magnitudes

of numbers.

Science

Social Studies

Parts per Billion Lab

Population of the Middle Ages

4.1.A.3. Understand and use ratios, rates, proportions,

and percents (including percents greater than 100 and

less than 1) in a variety of situations.

Social Studies Junior Scholatic Magazines

Flemington Raritan School District


Grades 7-8

7th Grade Interdisciplinary Connections

Standard Subject Learning Experience


10



Grades 7-8



4.2.E.1. Develop and apply strategies for finding

perimeter and area: Geometric figures made by

combining triangles, rectangles and circles or parts of

circles; Estimation of area using grids of various sizes.

Social Studies iSearch, population density

4.2.C.1. Use coordinates in four quadrants to represent

geometric concepts.

Social Studies Map Reading

4.2.D.1. Solve problems requiring calculations that

involve different units of measurement within a

measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

Science

Social Studies

Art

Labs, Metric system use

Reading a scale on a map

Making a scale drawing

4.2.B.1. Understand and apply transformations: Finding

the image, given the pre-image, and vice-versa; Finding

the image, given the pre-image, and vice-versa;

Sequence of transformations needed to map one figure

onto another; Reflections, rotations, and translations

result in images congruent to the pre-image; Dilations

(stretching/shrinking) result in images similar to the pre-

image.

Art Tessellations, Transformations


11



Grades 7-8



4.3.C.1. Analyze functional relationships to explain how

a change in one quantity can result in a change in

another, using pictures, graphs, charts, and equations.

Science Volume and Density labs

Motion and Sound labs

4.3.C.2. Use patterns, relations, symbolic algebra, and

linear functions to model situations: Using

manipulatives, tables, graphs, verbal rules, algebraic

expressions/equations/inequalities; Growth situations,

such as population growth and compound interest,

using recursive (e.g., NOW- NEXT) formulas (cf.

science standards and social studies standards).

Science Volume and Density labs

Motion and Sound labs

4.3.A.1. Recognize, describe, extend, and create patterns

involving whole numbers, rational numbers, and

integers: Descriptions using tables, verbal and symbolic

rules, graphs, simple equations or expressions; Finite

and infinite sequences; Arithmetic sequences (i.e.,

sequences generated by repeated addition of a fixed

number, positive or negative); Geometric sequences

(i.e., sequences generated by repeated multiplication by

a fixed positive ratio, greater than 1 or less than 1).

Social Studies iSearch data gathering


12



Grades 7-8



4.4.B.3. Estimate probabilities and make predictions

based on experimental and theoretical probabilities.

Economics Insurance Industry

4.4.A.2. Make inferences and formulate and evaluate

arguments based on displays and analysis of data.

Science Lab write-ups

Daily Discussions in Social Studies and

Science

4.4.B.1. Interpret probabilities as ratios, percents, and

decimals.

Science Probability of weather occurring

4.3.D.2. Solve simple linear equations informally and

graphically: Multi-step, integer coefficients only

(although answers may not be integers); Using paper-

and-pencil, calculators, graphing calculators,

spreadsheets, and other technology.

Science Motion and Sound unit

Volume and Density unit

4.4.A.1. Select and use appropriate representations for

sets of data, and measures of central tendency (mean,

median, and mode): Type of display most appropriate

for given data; Box-and-whisker plot, upper quartile,

lower quartile; Scatter plot; Calculators and computer

used to record and process information.

Social Studies

Discovering Algebra

iSearch Paper

Use of Statistics to compare gender equality,

life expectancy, zoology, election results,

deomgraphics, penny data


13



Grades 7-8



4.5.A.6. Distinguish relevant from irrelevant

information, and identify missing information.

Language Arts Reading Skills

4.5.B.1. Use communication to organize and clarify

mathematical thinking: Reading and writing;

Discussion, listening, and questioning.

Language Arts Grammar Usage, Paragraph Construction

Skills

4.4.C.2. Explore counting problems involving Venn

diagrams with three attributes.

Language Arts Venn Diagrams - compare and contrast

4.5.A.2. Solve problems that arise in mathematics and in

other contexts: Open-ended problems; Non-routine

problems; Problems with multiple solutions; Problems

that can be solved in several ways.

Language Arts Reading Skills

4.4.C.1. Apply the multiplication principle of counting:

Permutations: ordered situations with replacement

(e.g., number of possible license plates) vs. ordered

situations without replacement (e.g., number of possible

slates of 3 class officers from a 23 student class).

Social Studies Population increases and license plate

number, area codes, phone numbers

(availability)


14



Grades 7-8



4.5.C.3. Recognize that mathematics is used in a variety

of contexts outside of mathematics.

Science

Social Studies

Art

Computer Applications

Cooking and Sewing

Physics Formulas, graphs, tables

Statistics

Transformations, perspectives, scale

drawing, computer aided design

Marble maze

Measuring Ingredients, Measuring material

4.5.C.4. Apply mathematics in practical situations and

in other disciplines.

Science

Social Studies

Art

Computer Applications

Cooking and Sewing

Physics Formulas, graphs, tables

Statistics

Transformations, perspectives, scale

drawing, computer aided design

Marble maze

Measuring Ingredients, Measuring material

4.5.B.2. Communicate mathematical thinking

coherently and clearly to peers, teachers, and others,

both orally and in writing.

Language Arts Grammar Usage, Paragraph Construction

Skills

4.5.B.3. Analyze and evaluate the mathematical thinking

and strategies of others.

Language Arts Peer editing


15



Grades 7-8



4.5.E.3. Use representations to model and interpret

physical, social, and mathematical phenomena.

See 4.4 Standards

4.5.D.6. Evaluate examples of mathematical reasoning

and determine whether they are valid.

Science Scientific Method

4.5.E.1. Create and use representations to organize,

record, and communicate mathematical ideas: Concrete

representations (e.g., base-ten blocks or algebra tiles);

Pictorial representations (e.g., diagrams, charts, or

tables); Symbolic representations (e.g., a formula);

Graphical representations (e.g., a line graph).

Science

Social Studies

Gathering Data from Labs

Graph Population over time

4.5.D.2. Use reasoning to support their mathematical

conclusions and problem solutions.

Language Arts Persuasive writing, supporting their ideas

4.5.D.5. Make and investigate mathematical

conjectures: Counterexamples as a means of disproving

conjectures; Verifying conjectures using informal

reasoning or proofs.

Science Scientific Method


16



Grades 7-8



4.5.F.2. Use computer spreadsheets, software, and

graphing utilities to organize and display quantitative

information.

Computers

4.5.F.6. Use computer-based laboratory technology for

mathematical applications in the sciences.

Science Long run value

4.5.F.1. Use technology to gather, analyze, and

communicate mathematical information.

Science

Social Studies

Labs, temperature probes, sound waves,

light refraction

iSearch


17

7th Grade Math Curriculum

18

A. Number Sense

· How do mathematical ideas interconnect and build on one another to produce a coherent whole?

· How can we compare and contrast numbers?

· How can counting, measuring, or labeling help to make sense of the world around us?

Resources

Standard 4.1 Number and Numerical Operations

Teacher Observation

Test/Quiz

Do Now

iPod/iPad

Teacher Observation

Test/Quiz

Do Now

Teacher Observation

Test/Quiz

Do Now

Dilations, Reductions

Similarity Lab

Sales Tax

Newspaper Coupons

Grades

Real World Problems

Assessments


3. Understand and use ratios, rates,

proportions, and percents (including percents

greater than 100 and less than 1) in a variety

of situations.

Knowledge/Skills/Understanding Learning Experiences


Grades 7-8

McDougal Littell Chapter 8,9

Pre-Algebra With Pizzazz!

Math With Pizzazz! Books C-E

Holt Chapter 5,6*

Kuta Software

McDougal Littell Chapter 1,2,4,6



Holt Chapter 1,2,3*

Kuta Software

2. Demonstrate a sense of the relative

magnitudes of numbers.

Number Line Graphing

Comparing Bar Graphs

Spend $1000/sec, How long to

spend a trillion dollars?

Calculator Use

Essential Questions :

1. Extend understanding of the number

system by constructing meanings for the

following (unless otherwise noted, all

indicators for grade 7 pertain to these sets of

numbers as well): Rational numbers;

Percents; Whole numbers with exponents.

Interactive Student Line-Up

Games

Geometer’s Sketchpad- Lesson

Links

Newspaper Coupons


Pre-Algebra With Pizzazz!!


Developing Skills in Algebra One,

Book A

Holt Chapter 1,2,3*

Kuta Software

4.1.A 7th Grade Math

19

A. Number Sense




Resources


Assessments




Grades 7-8


Teacher Observation

Test/Quiz

Do Now

iPod/iPad

Interactive Student Line-Up

Graphing Ordered Pairs

Measures of Center

I Have-Who Has Game

White Board Activities

Teacher-Generated Questions

Daily Use of Common Fractions,

Decimal and Percents

Coupons

5. Use whole numbers, fractions, decimals,

and percents to represent equivalent forms of

the same number.

McDougal Littell Chapter 2,4,6

Pre-Algebra With Pizzazz

Math With Pizzazz Books C-E

Holt Chapter 2*

Kuta Software




Developing Skills in Algebra One,

Book A

Holt Chapter 2*

4. Compare and order numbers of all named

types.

Teacher Observation

Test/Quiz

Do Now

iPod/iPad


20

A. Number Sense




Resources


Assessments




Grades 7-8


6. Understand that all fractions can be

represented as repeating or terminating

decimals.




White Board Activities


Daily Use of Common Fractions,

Decimal and Percents

Coupons

Teacher Observation

Test/Quiz

Do Now

Teacher will emphasize the

difference through class

discussion and practice

problems

iPod/iPad


21

· What makes a computational strategy both effective and efficient?

· How do operations affect numbers?

· How do mathematical representations reflect the needs of society across cultures?

Resources Assessments





1. Use and explain procedures for performing

calculations with integers and all number

types named above with: Pencil-and-paper;

Mental math; Calculator.

McDougal Littell Chapter 1

Holt Chapter 1*

Kuta Software



Grades 7-8

Teacher Observation

Do Now

Test/Quiz

Use of Graphing Calculator

Minute Math*


Geometer’s Sketchpad Lesson

Links

Mad Minute

Holt Chapter 2,3*

Kuta Software

Teacher Observation

Do Now

Test/Quiz

iPod/iPad

Minute Math*

Geometer’s Sketchpad-Lesson

Links


Teacher-Created Worksheets

3. Understand and apply the standard

algebraic order of operations, including

appropriate use of parentheses.


Discovering Algebra Chapter 4

Holt Chapter 1*

Kuta Software

Teacher Observation

Do Now

Test/Quiz

Minute Math*

Geometer’s Sketchpad

Discovering Algebra 4.1


2. Use exponentiation to find whole number

powers of numbers.

4.1.B 7th Grade Math

22

C. Estimation

· How can we decide when to use an exact answer and when to use an estimate?

Resources



Grades 7-8



Knowledge/Skills/Understanding Learning Experiences Assessments

1. Use equivalent representations of numbers

such as fractions, decimals, and percents to

facilitate estimation.

McDougal Littell Chapter

1,2,4,5,6,9

Pgs 736-737 in Student Text

Teacher Edition A2

Holt Chapter 2,3*

Daily Warm-Ups

Everyday Use of Numbers


Teacher Observation

Test/Quiz

Do Now

4.1.C 7th Grade Math

23

Standard 4.2 Geometry and Geometrical Properties

· How can spatial relationships be described by careful use of geometric language?

· How do geometric relationships help to solve problems and/or make sense of phenomena?

Resources



Grades 7-8




1. Understand and apply properties of

polygons: Quadrilaterals, including squares,

rectangles, parallelograms, trapezoids,

rhombi; Regular polygons.


Math with Pizzazz! Books C-E

Pre-Algebra with Pizzazz!

Holt Chapter 8*

Kuta Software

Geoboards

White Boards

Communicators*

Polygon Name Projects

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises

iPod/iPad

2. Understand and apply the concept of

similarity: Using proportions to find missing

measures; Scale drawings; Models of 3D

objects.




Holt Chapter 5,6,10* Kuta

Software

Similarity Lab

Graphing Calculators

Flagpole Measurement by using

shadow of pole and student

Math Cartoons

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises


24




Resources



Grades 7-8




3. Use logic and reasoning to make and

support conjectures about geometric objects.




Holt Chapter 8,9*


Question of Same Perimeter,

What is the Maximum Area?

Give closed properties, have

class draw shape. If class has

different shapes, ask for more

properties. Discuss necessary

properties and subsets.

Teacher Observation

Test/Quiz

Do Now

Warm-up Exercises


25


· What situations can be analyzed using transformations and symmetries?

Resources

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

iPod/iPad






Grades 7-8

1. Understand and apply transformations:

Finding the image, given the pre-image, and

vice-versa; Sequence of transformations

needed to map one figure onto another;

Reflections, rotations, and translations result

in images congruent to the pre-image;

Dilations (stretching/shrinking) result in

images similar to the pre-image.




Holt Chapter 8*

Kuta Software

White Boards – Class Graphing

Activities

Can You Transform? Game

Communicators*

Hands-on rotations*

See 4.2 C


26


· How can geometric/algebraic relationships best be represented and verified?

Resources

White Boards – Graphing Points


Communicators*

Coordinate plane white boards

Geoboards



Grades 7-8



Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

2. Use a coordinate grid to model and quantify

transformations (e.g., translate right 4 units).




Holt Chapter 8*

Kuta Software


Can You Transform? Game

Communicators*

Coordinate plane white boards

Give coordinates for a figure,

then give new coordinates and

have students express in

algebraic terms. Ex (x,y)= (x+3,y-

2) or (x,y) = (3x,2y) which

preserve the shape

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Assessments

1. Use coordinates in four quadrants to

represent geometric concepts.




Holt Chapter 4, 8*

Kuta Software


27


· How can measurements be used to solve problems?

Resources



Grades 7-8

D. Units of Measurement

Learning Experiences


Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Measuring Length in the

Classroom

Measuring Student Heights

Measuring Lines

Constructing Graphs

Real-World Examples

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Assessments

Teacher Observation

Test/Quiz

Do Now

Daily Warm-ups

Various Investigations

On-Going Class Discussions

Geometer’s Sketchpad – Lesson

Link

3. Recognize that all measurements of

continuous quantities are approximations.

McDougal Littell Chapter 10-12



Holt Chapter 5,9*

1. Solve problems requiring calculations that

involve different units of measurement within

a measurement system (e.g., 4’3” plus 7’10”

equals 12’1”).


NJ ASK Coach



Holt Chapter 1,5*

2. Select and use appropriate units and tools to

measure quantities to the degree of precision

needed in a particular problem-solving

situation.

Knowledge/Skills/Understanding




Holt Chapter 9*

4.2.D 7th Grade Math

28



Resources

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



Grades 7-8



2. Recognize that the volume of a pyramid or

cone is one-third of the volume of the prism or

cylinder with the same base and height (e.g.,

use rice to compare volumes of figures with

same base and height).




Pages 750-751 in Student Text

Teacher Edition A16

Holt Chapter 10*

Kuta Software

Use 3-D objects to

demonstrate with water

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


1. Develop and apply strategies for finding

perimeter and area: Geometric figures made

by combining triangles, rectangles and circles

or parts of circles; Estimation of area using

grids of various sizes.




Holt Chapter 8,9,10*

Pattern Blocks

Kuta Software

Same Perimeter, Maximum Area

Problems

Use Geoboards*

Physically measuring objects

around room*

Find the value of pi by

measuring circumference and

diameter of circular objects*

4.2.E 7th Grade Math

29

· How can change be best represented mathematically?

Resources



Grades 7-8

1. Recognize, describe, extend, and create

patterns involving whole numbers, rational

numbers, and integers: Descriptions using

tables, verbal and symbolic rules, graphs,

simple equations or expressions; Finite and

infinite sequences; Generating sequences by

using calculators to repeatedly apply a

formula.


Holt Chapter 1,2*

Geometer’s Sketchpad-to graph

patterns

Use of Graphing Calculators

Teacher-Created Problems

Flashlight and Bridge

Locker Problem

Dot patterns that involve a

recursive routine. Students write

the recursive routine and then it's

explicit formula expressing the

number of dots as a function of

the term number.

Use a line-up to explore

patterns*

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

Standard 4.3 Patterns and Algebra

Assessments


A. Patterns


· How can patterns, relations, and functions be used as tools to best describe and

help explain real – life situations?


30

· How are patterns of change related to the behavior of functions?

Resources



Grades 7-8





1. Graph functions, and understand and

describe their general behavior: Equations

involving two variables.



Holt Chapter 1,4*

Kuta Software


Cartesian Cartoons

Input/Output tables


Links

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

4.3.B 7th Grade Math 31

· How can mathematical models be used to describe physical relationships?

· How can physical models be used to clarify mathematical relationships?

Resources


C. Modeling


Discovering Algebra - 1.6

Holt Chapter 4*

Kuta Software



Grades 7-8



Assessments

Input/Output Tables

Geometer’s Sketchpad –Lesson

Links

Population Growth Activity

Lesson Investigation 1.6

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

Graphing Lines-Describing the

Relationship


Measures of Center

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

1. Analyze functional relationships to explain

how a change in one quantity can result in a

change in another, using pictures, graphs,

charts, and equations.


NJ ASK Coach

TinkerPlots

Holt Chapter 4*

Kuta Software

2. Use patterns, relations, symbolic algebra,

and linear functions to model situations: Using

manipulatives, tables, graphs, verbal rules,

algebraic expressions/equations/inequalities;

Growth situations, such as population growth

and compound interest, using recursive (e.g.,

NOW- NEXT) formulas (cf. science standards

and social studies standards).


32

· What makes an algebraic algorithm both effective and efficient?

Resources



Holt Chapter 2*

Kuta Software

Geometer's Sketchpad-Lesson

Links

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

iPod/iPad



Grades 7-8


D. Procedures

2. Solve simple linear equations informally

and graphically: Multi-step, integer

coefficients only (although answers may not

be integers); Using paper-and-pencil,

calculators, graphing calculators,





Holt Chapter 12*

Kuta Software

Working Backwards Tables

Hands on Equations Balance

Graphing Calculator Use

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

3. Create, evaluate, and simplify algebraic

expressions involving variables: Order of

operations, including appropriate use of

parentheses; Substitution of a number for a

variable.



1. Use graphing techniques on a number line:

Absolute value; Arithmetic operations

represented by vectors (arrows) (e.g., “-3 + 6”

is “left 3, right 6”)


Discovering Algebra Chapter 4.1


Holt Chapter 1,2*

Kuta Software


Graphing/Scientific Calculator

Use

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

iPod/iPad


33


Resources



Grades 7-8


D. Procedures Essential Questions :


4. Understand and apply the properties of

operations, numbers, equations, and

inequalities: Additive inverse; Multiplicative

inverse.


Discovering Algebra 4.2/4.3

Holt Chapter 1*

Lesson Investigation 4.2/4.3

Hands on Equations Balance

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


34

Resources

Tinkerplots Prepared Data

Geometer's Sketchpad - Lesson

Links

Penny Data Investigation

Class Line-up to find the five

number summary


Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

· How can the collection, organization, interpretation, and display of data be used to answer

questions?



Grades 7-8

Standard 4.4 Data Analysis, Probability and Discrete

Mathematics

A. Data Analysis

2. Make inferences and formulate and

evaluate arguments based on displays and

analysis of data.


Student Pages 758-7579

TE A24


Holt Chapter 7*

Penny Data Investigation

Layer Various graphs on the

same number line

TinkerPlots Prepared Data

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



1. Select and use appropriate representations

for sets of data, and measures of central

tendency (mean, median, and mode): Type of

display most appropriate for given data; Box-

and-whisker plot, upper quartile, lower

quartile; Scatter plot; Calculators and

computer used to record and process

information.


Student Pages 756-757

TE A22


Holt Chapter 7*


35

Resources

· How can experimental and theoretical probabilities be used to make predictions or draw

conclusions?



Grades 7-8


Mathematics

B. Probability

"What Do You Expect?"

Investigations

Graph Class results as well as

group results, have students

compare/contrast results.

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up



1. Interpret probabilities as ratios, percents,

and decimals.


Connected Mathematics “What Do

You Expect?”

Holt Chapter 11*


Hands on Simulation -Rolling

Die, M & M's, Spinners

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

iPod/iPad

2. Model situations involving probability with

simulations (using spinners, dice, calculators

and computers) and theoretical models:

Frequency, relative frequency.



You Expect?”

Holt Chapter 11*


Investigations


Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

3. Estimate probabilities and make predictions

based on experimental and theoretical

probabilities.



You Expect?”

Holt Chapter 11*


36

Resources


conclusions?



Grades 7-8


Mathematics

B. Probability Essential Questions :


4. Play and analyze probability-based games,

and discuss the concepts of fairness and

expected value.



You Expect?”

Holt Chapter 11*


Investigations

Game Discussions

Candy land vs. Chutes and

Ladders

Design own "Zark" Game

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


37

· What counting strategy works best here?

Resources



Grades 7-8


Mathematics

C. Systematic Listing and Counting

Card Probabilities

Mutually Exclusive Events

Discussion of Overlap of Events

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up


· How can attributes be used to classify data/objects?

· What is the best way to solve this?


3. Apply techniques of systematic listing,

counting, and reasoning in a variety of

different contexts.


Connected Mathematics "What Do

You Expect?"

NJ ASK Coach

Holt Chapter 11*


Investigations

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

1. Apply the multiplication principle of

counting: Permutations: ordered situations

with replacement (e.g., number of possible

license plates) vs. ordered situations without

replacement (e.g., number of possible slates of

3 class officers from a 23 student class).


NJ ASK Coach

Holt Chapter 11*

Winning the Lottery

License Plate Combinations

Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

2. Explore counting problems involving Venn



Student Edition Pg 790

NJ ASK Coach

Holt Chapter 11*


38

· How can algorithmic thinking be used to solve problems?

Resources



Grades 7-8


Mathematics

D. Vertex-Edge Graphs and AlgorithmsEssential Questions :


1. Use vertex-edge graphs to represent and

find solutions to practical problems: Finding

the shortest network connecting specified

sites; Finding the shortest route on a map

from one site to another; Finding the shortest

circuit on a map that makes a tour of specified

sites.

Student Edition pg 744-745

TE A10

Rutgers Prepared Activities Teacher Observation

Quiz/Test

Do Now

Daily Warm-up

· How can visual tools such as networks (vertex-edge graphs) be used to answer questions?


39

Resources

1. Learn mathematics through problem

solving, inquiry, and discovery.

McDougal Littell Chapters 1-13

Menu Problems (Middle School

Math Teacher)

NCTM Navigations Series

Van De Walle

Connected Mathematics

Holt Chapters 1-12*

Direct Instruction

Investigations

Collaborative/Cooperative

Learning

Written Explanations

Student Directed Discussions

Written Test/Quiz

Written Explanation

Open-ended Questions

Teacher Observation

2. Solve problems that arise in mathematics

and in other contexts: Open-ended problems;

Non-routine problems; Problems with

multiple solutions; Problems that can be

solved in several ways.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


· How will learning to “think” mathematically enable us to make a life, make a living,

and make a difference?

· How does the use of technology enable us to have a deeper understanding of

mathematics?




Grades 7-8

Standard 4.5 Mathematical Processes

A. Problem Solving

4.5.A 7th Grade Math 40

Resources





mathematics?




Grades 7-8


A. Problem Solving

3. Select and apply a variety of appropriate

problem-solving strategies (e.g., “try a simpler

problem” or “make a diagram”) to solve

problems.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4. Pose problems of various types and levels of

difficulty.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources





mathematics?




Grades 7-8


A. Problem Solving

5. Monitor their progress and reflect on the

process of their problem solving activity.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Distinguish relevant from irrelevant




Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation



1. Use communication to organize and clarify





Grades 7-8


B. Communication



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning







mathematics?


Do Now

Quiz/Test

Teacher Observation

Open-Ended Questions



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


2. Communicate mathematical thinking

coherently and clearly to peers, teachers, and

others, both orally and in writing.


43




Grades 7-8


B. CommunicationEssential Questions :




mathematics?




Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


3. Analyze and evaluate the mathematical

thinking and strategies of others.

4. Use the language of mathematics to express

mathematical ideas precisely.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



44

Resources

1. Recognize recurring themes across

mathematical domains (e.g., patterns in

number, algebra, and geometry).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


2. Use connections among mathematical ideas

to explain concepts (e.g., two linear equations

have a unique solution because the lines they

represent intersect at a single point).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia




and make a difference?· How does the use of technology enable us to have a deeper understanding of

mathematics?




Grades 7-8


C. Connections

4.5.C 7th Grade Math 45

Resources




mathematics?




Grades 7-8


C. Connections

3. Recognize that mathematics is used in a

variety of contexts outside of mathematics.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


4. Apply mathematics in practical situations

and in other disciplines.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia



Resources




mathematics?




Grades 7-8


C. Connections

5. Trace the development of mathematical

concepts over time and across cultures (cf.

world languages and social studies standards).



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia


6. Understand how mathematical ideas

interconnect and build on one another to

produce a coherent whole.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation

Learnia



Resources

1. Recognize that mathematical facts,

procedures, and claims must be justified.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

2. Use reasoning to support their

mathematical conclusions and problem

solutions.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation





mathematics?




Grades 7-8


D. Reasoning


48

Resources





mathematics?




Grades 7-8


D. Reasoning

3. Select and use various types of reasoning

and methods of proof.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

4. Rely on reasoning, rather than answer keys,

teachers, or peers, to check the correctness of

their problem solutions.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


49

Resources





mathematics?




Grades 7-8


D. Reasoning

5. Make and investigate mathematical

conjectures: Counterexamples as a means of

disproving conjectures; Verifying conjectures

using informal reasoning or proofs.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Evaluate examples of mathematical

reasoning and determine whether they are

valid.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Written Test/Quiz

Written Explanation


Teacher Observation


50

Resources

1. Create and use representations to organize,

record, and communicate mathematical ideas:

Concrete representations (e.g., base-ten blocks

or algebra tiles); Pictorial representations

(e.g., diagrams, charts, or tables); Symbolic

representations (e.g., a formula); Graphical

representations (e.g., a line graph).



Math Teacher)


Van De Walle


Holt Chapters 1-12*



Grades 7-8




Math Teacher)


Van De Walle


Holt Chapters 1-12*


mathematics?


E. Representations

Do Now

Quiz/Test

Teacher Observation





Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


2. Select, apply, and translate among

mathematical representations to solve

problems.

Direct Instruction

Investigations


Learning



4.5.E 7th Grade Math 51

Resources



Grades 7-8



mathematics?


E. Representations Essential Questions :



3. Use representations to model and interpret

physical, social, and mathematical

phenomena.



Math Teacher)


Van De Walle


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation


4.5.E 7th Grade Math 52

Resources

1. Use technology to gather, analyze, and




Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation






mathematics?



Grades 7-8


F. Technology

4.5.F 7th Grade Math 53

Resources





mathematics?



Grades 7-8


F. Technology

2. Use computer spreadsheets, software, and

graphing utilities to organize and display

quantitative information.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Resources





mathematics?



Grades 7-8


F. Technology

3. Use graphing calculators and computer

software to investigate properties of functions

and their graphs.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Resources





mathematics?



Grades 7-8


F. Technology

4. Use calculators as problem-solving tools

(e.g., to explore patterns, to validate solutions).



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Resources





mathematics?



Grades 7-8


F. Technology

5. Use computer software to make and verify

conjectures about geometric objects.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Resources





mathematics?



Grades 7-8


F. Technology

6. Use computer-based laboratory technology

for mathematical applications in the sciences.



Math Teacher)


Van De Walle


TinkerPlots


Holt Chapters 1-12*

Direct Instruction

Investigations


Learning



Do Now

Quiz/Test

Teacher Observation



Equations, Inequalities and

Functions

7 8

Ratios and Proportions 8

Pacing Guide

UnitMcDougall Littell Mathematics

Course 2 ChaptersNumber of Blocks

Holt Mathematics Course

2 Chapters



Grades 7-8

7th Grade Math

Data Analysis and

Statistics

3 15 7 13

Number Sense, Patterns

and Algebraic Thinking

1 6 3

Number of Blocks

9 11 6 11

9

Integers 6 12

1

122

Percents

14 5 11

Mid-Year Benchmark

Assessment

1

12 10

7th Grade Math Pacing Guide 59

Pacing Guide


Course 2 ChaptersNumber of Blocks

Holt Mathematics Course

2 Chapters



Grades 7-8

7th Grade Math

Number of Blocks

2 2

Surface Area and Volume 12 1 10 2

5

End-of-the-Year

Benchmark Assessment

1 1

6

Measurement and Area 11 5 9

Discrete Math 1 1

Probability 13


7 11


Venn Diagrams with three

attributes

Geometric Figures 10 6 8

6

7th Grade Math Pacing Guide 60

Holt Mathematics Course 2 and all related

resources (differentiation including ELL)

Bennett, Burger, Chard, Jackson,

Kennedy, Renfro, Scheer & Waits

Holt, Rinehart and Winston 2007



Grades 7-8

7th Grade Math

Resources

Title of Resource Author(s) Publisher Copyright

McDougall Littell Course 2

and all related resources (differentiation

including ELL)

Larson, Boswell, Kanold & Stiff McDougal Littell 2008

Developing Skills in Algebra One - Books A

and B

Harold and Loretta Taylor Dale Seymour Publications 1984

Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002

Pre-Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002

Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002

New Jersey ASK Coach Jerome Kaplan Ed.D Triumph Learning 2005

Question Quest Level C Paul Lawrence LL Teach, Inc. 2002

Algebra Out Loud Pat Mower, PhD Jossey Bass 2003

Kuta Software: Infinite Pre-Algebra, Infinite

Algebra

Kuta Software LLC 2010, 2011

UCSMP Transitions Lesson Masters A and B Zal Usiskin Scott, Foresman 1995

7th Grade Resources 61



Grades 7-8

7th Grade Math

Resources


2006

1998

2001

2000

Pearson Education

The Center for Applied Research

Education

Evan-Moor Publishers

Steck-Vaugh Company

John A. Van de Walle & LouAnn

H. Lovin

Frances M. Thompson

Amy Beth Tuttle, Wes Tuttle

D.W. Skrabanek

Teaching Student-Centered Mathematics

Grades 5-8

Hands -On Algebra !

Daily Word Problems Grade 6

Middle School Collection: Geometry: Basic

Concepts, Geometry: Solids, Geometry:

Polygons, Pre-Algebra

Triumph Learning

Exemplars

2008

Explain It Lepore, Fleetwood & Hall Creative Publications 2001

ASK Workout

Differentiated Middle School Math

Jerome Kaplan Ed.D

UCSMP Algebra Lesson Masters A and B Zal Usiskin Scott, Foresman 1995

Tinker Plots Clifford Konold & Craig D. Miller Key Curriculum Press 2005

Geometer's Sketchpad 4 Nicholas Jackiw Key Curriculum Press 2006

1998

2003

Algebra Puzzles & Problems

Algebra Teacher's Activities Kit

Greenes/Findell

Judith & Robert Muschla

Creative Publications

Jossey Bass




Grades 7-8

7th Grade Math

Resources


2003

2004

1998

1999

Wyatt, Lawrence, Foletta

Michael T. Battista

Lappan, Fey, Fitzgerald, Friel

and Phillips

Weisenfeld, Coultas, Swalm

2003

2007

Geometry Activities for Middle School

Students

Shape Makers: Developing Geometric

Reasoning in Middle School

What Do You Expect?

Strategies for Success in Mathematics: Level

G

Key Curriculum Press

Key Curriculum Press

Dale Seymour Publications

Steck-Vaugh Company

Measuring Up to the NJ Core Curriculum

Content Standards

Kenneth Owens Peoples Publishing Group 2003

NCTM Navigation Series: Probability, Data

Analysis, Geometry

8-Step Model Drawing

Bright, Frierson Jr., Tarr,

Thomas, Brewer, McClain,

Mooney, Pugalee, Frykholm,

Johnson, Slovin, Malloy, Preston

Bob Hogan & Char Forsten

The National Council of

Teachers of Mathematics

Crystal Spring Books

2000

1991

Creative Teaching Press

Critical Thinking Books &

Software

Doug Stoffel

Warren Hill & Ronald Edwards

Middle Grade Math Minutes

Mathematical Reasoning Through Verbal

Analysis Book 2




Grades 7-8

7th Grade Math

Resources




1992Curriculum and Evaluation Standards for

School Mathematics Addenda Series Grades 5-

8

Geddes, Zawojewski, Reys,

Phillips, Curcio, Bezuk


Algebra 1A Math Curriculum

65

A. Number Sense



· How can counting, measuring or labeling help to make sense of the world around us?

Resources



Elementary and Middle School

Math Chapter 26

Number line graphing

Lesson Investigations throughout

the textbook

On-going




of situations.

Larson Algebra 1 Chapter 3 Lesson Investigations 2.2, 2.3,

3.1, 3.2, 3.3

Similarity Lab

Do Now

Quiz/Test

Class discussion

Teacher Observation







Percents; Exponents; Roots; Absolute Values;

Numbers represented in scientific notation

Larson Algebra 1 Chapter 1, 2 Investigate decimal patterns

using a calculator

Lesson Investigations

Direct Instruction

Do Now

Quiz/Test

Teacher Observation

iPod/iPad



Grades 7-8



4.1.A 7th Algebra 1A

66

A. Number Sense



· How can counting, measuring or labeling help to make sense of the world around us?

ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments



Grades 7-8



6. Recognize that repeating decimals

correspond to fractions and determine their

fractional equivalents .

Larson Algebra 1 Chapter 2 Lesson Investigation 2.1

Calculator Activities

Do Now

Quiz/Test

Class discussion

Teacher Observation


types.

Van De Walle Chapter 24 Student Line-Up Student Line Up



the same number.

Kuta Software

Teacher made materials

Teacher-created review

Calculator Activities

I have . . . who has


67




Resources


powers of numbers.

Teacher-created problems

Developing Skills in Algebra One –

Book A

Larson Algebra 1 Ch 1

Kuta Software

Review as needed Quiz

3. Solve problems involving proportions and

percents.


Kuta Software

Lesson Investigations 2.2, 2.3 Teacher Observation

Discussion of Lesson

Investigation results

Do Now




calculations involving addition, subtraction,

multiplication, division, and exponentiation

with integers and all number types named


Calculator.


Math With Pizzazz! Book E


Algebra with Pizzazz!


Kuta Software

Mental Math Warm-Ups Do Now

Quiz/Test

Teacher Observation



Grades 7-8



4.1.B 7th Algebra 1A

68




Resources





Grades 7-8








Kuta Software



Kuta Software - Infinite Pre-

Algebra

Do Now

Teacher Observation

Quiz/Test


69

C. Estimation


Resources

2. Recognize the limitations of estimation and

assess the amount of error resulting from

estimation.

Various Lesson Investigations

Daily discussions

Daily problems On-going





Various Lesson Investigations

Daily discussions

Daily problems Do Now

Teacher Observation



Grades 7-8



4.1.C 7th Algebra 1A

70




Resources




objects.


Van De Walle pg 365-366

Kuta Software

Measure shadow of flagpole and

person to determine height

Quiz/Test

Do Now

Teacher Observation





Direct Instruction Teacher Observation





rhombi; Regular polygons

Navigations Series – Geometry


Geoboard exploration

Manipulatives

Do Now

Teacher Observation



Grades 7-8




71












UCSMP Transitions Lesson

Masters

Kuta Software

Navigation Series – Geometry

Geometry in the Middle Grades

Kuta Software - Algebra

Van De Walle pg 371

NJ ASK Coach

Manipulatives

Give coordinates for a figure,

then give new coordinates and




preserve the shape

Do Now

Quiz/Test

Teacher Observation



Grades 7-8




72



Resources



NJ ASK Coach

Teacher-made materials

Kuta Software

Graphing Calculator

Give coordinates for a figure

then, give new coordinates and




preserve the shape

Do Now

Quiz/Test

Teacher Observation




• Slope of a line

Larson Algebra 1 Ch 4, 5



NJ ASK Coach


Book C

Kuta Software

Working Cooperatively

Graphing Calculator work

Do Now

Quiz/Test

Teacher Observation



Grades 7-8




73



Resources

2. Use approximate equivalents between

standard and metric systems to estimate

measurements (e.g., kilometers is about 3

miles).


UCSMP Transitions Chapter 3

Teacher made materials

Lesson Investigations 2.3, 3.2 Do Now

Teacher-Created problems

Quiz/Test

Teacher Observation


Investigation





equals 12’1”).

Discovering Algebra Chapter 2, 3

NJ ASK Coach



Quiz/Test

Teacher Observation


Investigation



Grades 7-8



4.2.D 7th Algebra 1A

74






Grades 7-8






situation.

On-going class discussions Various Lesson Investigations Do Now


Quiz/Test

Teacher Observation


Investigation





Quiz/Test

Teacher Observation


Investigation

3. Recognize that the degree of precision

needed in calculations depends on how the

results will be used and the instruments used

to generate the measurements.



Quiz/Test

Teacher Observation


Investigation


75






Grades 7-8



6. Solve problems that involve compound

measurement units, such as speed (miles per

hour), air pressure (pounds per square inch),

and population density (persons per square

mile).




Direct Instruction

Dimensional Analysis

Do Now


Quiz/Test

Teacher Observation


Investigation


76



Resources








Math with Pizzazz! Book D


NJ Ask Coach

Direct Instruction Teacher-created problems

Learnia

Do Now






grids of various sizes.



Math with Pizzazz! Book D


Kuta Software

Investigations Teacher-created problems

Learnia

Do Now



Grades 7-8



4.2.E 7th Algebra 1A

77


Resources










infinite sequences; Arithmetic sequences;

Geometric sequences; Generating sequences

by using calculators to repeatedly apply a

formula.

Larson Algebra 1 Chapter 4, 5 Direct Instruction

Modeling

Graphing Calculators

Do Now

Quiz/Test

Teacher Observation


Investigations



Grades 7-8


A. Patterns


78


Resources





involving two variables; Equations involving

two variables; Rates of change (informal

notion of slope).

Larson Algebra 1 Chapter 4 Direct Instruction

Teacher Created

Materials/Lessons

Do Now

Quiz/Test

Teacher Observation


Investigations



Grades 7-8




79



Resources



concrete materials (manipulatives), tables,

graphs, verbal rules, algebraic expressions/

equations/ inequalities; Growth situations,

such as population growth and compound

interest, using recursive (e.g., NOW-NEXT)

formulas (cf. science standards and social

studies standards).

Larson Algebra 1 Ch 4, 5 Direct Instruction

Modeling throughout lessons


Do Now

Quiz/Test

Teacher Observation


Investigations







Larson Algebra 1 Ch 4, 5 Direct Instruction

Modeling throughout lessons


Teacher observation


Investigations



Grades 7-8


C. Modeling


80


Resources

2. Solve simple linear equations informally,

graphically, and using formal algebraic

methods:

Multi-step, integer coefficients only (although

answers may not be integers) Simple literal

equations (e.g., A = lw) Using paper-and-

pencil, calculators, graphing calculators,


Larson Algebra 1 Ch 2, 3, 4, 5

Kuta Software

Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation






is “left 3, right 6”)


Larson Algebra 1 Chapter 2


Kuta Software

Direct Instruction


Link

Do Now

Quiz/Test

Teacher Observation



Grades 7-8


D. Procedures

4.3.D 7th Algebra 1A 81


Resources





Grades 7-8


D. Procedures




inverse; Addition and multiplication

properties of equality.

Larson Algebra 1 Ch 1-5



Book A

Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation




parentheses; Distributive property;

Substitution of a number for a variable;

Translation of a verbal phrase or sentence into

an algebraic expression, equation, or

inequality, and vice versa.



Kuta Software

Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation

4.3.D 7th Algebra 1A 82

Resources



analysis of data sets.


TinkerPlots

Direct Instruction

Graphing Calculator

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation



questions?









information; Finding the median and mean

(weighted average) using frequency data;

Effect of additional data on measures of

central tendency.



TinkerPlots

Direct Instruction

Graphing Calculator

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation



Grades 7-8


Mathematics

A. Data Analysis


83

Resources



questions?




Grades 7-8


Mathematics

A. Data Analysis

3. Estimate lines of best fit and use them to

interpolate within the range of the data.

Larson Algebra 1 Chapter 5 Lesson Investigation 5.3

Class Discussion

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


Investigation


84

Resources





Discovering Algebra 2.5, 2.6


Math with Pizzazz! Book E



Quiz/Test

Teacher Observation



probabilities.

Discovering Algebra 2.5, 2.6





Quiz/Test

Teacher Observation



conclusions?



and decimals.


Discovering Algebra - 2.5, 2.6




Quiz/Test

Teacher Observation



Grades 7-8


Mathematics

B. Probability

4.4.B 7th Algebra 1A 85

Resources



conclusions?




Grades 7-8


Mathematics

B. Probability



expected value.


You Expect?"



Experiments from Connected

Mathematics “What Do You

Expect?"

Do Now

Quiz/Test

Teacher Observation



Resources



with replacement vs. ordered situations

without replacement.

Larson Algebra 1 - Chapter 13

Math Counts


NJ ASK Coach

Experiments/Investigations Counting Trees

Teacher Observation

Quiz/Test



UCSMP Transitions Textbook

National Council of Teachers of

Mathematics Dealing with Data and

Chance Standards

NJ ASK Coach

Problems from UCSMP

Transitions Textbook and

UCSMP Algebra

Venn Diagrams

Teacher Observation

Quiz/Test







Grades 7-8


Mathematics



87


Resources







Grades 7-8


Mathematics




different contexts.

Larson Algebra 1 - Chapter 13

Math Counts


Mathematics Dealing with Data and

Chance Standards

Find number of ways to arrange

batters

Teacher Observation

Quiz/Test


88


Resources




1. Use vertex-edge graphs to represent and

find solutions to practical problems: Finding

the shortest network connecting specified

sites; Finding the shortest route on a map

from one site to another; Finding the shortest

circuit on a map that makes a tour of specified

sites.

Teacher-created materials

Pgs 744-745 McDougal Littell

Rutgers prepared worksheets

Write a tour guide with map

Teacher-Created

worksheets

Tour Guide Project



Grades 7-8


Mathematics

D. Vertex-Edge Graphs and Algorithms


89

Resources




Math Counts

NCTM Navigation Series

Kuta Software


Mathematics

Question Quest Level C

Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation







Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





mathematics?




Grades 7-8


A. Problem Solving

4.5.A 7th Algebra 1A 90

Resources





mathematics?




Grades 7-8


A. Problem Solving




problems.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


difficulty.

Larson Algebra 1 Chapters 1-5

Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources





mathematics?




Grades 7-8


A. Problem Solving




Math Counts




Mathematics

Question Test Level C

Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation

6. Distinguish relevant from irrelevant



Math Counts

Navigation Series



Mathematics


Direct Instruction



Learning


Open-Ended Question

Written Test/Quiz

Written Explanation


Teacher Observation


Resources





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




mathematics?




Grades 7-8


B. Communication


Resources




mathematics?




Grades 7-8


B. Communication




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




mathematics?




Grades 7-8


C. Connections


95

Resources




mathematics?




Grades 7-8


C. Connections




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


96

Resources




mathematics?




Grades 7-8


C. Connections





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


97

Resources




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation



solutions.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





mathematics?




Grades 7-8


D. Reasoning


98

Resources





mathematics?




Grades 7-8


D. Reasoning




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


99

Resources





mathematics?




Grades 7-8


D. Reasoning






Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation



valid.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


100

Resources









Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation



problems.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation





mathematics?


E. Representations



Grades 7-8


4.5.E 7th Algebra 1A 101

Resources





mathematics?


E. Representations



Grades 7-8




phenomena.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Journaling

Teacher Observation

4.5.E 7th Algebra 1A 102

Resources




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation





mathematics?




Grades 7-8


F. Technology

4.5.F 7th Algebra 1A 103

Resources





mathematics?




Grades 7-8


F. Technology



and their graphs.


Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Resources





mathematics?




Grades 7-8


F. Technology




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation




Math Counts




Mathematics


Direct Instruction



Learning



Written Test/Quiz

Written Explanation


Teacher Observation


Probability And Data

13 10

Geometry

Math with Pizzazz

Pre-Algebra with Pizzazz

Kuta Software

5

Linear Equations

2 15

Slope and Fitting a Line to Data

5 14

Proportional Reasoning

2 14

Variations and Graphs

3 14

UnitLarson Algebra 1

ChapterNumber of Blocks

Data Exploration

13 5



Grades 7-8

7th Grade Algebra 1A

Pacing Guide

7th Grade Algebra 1A Pacing Guide

106




Algebra Out Loud Pat Mower, Phd Jossey Bass 2003




Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002


and B

Harold and Loretta Taylor Dale Seymour Pulbications 1984



Larson Algebra 1 Ron Larson, Laurie Boswell,

Timothy D. Kanold, Lee Stiff

Houghton Mifflin Harcourt

Publishing Company

2012



Grades 7-8


Resources

7th Grade Algebra 1A Resources 107




Grades 7-8


Resources


Students

Wyatt, Lawrence, Foletta Key Curriculum Press 2004



Michael T. Battista Key Curriculum Press 2003

NCTM Navigation Series: Probability, Data

Analysis, Geometry

Bright, Frierson Jr., Tarr,

Thomas, Brewer, McClain,

Mooney, Pugalee, Frykholm,

Johnson, Sloving, Malloy,



2003

Hands -On Algebra ! Frances M. Thompson The Center for Applied Research

Education

1998

Differentiated Middle School Math Exemplars


Grades 5-8


H. Lovin

Pearson Education 2006


ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008

Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998

Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003






Grades 7-8


Resources

Curriculum and Evaluation Standards for


8

Geddes, Zawojewski, Reys,

Phillips, Curcio, Bezuk



1992

Kuta Software - Infinite Pre-Algebra, Infinite

Algebra, Infinite Geometry



G

Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999


Algebra 1B Math Curriculum

110




Resources




Mathematics, Developing Number

Sense

Spend national debt at a given

rate-how long?








Numbers represented in scientific notation


Math Counts

Teacher-created

worksheets/problems

Kuta Software

Investigate decimal patterns

using a calculator

Applicable Problems

Recursive Routines

Through the use of geometry of

squares and cubes

Applicable Lesson Investigations

Direct Instruction

Cooperative student exploration

of “undoing” operations of

functions

Teacher-created review

examples

Do Now

Quiz/Test

Teacher Observation

Class Discussions




Grades 7-8



A. Number Sense

4.1.A 7th Algebra 1B

111







Grades 7-8



A. Number Sense


types.

UCSMP Transitions Chapter 12 Graphing on a number line



the same number.

Larson Algebra 1 Chapter 5-12

UCSMP Algebra

Spiral of right triangles –

Pythagorean Theorem




of situations.

Math Counts

Real-world examples

Problem solving

Collaborative discussions

Do Now

Quiz/Test

Class discussion

Teacher Observation


112




Resources

2. Find cube roots of numbers and understand

the inverse nature of powers and roots.



Finding the length of the edge of

a cube knowing volume

Do Now

Quiz/Test

Teacher Observation


percents.


Math Counts

Do Nows Teacher Observation


Investigation results

Do Now








Calculator.

Developing Skills in Algebra One

Book A & B

Kuta Software

Mental Math Warm-Ups

Do Now

Use Applications

Do Now

Quiz/Test

Teacher Observation



Grades 7-8



4.1.B 7th Algebra 1B

113




Resources





Grades 7-8



4. Understand and apply the laws of exponents

to simplify expressions involving numbers and

variables raised to powers.



Book B


Kuta Software

Quizzes

Class Discussions

Do Now

Quiz/Test

Teacher Observation


114

C. Estimation


Resources



estimation.


Mathematics – Data Analysis and

Statistics Addenda series

Physically measure lengths and

discuss why disparities occur

when using π or 3.14 for surface

area and volumes (cones and

cylinders)

Measure/Justify


1. Estimate square and cube roots of numbers. Teacher-Created Problems Class Discussions Mental Practice

Calculator Teacher

Observation



Grades 7-8



4.1.C 7th Algebra 1B 115




Resources




objects.



Manipulatives Quiz/Test

Do Now

Teacher Observation



Navigating through Geometry 9-12



Direct Instruction Teacher Observation


1. Understand and apply the Pythagorean

Theorem.




Math Counts

Real-world application problems Do Now

Teacher Observation



Grades 7-8



4.2.A 7th Algebra 1B 116













UCSMP Transitions Lesson

Masters

UCSMP Transitions Chapter 8


Kuta Software

Use calculator to compare

graphs of equations that involve

transformations


Do Now

Quiz/Test

Coordinate grid drawings

Teacher Observation



Grades 7-8



4.2.B 7th Algebra 1B 117




1. Use coordinate geometry to represent and

verify properties of lines.

• Finding the intersection of two lines

• Lines with the same slope are parallel

• Lines that are perpendicular have slopes

whose product is -1



Kuta Software

Class Discussions

Graphing Calculator work

Applications in coordinate

geometry

Do Now

Quiz/Test

Teacher Observation



Grades 7-8



4.2.C 7th Algebra 1B

118



Resources





Larson Algebra 1 Ch 5-13 Appropriate use throughout Do Now


Quiz/Test

Teacher Observation




situation.



Quiz/Test

Teacher Observation


1. Use appropriate equivalents between



miles)



Quiz/Test

Teacher Observation



Grades 7-8



4.2.D 7th Algebra 1B 119






Grades 7-8





Larson Algebra 1 Ch 5-13 Appropriate use throughout


Do Now


Quiz/Test

Teacher Observation





mile).



Quiz/Test

Teacher Observation




Resources

4. Use formulas to find the volume of a sphere. Geometer’s Sketchpad

Math Counts


Cooperative Investigations NJ ASK Coach



cylinder with the same base and height


Math Counts



2. Develop and apply strategies and formulas

for finding the volume of a three-dimensional

figure.


Math Counts



3. Impact of a dilation on the volume of a

three-dimensional figure.


Math Counts





perimeter and area: Impact of a dilation on

the perimeter and area of a 2-dimensional

figure.


Math Counts





Grades 7-8



4.2.E 7th Algebra 1B

121


Resources










infinite sequences; Arithmetic sequences (i.e.,

sequences generated by repeated addition of a

fixed number, positive or negative);

Geometric sequences (i.e., sequences

generated by repeated multiplication by a

fixed positive ratio, greater than 1 or less than

1); Generating sequences by using calculators

to repeatedly apply a formula.



Navigating through Algebra Grades

9-12

Given terms in a pattern,

describe patterns in words

Recursive investigations

Real-world problem solving

U.S. Census Activity

Do Now

Quiz/Test

Teacher Observation



Grades 7-8


A. Patterns



Resources

2. Recognize and describe the difference

between linear and exponential growth, using

tables, graphs, and equations.

Larson Algebra 1 Ch 7 Skittle Activity Do Now

Quiz/Test

Teacher Observation






involving two variables; Equations involving

two variables; Rates of change (informal

notion of slope).



Direct Instruction

Real-world problems

Lesson Investigations from


Do Now

Quiz/Test

Teacher Observation



Grades 7-8






Resources







interest, using recursive (e.g., NOW-NEXT)

formulas (cf. science standards and social

studies standards).

Larson Algebra 1 Ch 5-7 Direct Instruction Do Now

Quiz/Test

Teacher Observation









Direct Instruction

Lesson Investigations 8.1, 8.3,

8.4, 8.5, 8.7

Teacher observation

Do Now

Quiz/Test



Grades 7-8


C. Modeling


124


Resources



methods: Multi-step, integer coefficients only

(although answers may not be integers);

Absolute value; Compound inequalities;

Rational expressions; Using paper-and-pencil,

calculators, graphing calculators,



Kuta Software

Teacher-created material

Direct Instruction Do Now

Quiz/Test

Teacher Observation

3. Solve systems of equations:

• Graphically

• Algebraic methods



Book B

Kuta Software

Direct Instruction

Graphing Calculator

Do Now

Quiz/Test

Teacher Observation

Teacher-Created materials




Absolute value.


Kuta Software

Direct Instruction


Do Now

Quiz/Test

Teacher Observation



Grades 7-8


D. Procedures



Resources





Grades 7-8


D. Procedures

6. Evaluate and simplify algebraic

expressions:

• Add and subtract polynomials

• Multiply a polynomial by a monomial or

binomial

• Divide a polynomial by a binomial

• Use laws of exponents



Books B-D


Direct Instruction

Algebra Tiles

Do Now

Quiz/Test

Teacher Observation


4. Factor polynomials Larson Algebra 1 Ch 9, 10


Book B

Kuta Software

Direct Instruction

Algebra Tiles

Do Now

Quiz/Test

Teacher Observation

5. Rational Expressions

• Add and Subtract

• Multiply and Divide


Book D


Kuta Software

Direct instruction Do Now

Quiz/Test

Teacher Observation



Resources




Navigation through Data Analysis

Grades 6-8

Larson Algebra 1

Prediction

Using graphing calculator to

show two statistical graphs at the

same time to compare various

statistical averages

Graphing Calculator

Teacher Observation



questions?




tendency (mean, median, and mode); Finding

the median and mean (weighted average)

using frequency data; Effect of additional

data on measures of central tendency.

Math Counts

Larson Algebra 1

Graphing Calculator


Class Discussion


Graphing Calculator

Teacher Observation



Grades 7-8


Mathematics

A. Data Analysis


127

Resources



questions?




Grades 7-8


Mathematics

A. Data Analysis




TinkerPlots

Internet Resources

Class Discussion

Internet Resources

TinkerPlots Activities

Do Now

Graphing Calculator

Quiz/Test

Teacher Observation


128

Resources

2. Explore the probabilities of conditional

events.

Larson Algebra 1

USCMP Transitions

Manipulatives

Use of collaborative

investigations






Dealing with Data and Chance –


Mathematics Addenda Series

Navigating through Data and

Chance Grades 6-8

Graphing calculator probability

simulation programs

Teacher observation

Written explanation of how

the two ideas are related in

given situations



conclusions?


1. Determine probabilities of compound

events.

Larson Algebra 1

USCMP Transitions

Manipulatives

Use of collaborative

investigations




Grades 7-8


Mathematics

B. Probability


129

Resources



conclusions?




Grades 7-8


Mathematics

B. Probability



probabilities.

Dealing with Data and Chance –


Mathematics Addenda Series

Navigating through Data and

Chance Grades 6-8

Graphing calculator probability

simulation programs

Investigation write-up



expected value.

Larson Algebra 1

Math Counts

Analyze size of sections on dart

boards for area versus

probability

Investigation write-up


130


Resources



different contexts.

Math Counts

Larson Algebra 1

Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests






3 class officers from a 23 student class).

Math Counts

Larson Algebra 1

UCSMP Algebra

Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests



Math Counts

Larson Algebra 1

Direct Instruction

Manipulatives

Investigations

Textbook-generated

quizzes and tests







Grades 7-8


Mathematics



131


Resources




1. Use vertex-edge graphs and algorithmic

thinking to represent and find solutions to

practical problems: Finding the shortest

network connecting specified sites; Finding a

minimal route that includes every street (e.g.,

for trash pick-up); Finding the shortest route

on a map from one site to another; Finding

the shortest circuit on a map that makes a

tour of specified sites.

Rutgers workshop on Discrete

Mathematics


Rutgers prepared worksheets

Write a tour guide with map

Teacher-Created

worksheets

Teacher-created quiz

Tour Guide Project



Grades 7-8


Mathematics


4.4.D 7th Algebra 1B

132

Resources




Website Standards

www.nctm.org

Connected Math Series


TinkerPlots

Math Counts

Brainstorming

Journaling

Classroom Discussion

Predictions







Question Quest level C

Teacher-Created Materials



Tinkerplots

Math Counts

Students analyze each others

written responses

Share solution methods






mathematics?




Grades 7-8


A. Problem Solving


Resources





mathematics?




Grades 7-8


A. Problem Solving




problems.

Math Counts




TinkerPlots

Brainstorming

Journaling


Predictions



difficulty.

Math Counts




TinkerPlots

Brainstorming

Journaling


Predictions



Resources





mathematics?




Grades 7-8


A. Problem Solving



New Jersey Frameworks


Mathematics: Curriculum and

Evaluation Standards for School

Mathematics


Mathematics

Strategies for Success Level G

Brainstorming

Journaling


Predictions



Resources








Mathematics


Mathematics


Brainstorming

Journaling


Predictions









Mathematics


Mathematics


Brainstorming

Journaling


Predictions






mathematics?




Grades 7-8


B. Communication


Resources





mathematics?




Grades 7-8


B. Communication







Mathematics


Mathematics


Brainstorming

Journaling


Predictions



Resources








Mathematics


Mathematics


Brainstorming

Journaling


Predictions






mathematics?




Grades 7-8


C. Connections


139

Resources





mathematics?




Grades 7-8


C. Connections







Mathematics


Mathematics


Brainstorming

Journaling


Predictions










Mathematics


Mathematics


Brainstorming

Journaling


Predictions



140

Resources





mathematics?




Grades 7-8


C. Connections








Mathematics


Mathematics


Brainstorming

Journaling


Predictions

Class Discussions







Mathematics


Mathematics


Brainstorming

Journaling


Predictions



141

Resources





mathematics?




Grades 7-8


C. Connections








Mathematics


Mathematics


Brainstorming

Journaling


Predictions

Class Discussions


142

Resources







Mathematics


Mathematics


Give examples and

counterexamples




solutions.





Mathematics


Mathematics


Brainstorming

Journaling


Predictions






mathematics?




Grades 7-8


D. Reasoning


143

Resources





mathematics?




Grades 7-8


D. Reasoning







Mathematics


Mathematics


Share methods

Students analyze each others’

responses









Mathematics


Mathematics


Estimations and predictions Written Explanations


144

Resources





mathematics?




Grades 7-8


D. Reasoning









Mathematics


Mathematics


Test x ^2 > x for all real

numbers



145

Resources





mathematics?




Grades 7-8


D. Reasoning



valid.





Mathematics


Mathematics


Brainstorming

Journaling


Predictions



146

Resources









Math Counts

Algebra Out Loud

Navigating Algebra grades 9-12

Use algebra tiles to show

multiplication of polynomials

Use tables to find algebraic

functions relating quantities

Use area formula and graphing

calculator to predict maximum

area

Graphs




problems.


Math Counts

Algebra Out Loud


Brainstorming

Journaling







mathematics?




Grades 7-8


E. Representations

4.5.E 7th Algebra 1B 147

Resources





mathematics?




Grades 7-8


E. Representations



phenomena.


Math Counts

Algebra Out Loud


Brainstorming

Journaling



4.5.E 7th Algebra 1B 148

Resources



and their graphs.


Geometer's Sketchpad

Graph rational expressions and

discuss asymptotes






Use graphing calculator or

computer to compare various

ways of finding “Line of best fit”







Compare two teams batting

averages using various graphical

representations






mathematics?




Grades 7-8


F. Technology

4.5.F 7th Algebra 1B 149

Resources





mathematics?




Grades 7-8


F. Technology





Test Triangle Similarity

Theorem




Core math textbooks

Various workbooks


Use CBL’s to collect data on

motion sensor or temperature

and analyze for algebraic

patterns





Developing Number Sense

Addenda series National Council of


Discover patterns from positive

to negative through investigation

with graphing calculator


4.5.F 7th Algebra 1B 150

Radicals Developing Skills in Algebra

One Books A-D

6

Quadratics 10 15

Rational Expressions Developing Skills in Algebra

One Books A-D

4

Transformations Teacher Created Materials

Kuta Software

4

Polynomials 9 15

Exponents and Exponential Models 7 12

Functions 8

Discovering Algebra

8

Graphing, Slope, and Writing the Equation of

a Line

5 8

Systems of Equations and Inequalities 6 10

UnitLarson Algebra 1

ChapterNumber of Blocks

Linear Equations 5 8



Grades 7-8

7th Grade Algebra 1B

Pacing Guide

7th Grade Algebra 1B Pacing Guide

151


Publishing Company

2012

Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998





Algebra Out Loud Pat Mower, PhD Jossey Bass 2003





and B

Harold and Loretta Taylor Dale Seymour Publications 1984



Discovering Algebra An Investigative

Approach

Jerald Murdock, Ellen Kamischke,

Eric Kamischke

Key Curriculum Press 2002

Larson Algebra 1 Ron Larson, Laurie Boswell,




Grades 7-8


Resources

7th Grade Algebra 1B Resources 152




Grades 7-8


Resources

Curriculum and Evaluation Standards for


12

Burrill The National Council of


1992


Students

Wyatt, Lawrence, Foletta Key Curriculum Press 2004

Kuta Software - Infinite Algebra 1, Infinite

Geometry



G

Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999



Michael T. Battista Key Curriculum Press 2003

NCTM Navigation Series: Algebra Burke, Erickson, Lott, Obert The National Council of


2001

Hands -On Algebra ! Frances M. Thompson The Center for Applied Research

Education

1998


Grades 5-8


H. Lovin

Pearson Education 2006


ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008

Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003

7th Grade Algebra 1B Resources 153

8th Grade Curriculum

154

4.1.A.1. Extend understanding of the number system by

constructing meanings for the following (unless

otherwise noted, all indicators for grade 8 pertain to

these sets of numbers as well): Rational numbers;

Percents; Exponents; Roots; Absolute Values; Numbers

represented in scientific notation.

Science Astonomy Unit

4.1.A.3. Understand and use ratios, rates, proportions,

and percents (including percents greater than 100 and

less than 1) in a variety of situations.

Science

Music

Art

Cooking

Genetics - Punnet Squares

Chemistry

Notes (1/4,1/16)

Scale Drawing

Recipes



Grades 6-8

Standard Subject


Learning Experience

4.1.A.2. Demonstrate a sense of the relative magnitudes

of numbers.

Science

Social Studies

Astonomy Unit

Holocaust Unit - visual representation of

numbers

4.1.A.5. Use computer software to make and verify


Technology Creating models


155



Grades 6-8

Standard Subject


Learning Experience


4.1.C.2. Use equivalent representations of numbers such

as fractions, decimals, and percents to facilitate

estimation.


4.1.C.3. Recognize the limitations of estimation and

assess the amount of error resulting from estimation.


4.1.B.1. Use and explain procedures for performing


multiplication, division, and exponentiation with

integers and all number types named above with: Pencil-

and-paper; Mental math; Calculator.

Science Wave activity

4.1.B.4. Solve problems involving proportions and

percents.

4.2.A.1. Understand and apply concepts involving lines,

angles, and planes: Complementary and supplementary

angles; Vertical angles; Bisectors and perpendicular

bisectors; Parallel, perpendicular, and intersecting

planes; Intersection of plane with cube, cylinder, cone,

and sphere.

Sewing Creating quilts


156



Grades 6-8

Standard Subject


Learning Experience

4.2.C.1. Use coordinates in four quadrants to represent

geometric concepts.

Social Studies Reading a map

Art Polygon project and tessellations

4.2.B.1. Understand and apply transformations: Finding

the image, given the pre-image, and vice-versa;

Sequence of transformations needed to map one figure

onto another; Reflections, rotations, and translations

result in images congruent to the pre-image; Dilations

(stretching/shrinking) result in images similar to the pre-

image.

Art Reflections and rotations

4.2.A.4. Understand and apply the concept of similarity:

Using proportions to find missing measures; Scale

drawings; Models of 3D objects.

Technology

Art

Creating Models

Scale drawings, creating lables for cans

4.2.A.3. Understand and apply properties of polygons:

Quadrilaterals, including squares, rectangles,

parallelograms, trapezoids, rhombi; Regular polygons;

Sum of measures of interior angles of a polygon; Which

polygons can be used alone to generate a tessellation

and why.


157



Grades 6-8

Standard Subject


Learning Experience

4.2.E.1. Develop and apply strategies for finding

perimeter and area: Geometric figures made by

combining triangles, rectangles and circles or parts of

circles; Estimation of area using grids of various sizes;

Impact of a dilation on the perimeter and area of a 2-

dimensional figure; Impact of a dilation on the

perimeter and area of a 2-dimensional figure.

Sewing

Art

Creating a quilt

Polygon project

4.3.B.1. Graph functions, and understand and describe

their general behavior: Equations involving two

variables; Rates of change (informal notion of slope).

4.3.B.2. Recognize and describe the difference between

linear and exponential growth, using tables, graphs, and

equations.

Social Studies Population growth, immigration information

Science On-going through science labs, metric

system

4.2.D.2. Use approximate equivalents between standard

and metric systems to estimate measurements (e.g.,

kilometers is about 3 miles).

Science Ongoing through science labs, metric

system

4.2.D.1. Solve problems requiring calculations that

involve different units of measurement within a

measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

Science Half-life lab


158



Grades 6-8

Standard Subject


Learning Experience

4.3.C.1. Analyze functional relationships to explain how

a change in one quantity can result in a change in

another, using pictures, graphs, charts, and equations.


4.3.C.2. Use patterns, relations, symbolic algebra, and

linear functions to model situations: Using concrete

materials (manipulatives), tables, graphs, verbal rules,

algebraic expressions/ equations/ inequalities; Growth

situations, such as population growth and compound

interest, using recursive formulas.

Social Studies Population growth

4.3.D.2. Solve simple linear equations informally,

graphically, and using formal algebraic methods:

Multi-step, integer coefficients only (although answers

may not be integers) Simple literal equations (e.g., A =

lw) Using paper-and-pencil, calculators, graphing

calculators, spreadsheets, and other technology.

Science Equation balancing in chemistry


159



Grades 6-8

Standard Subject


Learning Experience

Fairness of games

4.4.A.3. Estimate lines of best fit and use them to


Science Half-life graphs

4.4.A.4. Use surveys and sampling techniques to

generate data and draw conclusions about large groups.

4.4.B.6. Play and analyze probability-based games and

discuss the concepts of fairness and expected value.

Social Studies Current events

4.4.A.2. Make inferences and formulate and evaluate

arguments based on displays and analysis of data sets.

Social Studies Data analysis from graphs

4.4.A.1. Select and use appropriate representations for

sets of data, and measures of central tendency (mean,

median, and mode): Type of display most appropriate

for given data; Box-and-whisker plot, upper quartile,

lower quartile; Scatter plot; Calculators and computer

used to record and process information; Finding the

median and mean (weighted average) using frequency

data; Effect of additional data on measures of central

tendency.

Social Studies

Science

Current events

Environmental unit

Physical Education


160



Grades 6-8

Standard Subject


Learning Experience

4.5.A.5. Monitor their progress and reflect on the


All disciplines Discussions throughout

All disciplines Discussions throughout4.5.A.4. Pose problems of various types and levels of

difficulty.

4.4.C.3. Apply techniques of systematic listing, counting,

and reasoning in a variety of different contexts.


4.4.D.1. Use vertex-edge graphs and algorithmic

thinking to represent and find solutions to practical

problems: Finding the shortest network connecting

specified sites; Finding a minimal route that includes

every street; Finding the shortest route on a map from

one site to another; Finding the shortest circuit on a

map that makes a tour of specified sites; Limitations of

computers.

Science

Social Studies

Circuit labs

Shortest route on a map

4.5.A.2. Solve problems that arise in mathematics and in

other contexts: Open-ended problems; Non-routine

problems; Problems with multiple solutions; Problems

that can be solved in several ways.

Language Arts Reading skills


161



Grades 6-8

Standard Subject


Learning Experience

4.5.D.4. Rely on reasoning, rather than answer keys,

teachers, or peers, to check the correctness of their

problem solutions.


Language Arts

Social Studies

World Languages

Discussions throughout

Discussions throughout

4.5.B.2. Communicate mathematical thinking

coherently and clearly to peers, teachers, and others,

both orally and in writing.

Science


4.5.C.4. Apply mathematics in practical situations and

in other disciplines.


4.5.D.3. Select and use various types of reasoning and

methods of proof.

Discussions and persuasive essays

4.5.C.3. Recognize that mathematics is used in a variety

of contexts outside of mathematics.

4.5.C.5. Trace the development of mathematical

concepts over time and across cultures.

Ongoing throughout

4.5.B.1. Use communication to organize and clarify



Language Arts Ongoing throughout


162



Grades 6-8

Standard Subject


Learning Experience

4.5.D.5. Make and investigate mathematical

conjectures: Counterexamples as a means of disproving

conjectures; Verifying conjectures using informal

reasoning or proofs.

Science

4.5.F.2. Use computer spreadsheets, software, and

graphing utilities to organize and display quantitative

information.

4.5.D.6. Evaluate examples of mathematical reasoning

and determine whether they are valid.

Software Applications Creating excel spreadsheets

4.5.F.5. Use computer software to make and verify


Technology Creating models

Scientific method

Science Scientific method

4.5.E.1. Create and use representations to organize,

record, and communicate mathematical ideas: Concrete

representations (e.g., base-ten blocks or algebra tiles);

Pictorial representations (e.g., diagrams, charts, or

tables); Symbolic representations (e.g., a formula);

Graphical representations (e.g., a line graph).

Science Data collection from labs


163

Pre-Algebra Curriculum

164

A. Number Sense

· How can problems in the real world be solved with Mathematics?

· How can estimation be useful to us to reason out solutions to problems?


Resources




Grades 7-8


Assessments



Students discuss why

numbers are easier to

compare when written in

scientific notation







Numbers represented in scientific notation.

- Students calculate relative

change in quantity

- Number line in classroom

- Students use calculators to

work with numbers with more

than 10 digits

McDougal Littell

7.3 - 7.7 (Rational Numbers)

1.4, 4.6, 4.7 (Exponents)

9.1 (Roots)

2.1 (Absolute Value)

4.8 (Scientific Notation)

_______________________

Holt

Ch. 6 (Rational Numbers)

4.1 - 4.3 (Exponents)

4.5 - 4.6 (Roots)

1.3 (Absolute Value)

4.4 (Scientific Notation)

4.1.A 8th Grade Pre-Algebra

165

A. Number Sense




Resources




Grades 7-8


Assessments






of situations.

McDougal Littell

7.1 - 7.7, 8.8

_______________________

Holt

5.1 - 5.4, 5.5

McDougal Littell

2.1, 5.5

_______________________

Holt

2.2

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Ongoing in all investigations4. Compare and order numbers of all named

types.

McDougal Littell

2.1 - 2.5

_______________________

Holt

2.3 - 2.5



- Geometer's Sketchpad

- Activity to show integers on a

number line

- Students use real world data to

discover relationships of

numbers


166

A. Number Sense




Resources




Grades 7-8


Assessments





fractional equivalents:

5/7 = 0.714285714285...

= 0.714285

McDougal Littell

5.5

_______________________

Holt

2.1 - 2.6

Calculator Exploration

Ongoing in all investigations

Classwork Activity/Accuracy

of Student work

7. Construct meanings for common irrational

numbers, such as pi (π) and the square root of

two.

McDougal Littell

9.2

_______________________

Holt

4.5 - 4.6

Students explore irrational

numbers through Pythagorean's

Theorem

Classwork Activity/Accuracy

of Student work

McDougal Littell

4.3, 4.5, 5.1 - 5.7, 7.3 - 7.7

_______________________

Holt

6.1 - 6.6

Do Now

Written assessments

Teacher Observation




167




Resources



Grades 7-8

McDougal Littell

4.6 - 4.8

_________________________

Holt

4.1 - 4.4


Do Now

Written assessments

Teacher Observation



AssessmentsLearning ExperiencesKnowledge/Skills/Understanding







Calculator.

McDougal Littell

2.2 - 2.5

_________________________

Holt

1.4 - 1.6


3. Find square and cube roots of numbers and

understand the inverse nature of powers and

roots.

McDougal Littell

9.1

_________________________

Holt

4.5 - 4.6


powers of numbers.

Technology exploration

Do Now

Written assessments

Teacher Observation


Do Now

Written assessments

Teacher Observation

4.1.B 8th Grade Pre-Algebra

168




Resources



Grades 7-8



AssessmentsLearning ExperiencesKnowledge/Skills/Understanding

B. Numerical OperationsEssential Questions :

Solving real world problems




McDougal Littell

1.2

_________________________

Holt

1.1

Do Now

Written assessments

Teacher Observation



percents.

Do Now

Written assessments

Teacher Observation

McDougal Littell

7.2 - 7.7

_________________________

Holt

5.1, 5.4, 6.2 - 6.6


169

C. Estimation




Resources




McDougal Littell

7.4

_______________________

Holt

6.1

Ongoing through investigations Do Now

Written assessments

Teacher Observation


1. Estimate square and cube roots of numbers. NJ Frameworks Students use the multiplication

function to perform successive

approximations to find

acceptable values for several

square roots (the square roots of

2, 3, 7, 19 and the cube roots of

10 and 100)

Do Now

Written assessments

Teacher Observation




Grades 7-8



4.1.C 8th Grade Pre-Algebra

170

C. Estimation








Grades 7-8





estimation.

NJ Frameworks Students make estimates of the

number of times things happen in

a lifetime and compare

estimations to referenced

materials

Do Now

Written assessments

Teacher Observation


171

· How can knowledge of geometric properties help in problem solving situations?

· How can coordinate grid systems help us analyze situations?



1. Understand and apply concepts involving

lines, angles, and planes: Complementary and

supplementary angles; Vertical angles;

Bisectors and perpendicular bisectors;

Parallel, perpendicular, and intersecting

planes; Intersection of plane with cube,

cylinder, cone, and sphere.

McDougal Littell

8.1 - 8.2

_______________________

Holt

7.1 - 7.2

Geometer's Sketchpad Do Now

Written assessments

Teacher Observation



Theorem.

McDougal Littell

9.3 - 9.4

_______________________

Holt

4.8

- Using manipulatives


· How does the mathematics of geometry enable us to wonder and understand our natural

and physical world?

Do Now

Written assessments

Teacher Observation






Grades 7-8


172







and physical world?






Grades 7-8




objects.

Do Now

Written assessments

Teacher Observation

Use proportions to investigate

real world problems

Do Now

Written assessments

Teacher Observation




rhombi; Regular polygons; Sum of measures

of interior angles of a polygon; Which

polygons can be used alone to generate a

tessellation and why.

McDougal Littell

8.3 - 8.4

_______________________

Holt

7.4

- Direct instruction

- Using manipulatives

McDougal Littell

8.8

_______________________

Holt

5.5


173







and physical world?






Grades 7-8



McDougal Littell

Ch. 8

_______________________

Holt

Ch. 7

Ongoing through Geometry

Investigations

Do Now

Written assessments

Teacher Observation


174




Resources

2. Use iterative procedures to generate

geometric patterns: Fractals (e.g., the Koch

Snowflake); Self-similarity; Construction of

initial stages; Patterns in successive stages

(e.g., number of triangles in each stage of

Sierpinski’s Triangle).

NJ Frameworks - Students explore shapes with

tangrams

- Students build a Sierpinski's

Triangle




Grades 7-8


Assessments

Do Now

Written assessments

Teacher Observation










McDougal Littell

8.6 - 8.8

_______________________

Holt

7.7

- Exploring through Geometer's

Sketchpad

- Rotation art activity

Students describe sizes,

positions, orientation of

shapes such as flips, slides,

turns, and scaling



and physical world?



175




Resources Learning Experiences



McDougal Littell

2.8

_______________________

Holt

7.5

Students explore properties of

shapes in a coordinate system

Do Now

Written assessments

Teacher Observation



McDougal Littell

8.7

_______________________

Holt

7.7

Students will perform

transformations on a coordinate

grid

Do Now

Written assessments

Teacher Observation


Assessments


and physical world?



Grades 7-8

C. Coordinate Geometry Essential Questions :



176




Resources



Grades 7-8

Students reflect on close they

are to degree of accuracy and

how it affects results

McDougal Littell

7.1

_______________________

Holt

5.2

Using real life examples




miles).

NJ Frameworks

NJ Frameworks

Ongoing with all measurement

activities

Do Now

Written assessments

Teacher Observation

Students plan a new Olympics by

renaming standard events in

different measurement units





equals 12’1”).





Students develop a project, for

example, scale drawing of an

apartment floor plan

D. Units of Measurement Essential Questions :


Accuracy of student work

Assessments


and physical world?


4.2.D 8th Grade Pre-Algebra

177




Resources



Grades 7-8




Assessments


and physical world?




Teacher created materials

Various workbooks

Using real life examples Do Now

Written assessments

Teacher Observation




situation.





mile).


Various workbooks

Students will use their

knowledge of mathematics to

plan and carry out scientific

experimentation

Reflection on results of

student created experiments


Various workbooks

Students are asked to find the

height of a tall tree if the

height of a small tree is

known



178




Resources


and physical world?






McDougal Littell

10.7

_______________________

Holt

8.6

Teacher demonstration with

manipulatives

Do Now

Written assessments

Teacher Observation





grids of various sizes; Impact of a dilation on


figure; Impact of a dilation on the perimeter

and area of a 2-dimensional figure.

McDougal Littell

1.6, 10.1 - 10.2

_______________________

Holt

8.1 - 8.3

Students investigate the

relationship between perimeter

and area

Do Now

Written assessments

Teacher Observation






Grades 7-8


4.2.E 8th Grade Pre-Algebra

179




Resources


and physical world?






Grades 7-8


4. Use formulas to find the volume and surface

area of a sphere.

McDougal Littell

10.7

_______________________

Holt

8.9

Students will evaluate problems Do Now

Written assessments

Teacher Observation


for finding the surface area and volume of a

three-dimensional figure: Volume —prism,

cone, pyramid; Surface area —prism

(triangular or rectangular base), pyramid

(triangular or rectangular base); Impact of a

dilation on the surface area and volume of a


McDougal Littell

10.4 - 10.7

_______________________

Holt

8.5 - 8.8

Students investigate the nets of

three dimensional figures

Students build models and

explain how changes in

surface area and volume are

impacted as lengths are

changed


180


Resources

Do Now

Written assessments

Teacher Observation


Assessments


A. Patterns













formula.

McDougal Littell

11.1

_______________________

Holt

13.1 - 13.3

- Direct Instruction




Grades 7-8


181


Resources




McDougal Littell

11.6

_______________________

Holt

13.4 - 13.5

Cooperative Learning Activities Do Now

Written assessments

Teacher Observation



involving two variables; Rates of change

(informal notion of slope).

McDougal Littell

11.3 - 11.7

_______________________

Holt

13.4 - 13.7

Technology Exploration Do Now

Written assessments

Teacher Observation










Grades 7-8


182


Resources









Various workbooks

Ongoing through all

investigations

Do Now

Written assessments

Teacher Observation

Technology exploration Do Now

Written assessments

Teacher Observation



Grades 7-8





McDougal Littell

11.6

_______________________

Holt

12.2



C. Modeling






183


Resources

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

McDougal Littell

3.1 - 3.4, 6.1 - 6.4

_______________________

Holt

11.2


- Real world problem solving






is “left 3, right 6”).

McDougal Littell

2.1

_______________________

Holt

1.3

Number Line in classroom



Grades 7-8



methods:


answers may not be integers) Simple literal

equations (e.g., A = lw) Using paper-and-

pencil, calculators, graphing calculators,


Assessments


help explain real-life situations?



D. Procedures


184


Resources





Grades 7-8

Assessments





D. Procedures

3. Solve simple linear inequalities.




parentheses; Distributive property;

Substitution of a number for a variable;

Translation of a verbal phrase or sentence into

an algebraic expression, equation, or

inequality, and vice versa.

McDougal Littell

1.3, 2.6, 2.7

_______________________

Holt

11.1

Applied throughout

investigations

Do Now

Written assessments

Teacher Observation

McDougal Littell

3.6 - 3.7, 6.5

_______________________

Holt

11.4


Written assessments

Teacher Observation


185


Resources





Grades 7-8

Assessments





D. Procedures




inverse; Addition and multiplication

properties of equality; Addition and

multiplication properties of inequalities.

McDougal Littell

3.1 - 3.4

_______________________

Holt

1.7 - 1.8


Written assessments

Teacher Observation


186


Resources

· How can experimental and theoretical probability be used to make predictions or draw

conclusions?

· How can statistics help us to understand real world situations?












central tendency.

McDougal Littell

5.8, 12.1 - 12.3

_______________________

Holt

9.3 -9.4, 9.8

Real world problem solving



Grades 7-8

Graphing project


· How can classifying help me in organizing data to solve problems?


Mathematics

A. Data Analysis


187


Resources


conclusions?





Grades 7-8




Mathematics

A. Data Analysis


Student project



McDougal Littell

11.2

_______________________

Holt

12.7

Real world problem solving Students produce a scatterplot

to determine line of best fit




4. Use surveys and sampling techniques to

generate data and draw conclusions about

large groups.

Teacher created material

Various worbooks


McDougal Littell

5.8, 12.1 - 12.3

_______________________

Holt

9.3 -9.4, 9.8

Do Now

Written assessments

Teacher Observation


188


Resources


and decimals.

McDougal Littell

7.8, 12.7

_______________________

Holt

10.1

Cooperative Learning activities Do Now

Written assessments

Teacher Observation


events.



conclusions?


McDougal Littell

12.8

_______________________

Holt

10.5

Stations in classroom Results from stations



Mathematics



Grades 7-8



189


Resources



conclusions?




Mathematics



Grades 7-8






McDougal Littell

12.7 - 12.8

_______________________

Holt

10.4



events (e.g., if there are seven marbles in a

bag, three red and four green, what is the

probability that two marbles picked from the

bag, without replacement, are both red).

McDougal Littell

12.7 - 12.8

_______________________

Holt

10.5



190


Resources



conclusions?




Mathematics



Grades 7-8




probabilities.

McDougal Littell

7.8

_______________________

Holt

10.2, 10.4


Written assessments

Teacher Observation

6. Play and analyze probability-based games


expected value.


_______________________

Holt

Ch. 10 ending activity

Cooperative Learning activities Do Now

Written assessments

Teacher Observation


191


Resources



Various workbooks Direct instruction Do Now

Written assessments

Teacher Observation



different contexts.

McDougal Littell

12.4

_______________________

Holt

10.8

Ongoing throughout

investigations

Do Now

Written assessments

Teacher Observation


conclusions?




with replacement vs. ordered situations

without replacement; Factorial notation;

Concept of combinations.

McDougal Littell

12.4 - 12.6

_______________________

Holt

10.8 - 10.9


- Ice cream activity

Student projects



Grades 7-8



Mathematics

C. Systematic Listing and CountingEssential Questions :



192


Resources


conclusions?






minimal route that includes every street;

Finding the shortest route on a map from one

site to another; Finding the shortest circuit on

a map that makes a tour of specified sites;

Limitations of computers.

NJ Frameworks - Students explore common

discrete mathematical models,

explore their properties, and

design them for specific

situations

- Students devise, describe, and

test algorithms for solving

optimization and search options

Do Now

Written assessments

Teacher Observation



Grades 7-8



Mathematics




193


Resources






McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

Incorporated throughout

investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Grades 7-8


mathematics?


A. Problem SolvingEssential Questions :




194





Grades 7-8


mathematics?






difficulty.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation




problems.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


195


Resources



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation







McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


mathematics?




Grades 7-8



Assessments


196


Resources





mathematics?




Grades 7-8



Assessments



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


197


Resources





McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation





McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Grades 7-8


mathematics?


C. ConnectionsEssential Questions :




198





Grades 7-8


mathematics?








McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


199


Resources



solutions.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Grades 7-8


mathematics?


D. ReasoningEssential Questions :




200





Grades 7-8


mathematics?







valid.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation





McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


201


Resources



problems.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation









McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation



Grades 7-8


mathematics?


E. RepresentationsEssential Questions :




202





Grades 7-8


mathematics?







phenomena.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


203


Resources




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks

- Technology exploration


Do Now

Written assessments

Teacher Observation




McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation



Grades 7-8


mathematics?


F. TechnologyEssential Questions :



4.5.F 8th Grade Pre-Algebra

204





Grades 7-8


mathematics?







McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation



McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation



and their graphs.

McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks



Do Now

Written assessments

Teacher Observation


205





Grades 7-8


mathematics?





6. Use computer-bases laboratory technology


McDougal Littell

Chapters. 1 - 12

Holt

Chapters 1 - 14

Various Workbooks


investigations

Do Now

Written assessments

Teacher Observation


206

Nasco 2006

Nasco 2003

Nasco 2002

Holt Course 3: Pre-Algebra


including ELL)

Jeanine M. Bennett, Edward B.

Burger, David J. Chard, Audrey

L. Jackson, Paul A. Kennedy,

Freddie L. Renfro, Janet K.

Scheer, and Bert K. Waits

Holt, Reinhart and Winston

8th Grade Pre-Algebra

Resources

Title of Resource Publisher Copyright

2007



Grades 7-8

2008

Author(s)

McDougall Littell Course 3


including ELL)

Ron Larson, Laurie Boswell,

Timothy D. Kanold, and Lee

Stiff

McDougal Littell

McGraw Hill 2002

Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989

Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002

Algebra Joke Worksheets Christine A. Koers Nasco 2003

Geo Joke Worksheets Christine A. Koers

Pre-Algebra Joke Worksheets Christine A. Koers

Algebra with Pizzazz! Steve and Janis Marcy

Fractions, Decimals, and Percents Joke

WorksheetsChristine A. Koers

8th Grade Pre-Algebra Resources

207


Resources




Grades 7-8

Author(s)

Frank Schaffer Publications

Kelley Wingate Publications

Incentive Publications Inc.

Algebra Puzzlers

Pre-Algebra

Masterminds Riddle Math Series - Pre-Algebra

Theresa Kane McKell

Dawn Talluto Jacobi

Brenda Opie and Douglas

McAvinn

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla

The 100+ Series - Algebra Grades 5-8Mary Lee Vivian and Margaret

ThomasFrank Schaffer Publications 2003

Jossey-Bass 2003

The 100+ Series - Pre-Algebra Grades 5-8Mary Lee Vivian and Margaret


The 100+ Series - Intro to GeometryMary Lee Vivian and Margaret

Thomas

The 100+ Series - Math Grades 7-8Mary Lee Vivian and Margaret


Frank Schaffer Publications 2003

Carson-Dellosa Publishing

Company, Inc.2003

1998

1996

1996

Pre-Algebra Brain Teasers Lorin Olschanski

Skills for Success - Algebra Theresa Kane McKell

The 100+ Series - Standard Based Math

Grades 7-8

Mary Lee Vivian and Margaret


Teacher Created Resources Inc. 1999


208


Resources




Grades 7-8

Author(s)

Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005

New Jersey Department of

Education and Rutgers

Quadrant Quandries Julie K. Cohen Nasco 2007

The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001

New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008

Adventures with Area Evelyn B. Christensen Nasco 2007

Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002

Preparing for the New Jersey GEPA - Grade 8David J. Glatzer and Joyce

GlatzerAmsco School Publications, Inc. 2005

Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006

GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000

Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006

Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006

NJ Frameworkshttp://www.state.nj.us/education/

frameworks/math/index.html-------


209


Resources




Grades 7-8

Author(s)

Kuta Software- Infinite Pre-Algebra Kuta Software LLC 2010

Power Practice Geometry Pamela Jennett

Power Practice Pre-Algebra Wendy Osterman Creative Teaching Press 2004

J. Weston Walch Publisher 1996

Creative Teaching Press 2007

Scratch Your Brain AlgebraDoug Brumbaugh and David

RockThe Critical Thinking Co. 2008

Algebra Practice Exercises Thomas E. Campbell

Creative Teaching Press 2006

Plotting Pictures Paula Rozell Dale Seymour Publications 1995

Algebra Puzzles Hank Garcia

Measuring Up - Grade 8 Michael Goodman People's Publishing Group 2003

Skills for Success - GeometryTiffany Moore and Jenae

Hawkins


Company, Inc.2007


210

Number of Blocks


Pacing Guide

Unit

Variables and Expressions 1

McDougall Littell Mathematics

Course 3 Chapter

4,5

7

Benchmark Assessment -

Pre-Test-----

Equations and Inequalities 3

10

6

-----


Midtem

Factors, Fractions, Exponents,

Rational Number Operations

----------



Grades 7-8

Ratio, Proportion, Percent 7

5

11

Integer Operations 2

8th Grade Pre-Algebra Pacing Guide

211

Number of Blocks


Pacing Guide


Course 3 Chapter



Grades 7-8

Data Analysis and Probability 11

Real Numbers and Right

Triangles9

12

Polygons and Transformations 8 10

4

5

Measurement, Area, Volume 10 6

6

Linear Equations and Graphs

Multi-Step Equations and

Inequalities5 7


Post-Test----- -----


212

6 5Percents

Fractions, Decimals, and

Percents

11

8

9

10



Grades 7-8

Unit


Pacing Guide

4

10

-----

Number of Blocks

3

Variables, Expressions, Integers 1

Ratios, Proportion, Similarity 5

Exponents, Square roots,

Pythagorean Theorem, and

Scientific Notation

Graphs, Functions, and

Sequences


Pre-Test-----

Holt Course 3 Chapter

2


213



Grades 7-8

Unit


Pacing Guide

Number of BlocksHolt Course 3 Chapter


Post-Test----- -----

5

4

12

Data and Statistics 9

Probability 10 7

Two Dimensional Geometry 7

-----

Measurement, Area, and

Volume8


Midterm-----


214

Algebra 1B Curriculum

215

A. Number Sense




Resources

Ongoing through problems

- Problem Solving

- Collaborative discussions

- Brainstorming


Various workbooks

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation






Percents; Exponents; Roots; Absolute Values.

- Investigate decimal patterns

using a caluclator

- Class discussions

- Written explanations

- Recursive Routines

- Through the use of geometry

and squares and cubes


Larson Algebra 1

Sections 2.1, 2.7, 3.7, 6.5

and Chapter 8


Various workbooks





Assessments




of situations.




Grades 7-8


Do Now

Written assessments

Teacher Observation

4.1.A 8th Grade Algebra 1B

216

A. Number Sense




Resources



Assessments




Grades 7-8





5/7 = 0.714285714285...

= 0.714285


Various workbooks

Graphing on a number line

Line-up in classroom

Use equations method


Various workbooks

Do Now

Written assessments

Teacher Observation



two.


types.

Spiral of Right Triangles

(Pythagorean Theorem)

Circle - develop pi from

circumference formula


Various workbooks

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation



the same number.


Various workbooks

Ongoing throughout problems


217




Resources


percents.

Teacher created packet of percents,

proportion, and interest

Do Now

Written assessments

Teacher Observation

Mental Math Warmups

Knowledge/Skills/Understanding AssessmentsLearning Experiences






Calculator.


Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Extension of 8.3



- Real world problems


Grades 7-8



Do Now

Written assessments

Teacher Observation

Finding the length of the edge of

a cube knowing the volume





powers of numbers.

Larson Algebra 1

Chapter 8

Do Now

Written assessments

Teacher Observation


3. Find square and cube roots of numbers and

understand their inverse relationships.

4.1.B 8th Grade Algebra 1B

218




ResourcesKnowledge/Skills/Understanding AssessmentsLearning Experiences


Grades 7-8






6. Perform operations on matrices (Addition

and Subtraction, Scalar Multiplication,

Multiplication).

Larson Algebra 1

Section 2.4





Larson Algebra 1

Section 1.2

Do Now

Written assessments

Teacher Observation

Pattern investigation


Written assessments

Teacher Observation


219

C. Estimation




Resources




Grades 7-8




1. Estimate cube roots of numbers. Larson Algebra 1

Extension of 8.3

Teacher created problems

Technology Exploration Do Now

Written assessments

Teacher Observation



estimation.


Various workbooks

Physically measure lengths and

discuss why disparities occur

Do Now

Written assessments

Teacher Observation





Various workbooks


Written assessments

Teacher Observation

4.1.C 8th Grade Algebra 1B

220




Resources


and physical world?



Grades 7-8






Various workbooks

Direct instruction


Theorem.

Larson Algebra 1

Section 11.4

Various workbooks

1. Understand and apply concepts involving

lines, angles, and planes: Complementary and

supplementary angles; Bisectors and

perpendicular bisectors; Parallel,

perpendicular, and intersecting planes;

Intersection of plane with cube, cylinder, cone,

and sphere.


Do Now

Written assessments

Teacher Observation

Assessments

Do Now

Written assessments

Teacher Observation

Exploration and Investigation Do Now

Written assessments

Teacher Observation


polygons.

Real world application problems


221




Resources


and physical world?



Grades 7-8





Assessments

Do Now

Written assessments

Teacher Observation


Various workbooks

Cooperative Learning activity Do Now

Written assessments

Teacher Observation




objects.





Various workbooks

Exploration and Investigation


222




Resources Learning Experiences Assessments



Grades 7-8



and physical world?








Larson Algebra 1

Section 8.6


Written assessments

Teacher Observation











Larson Algebra 1

Section 4.1

Use calculator to compare

graphs of equations that involve

transformations

Coordinate grid drawings

Teacher Observation



223




Resources




Larson Algebra 1

Section 4.1

Direct Instruction Coordinate grid drawings

Teacher Observation



Larson Algebra 1

Section 4.1

Determine if a quadrilateral is a

parallelogram or a rectangle

Do Now

Written assessments

Teacher Observation



Grades 7-8




and physical world?

AssessmentsKnowledge/Skills/Understanding



224




Resources



the same system.

Larson Algebra 1

Section 3.8 and Skills

Review Handbook

Teacher Created Problems






Larson Algebra 1


Review Handbook


Students develop a project, for

example, scale drawing of an

apartment floor plan




Grades 7-8


Do Now

Written assessments

Teacher Observation





miles).

Larson Algebra 1


Review Handbook


Ongoing in all investigations Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation

Assessments


and physical world?


4.2.D 8th Grade Algebra 1B

225







Grades 7-8



Assessments


and physical world?


Do Now

Written assessments

Teacher Observation



hour).

Larson Algebra 1

Skills Review Handbook





Larson Algebra 1




Written assessments

Teacher Observation




situation.

Larson Algebra 1




Written assessments

Teacher Observation


226




Resources





grids of various sizes; Impact of a dilation on


figure; Impact of a dilation on the perimeter

and area of a 2-dimensional figure.


Larson Algebra 1


Various workbooks




and physical world?

Students investigate the

relationship between perimeter

and area

Do Now

Written assessments

Teacher Observation



Grades 7-8


Larson Algebra 1


Various workbooks

Teacher demonstration with

manipulatives

Do Now

Written assessments

Teacher Observation



cylinder with the same base and height.

4.2.E 8th Grade Algebra 1B

227




Resources





and physical world?



Grades 7-8


Do Now

Written assessments

Teacher Observation

Do Now

Written assessments

Teacher Observation









Larson Algebra 1


Various workbooks

Students investigate the nets of

three dimensional figures


area of a sphere.

Larson Algebra 1


Various workbooks

Students evaluate problems


228


Resources

Larson Algebra 1

Section 5.3, 8.6


- Given terms in a pattern,

describe patterns in words




Grades 7-8

Do Now

Written assessments

Teacher Observation


Assessments


A. Patterns













formula.


229


Resources





Grades 7-8








involving two variables; Rates of change

(informal notion of slope).

Larson Algebra 1

Chapter 4


- Discussion

Do Now

Written assessments

Teacher Observation




Larson Algebra 1

Chpater 8


- Discussion

Do Now

Written assessments

Teacher Observation


230


Resources



Grades 7-8

Assessments


C. Modeling





Do Now

Written assessments

Teacher Observation

- Reasoning

- Discussions

Do Now

Written assessments

Teacher Observation






Larson Algebra 1



and linear functions to model situations:

Growth situations, such as population growth

and compound interest, using recursive

formulas.

Larson Algebra 1



- Collaborative investigations


231


Resources



2. Solve linear equations and inequalities

informally, graphically, and using formal

algebraic methods:


answers may not be integers); absolute value;

compound inequalities; rational expressions;

using paper-and-pencil, calculators, graphing

calculators, spreadsheets, and other

technology.


Grades 7-8

Larson Algebra 1

Section 2.1


Direct instruction



Absolute value.

Do Now

Written assessments

Teacher Observation


Do Now

Written assessments

Teacher Observation




Larson Algebra 1

Chapter 3



Written assessments

Teacher Observation

3. Solve systems of equations: graphically;

algebraic methods; using matrices.

Larson Algebra 1

Chapter 7


Direct instruction


232


Resources




Grades 7-8






Do Now

Written assessments

Teacher Observation

4. Factor polynomials.

6. Evaluate and simplify algebraic

expressions: add and subtract polynomials;

multiply a polynomial by a monomial or

binomial; divide a polynomial by a monomial;

use laws of exponents.

Larson Algebra 1

Chapters 2, 8 and 9


Various workbooks

Larson Algebra 1

Chapter 9



Written assessments

Teacher Observation

5. Rational expressions: add and subtract;

mulitply and divide.

Larson Algebra 1

Chpater 12


Do Now

Written assessments

Teacher Observation

Direct instruction

Direct instruction


233


Resources





Grades 7-8

Learning ExperiencesKnowledge/Skills/Understanding


Mathematics

A. Data Analysis Essential Questions :


conclusions?




Larson Algebra 1

Sections 13.5, 13.6, 13.7,

13.8 and Skills Review

Handbook


Real world problem solving Do Now

Written assessments

Teacher Observation


Assessments

Do Now

Written assessments

Teacher Observation



tendency (mean, median, and mode): Finding

the median and mean (weighted average)

using frequency data; Effect of additional

data on measures of central tendency.

Larson Algebra 1

Sections 13.5 and 13.6 and




234


Resources


conclusions?






Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4




- Manipulatives

- Probability stations


- Manipulatives



Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


Do Now

Written assessments

Teacher Observation



Grades 7-8



Mathematics

Assessments






- Manipulatives




events.

Larson Algebra 1

Section 13.4



235


Resources


conclusions?






Grades 7-8



Mathematics

Assessments



probabilities.

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


- Manipulatives



Do Now

Written assessments

Teacher Observation

5. Play and analyze probability-based games


expected value.

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


- Manipulatives



Do Now

Written assessments

Teacher Observation


236


Resources



Mathematics





Grades 7-8





replacement.

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


- Manipulatives


Do Now

Written assessments

Teacher Observation


conclusions?




different contexts.

Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


- Manipulatives


Do Now

Written assessments

Teacher Observation



Larson Algebra 1

Sections 13.1, 13.2, 13.3,

and 13.4


- Manipulatives


Do Now

Written assessments

Teacher Observation


237


Resources



Mathematics





Grades 7-8









Limitations of computers (overwhelming the

capacity).

Teacher created materials - Students explore common

discrete mathematical models,

explore their properties, and

design them for specific

situations

- Students devise, describe, and

test algorithms for solving

optimization and search options

Do Now

Written assessments

Teacher Observation


conclusions?



238


Resources


mathematics?







Grades 7-8




Larson Algebra 1

Chapters 4 - 13

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling

- Classroom discussion

- Predictions

Do Now

Written assessments

Teacher Observation






Larson Algebra 1

Chapters 4 - 13

Question Quest

Level D

Various workbooks

- Students analyze their own

written response compared to

teacher created examples

- Students analyze each other's

written responses

Do Now

Written assessments

Teacher Observation


239


Resources


mathematics?







Grades 7-8



problem-solving strategies to solve problems.

Larson Algebra 1

Chapters 4 - 13

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation


difficulty.

Larson Algebra 1

Chapters 4 - 13

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation


240


Resources


mathematics?







Grades 7-8




Larson Algebra 1

Chapters 4 - 13

Question Quest

Level D

Various workbooks

- Brainstorming

- Journaling


- Predictions

Do Now

Written assessments

Teacher Observation


241


Resources


mathematics?



Assessments







Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation




Larson Algebra 1

Chapters 4 - 13


Various workbooks



Grades 7-8


B. Communication



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


242


Resources


mathematics?



Assessments






Grades 7-8


B. Communication



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


243


Resources



Grades 7-8

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation






mathematics?









Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations


244


Resources



Grades 7-8


mathematics?






Do Now

Written assessments

Teacher Observation




Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation



Larson Algebra 1

Chapters 4 - 13


Various workbooks


245


Resources



Grades 7-8

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



solutions.


mathematics?








Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations


246


Resources



Grades 7-8


mathematics?






Do Now

Written assessments

Teacher Observation



valid.

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations





Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation




Larson Algebra 1

Chapters 4 - 13


Various workbooks


247


Resources


mathematics?







Grades 7-8









Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



problems.

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


248


Resources


mathematics?







Grades 7-8




phenomena.

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


249


Resources



Grades 7-8

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation





mathematics?








Do Now

Written assessments

Teacher Observation

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation



and their graphs.

Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

4.5.F 8th Grade Algebra 1B

250


Resources



Grades 7-8


mathematics?






Do Now

Written assessments

Teacher Observation

6. Use computer-bases laboratory technology


Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations



Larson Algebra 1

Chapters 4 - 13


Various workbooks


investigations

Do Now

Written assessments

Teacher Observation


investigations

Do Now

Written assessments

Teacher Observation



Larson Algebra 1

Chapters 4 - 13


Various workbooks

4.5.F 8th Grade Algebra 1B

251

The 100+ Series - Pre-AlgebraMary Lee Vivian and Margaret

ThomasMcGraw Hill 2003

The 100+ Series - AlgebraMary Lee Vivian and Margaret


Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003

Fractions, Decimals, and Percents Joke

WorksheetsChristine A. Koers Nasco 2006

Geo Joke Worksheets Christine A. Koers Nasco 2002

Pre-Algebra Joke Worksheets Christine A. Koers Nasco 2003


Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002

Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002

Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989


Larson Algebra 1Ron Larson, Laurie Boswell,

Timothy D. Kanold, and Lee StiffHolt McDougal 2011

Author(s)


Resources



Grades 7-8

8th Grade Algebra 1B Resources

252

Title of Resource Publisher CopyrightAuthor(s)


Resources



Grades 7-8



Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006

Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006



NJ Frameworkshttp://www.state.nj.us/education/f

rameworks/math/index.html

New Jersey Department of

Education and Rutgers-------

Masterminds Riddle Math Series - Pre-AlgebraBrenda Opie and Douglas

McAvinnIncentive Publications Inc. 1996

1998

1996

Skills for Success - Algebra

Pre-Algebra Brain Teasers

Algebra Puzzlers

Pre-Algebra

Theresa Kane McKell

Lorin Olschanski

Theresa Kane McKell

Dawn Talluto Jacobi


Company, Inc.

Teacher Created Resources Inc.


Kelley Wingate Publications

2003

1999


253



Resources



Grades 7-8

Milliken Publishing Company 2004

Test Time Algebra Maureen Steddin J. Weston Walch Publisher 2003

The Univeristy of Chicago School Mathematics

Project - AlgebraScott Foresman Harper Collins Publishers 1996

What's My Rule? (Using Problem Solving

Strategies Grades 6 - 12)Dave and Teddy Logothetti Dale Seymour Publications 1983

Geometry Reproducibles Sara Freeman

Developing Skills in Algebra 1: Book C Harold and Loretta Taylor Dale Seymour Publications 1984

Algebra Practice Exercises Thomas E. Campbell J. Weston Walch Publisher 1996

Scratch Your Brain AlgebraDoug Brumbaugh and David

RockThe Critical Thinking Co. 2008


Quadrant Quandries Julie K. Cohen Nasco 2007

Adventures with Area Evelyn B. Christensen Nasco 2007





254



Resources



Grades 7-8

Kuta Software - Infinite Pre-Algera, Algebra 1 Kuta Software LLC 2010, 2011


255

Radicals

11 6

4 and 5 10

8



Grades 7-8

Unit Number of Blocks

Benchmark Assessment - Pretest -----


Pacing Guide

Larson Algebra 1

7 10


a Line

Benchmark Assessment - Midterm

----- -----

Exponents and Exponential Models

8

-----

Linear Equations

3 and 6 10

Systems of Equations and Inequalities


256



Grades 7-8



Pacing Guide

Larson Algebra 1

12 6

Quadratics

10 12

Rational Expressions and Functions

Benchmark Assessment - Final

----- -----

Polynomials

9 7


257

Advanced Algebra Curriculum

258

A. Number Sense






Resources





numbers as well): Roots of monomials,

Variables in exponents, Roots, Know the

meaning on square/cubic roots, Understand

the inverse relationship between powers and

roots.

- Use of geometry connections

through squares and cubes



Written assessments

Class discussions

Teacher observations

Do now

Written assessments

Teacher observation

Larson Algebra 2

Chapter 6


Various Workbooks


Various Workbooks

Written classwork



Grades 7-8




4.1.A 8th Grade Advanced Algebra

259

A. Number Sense







Grades 7-8




Larson Algebra 2

Pages 589-595


Various Workbooks

Do now

Written assessments

Teacher observation

Do now

Written assessments

Teacher observation

Class discussion




of situations. Solving ratios and proportions

involving polynomials.

Larson Algebra 2

Page 5, 7


Various Workbooks



two. Prove the square root of two is irrational.

Teacher created mateirals Direct instruction

Do now

Written assessments

Teacher observation

Solving real world problems

Graphing on a number line4. Compare and order rational and irrational

numbers.


260





2. Perform operations on Matrices. Larson Algebra 2

Sections 3.5 and 3.6

Do now

Written assessments

Teacher observation

Students investigate weekly

movement of rental cars between

cities and analyze results

Various workbooks




Grades 7-8


Do now

Written assessments

Teacher observation





above with: Mental math.




- Mental Math classwork

worksheets

- Ongoing throughout

investigations

ResourcesKnowledge/Skills/Understanding Assessments

4.1.B 8th Grade Advanced Algebra

261

C. Estimation







Grades 7-8





estimation.

Various workbooks


Take results of experiments done

in class and make conclusions

for a larger/smaller group or

time.

Do now

Written assessments


Knowledge/Skills/Understanding Learning Experiences AssessmentsResources

4.1.C 8th Grade Advanced Algebra

262








Grades 7-8

3. Use geometric models to represent real

world situations and to solve problems.

Various workbooks Solve real world problems


and physical world?

Resources

Do now

Written assessments

Teacher observation

Do now

Written assessments

Teacher observation



Various workbooks


Solve real world problems Do now

Written assessments

Teacher observation

Assessments


similarity using:

Models of 3D objects

Polynomials used sometimes as dimensions.


Various workbooks

- Cooperative learning activity

- Solve real world problems



263





Do now

Written assessments









Larson Algebra 2

Page 816, 825, 838

- Investigations

- Cooperative learning activities

- Students investigate the

Mandelbot set.

Assessments

Do now

Written assessments


- Graphing activities



and physical world?


Grades 7-8






needed to map one figure onto another.

Teacher Created Resources

Various workbooks




264






Assessments


and physical world?


Grades 7-8





Direct instruction Do now

Written assessments


3. Determine whether two or more given

shapes can be used to generate a tessellation.

Teacher Created Resources

Various workbooks


265






1. Use coordinate geometry to represent and

verify properties of lines; distances between

two points; midpoint and slope of a line

segment; finding the intersection of two lines;

lines with the same slope are parallel; lines

that are perpendicular have slopes whose

product is -1.

Resources



Grades 7-8

Do now

Written assessments

Teacher observation

Assessments


and physical world?



- Students investigate and

explore what happens to the

equation of a linear function

when they translate the graph of

a line

- Students use motion detectors,

graphing calculators, fathom

software to investigate parallel

lines

Larson Algebra 2

Chapters 2 and 3

Various workbooks


2. Show position and represent motion in the

coordinate plane using vectors.

Larson Algebra 2

Pages A7- A11

Students perform investigations Do now

Written assessments

Teacher observation


266






Resources



Grades 7-8

Assessments


and physical world?



support conjectures and geometric objects.

Various workbooks


Ongoing throughout

investigations

Do now

Written assessments

Teacher observation


polygons. Quadrilaterals, including squares,

rectangles, parallelograms, trapezoids and

rhombi; regular polygons; sum of measures of

interior angles of a polygon.

Various workbooks


- Solving real world problems


Do now

Written assessments

Teacher observation


267







Grades 7-8


Assessments


and physical world?

Knowledge/Skills/Understanding Learning ExperiencesResources



needed in a particular problem solving

situation.

Various workbooks Direct instruction Do now

Written assessments

Teacher observation

2. Understand and use the concept of

significant digits.

Teacher created materials Direct instruction Do now

Written assessments

Teacher observation

4.2.D 8th Grade Advanced Algebra

268




Various workbooks


-Students explore the volume of

cones and pyramids by

constructing

- Solve real world problems



AssessmentsResources


and physical world?



Grades 7-8

Do now

Written assessments

Teacher observation


perimeter and area:

Impact of a dilation on the perimeter and are

of a two dimensional figure.

Various workbooks


Group activities Do now

Written assessments

Teacher observation

Class discussion








4.2.E 8th Grade Advanced Algebra

269








and physical world?



Grades 7-8




area of a sphere.

Various workbooks


Direct Instruction Do now

Written assessments

Teacher observation









Various workbooks


- Cooperative learning

- Investigations

Do now

Written assessments

Teacher observation


270


Larson Algebra 2

Chapter 12

- Students investigate, compare

and contrast formulas: three

recursive, three graphs, three

linear equations

- Students investigate arithmetic

number sequences and find the

partial sum formula



Grades 7-8

Resources

Do now

Written assessments

Teacher observation


Assessments


A. Patterns





1. Use models and algebraic formulas to

represent and analyze sequences and series:

Explicit formulas for nth terms, sums of finite

arithmetic series, sums of finite and infinite

geometric series, develop and informal notion

of limit, use inductive reasoning to form

generalizations.


271




Grades 7-8





Resources



1. Analyze and explain the general properties

and behavior of functions of one variable,

using appropriate graphing technologies:

Slope of a line or curve, domain and range,

intercepts, maximum/minimum, estimating

roots of an equation, intersecting points as

solutions of systems of equations, rates of

change.

Larson Algebra 2

Chapters 2 and 3

Various workbooks

- Students use motion sensor to

calculate the speed of a balloon

rocket

- Cooperative learning graphing

activities

Do now

Written assessments



2. Understand and perform transformations

on commonly used functions; translations,

reflections, dilations; effects on linear and

quadratic graphs of parameter changes in

equations.

Larson Algebra 2

Sections 2.3, 4.1, and 4.2


Students investigate using a

graphing calculator what

happens to the equation of a

linear function when you

translate the graph of a line

Do now

Written assessments



272




Grades 7-8





Resources




- Cooperative learning graphing

activities


- Graphing calculator

Do now

Written assessments


3. Understand and compare the properties of

classes of functions, including exponential,

polynomial, rational, and trigonometric

functions; linear vs. non-linear.

Various workbooks


273








Resources

Students investigate using

exponential functions to model

real world growth and decay

scenarios

Larson Algebra 2

Chapter 2 and 4



Grades 7-8

Assessments

Do now

Written assessments

Teacher observation


C. Modeling




Larson Algebra 2

Sections 7.1 and 7.2








- Students solve real world

problems to understand finite

differences/functions using

physical representations

- Students investigate cost of

living growth exponentially

Do now

Written assessments

Teacher observation


274






Grades 7-8

Assessments


C. Modeling




3. Use functions to model real-world

phenomena and solve problems that involve

varying quantities: Linear, quadratic,

exponential, periodic (sine, cosine), and step

functions (e.g. price of mailing a first class

letter over the past 200 years), direct and

inverse variation, absolute value, expressions,

equations and inequalities, same function can

model variety of phenomena, growth/decay

and change in the natural world, application

in mathematics, biology, and economics

(including compound interest).

4. Analyze and describe how a change in an

independent variable leads to change in a

dependent one.

Larson Algebra 2

Chapters 1 - 14



- Cornering the Market

investigation: students simulate

what happens when a popular

new product enters the Market

- Students investigate the

breaking point of spaghetti

- Students use recursion to

explore loan balances and

payment opt

Cooperative learning activities

using the graphing calculator

Do now

Written assessments

Teacher observation

Do now

Teacher observation


275






Grades 7-8

Assessments


C. Modeling




5. Convert recursive formulas to linear or

exponential functions (e.g. Tower of Hanoi

and doubling).

Larson Algebra 2

Pages 826-827

Investigation on the Tower of

Hanoi.

Do now

Written assessments

Teacher observation


276



D. Procedures



Grades 7-8

Do now

Written assessments

Teacher observation

3. Select and use appropriate methods to solve

equations and inequalities: Linear equations -

algebraically, Quadratic equations - factoring

(when the coefficient of x2 is 1) and using the

quadratic formula, All types of equations

using graphing, computer, and graphing

calculator techniques.






Resources

1. Solve simple linear inequalities. Teacher created materials

Various workbooks


- Investigations through graphing

Do now

Written assessments

Teacher observation

Larson Algebra 2

Sections 1.3, 1.6, 4.3, 4.4,

4.5 and 4.8


Various workbooks


- Investigations using the

graphing calculator

- Geometer's Sketchpad activity

Do now

Written assessments

Teacher observation

2. Evaluate and simplify expressions, add and

subtract polynomials, multiply a polynomial

by a monomial or binomial, divide a

polynomial by a monomial.

Larson Algebra 2

Chapter 5

Various workbooks


using the algebra tiles

- Investigations using the column

method and area method


277



D. Procedures



Grades 7-8






Resources

4. Judge the meaning, utility and

reasonableness of the results of symbol

manipulations, including those carried out by

technology.


Various workbooks

Investigations using the graphing

calculator

Do now

Written assessments

Teacher observation


- Cooperative learning activites

Do now

Written assessments

Teacher observation

5. Students perform arithmetic operations on

rational expressions.


Various workbooks


278



ResourcesKnowledge/Skills/Understanding




conclusions?



Grades 7-8


Mathematics











central tendency.

Assessments

Larson Algebra 2

Chapter 11

Do now

Written assessments

Teacher observation

Projects


- Students investigate pulse rates

and practice making box plots

- Students analyze data about

backpacks and determine how

much the typical backpack

weighs

- Graphing calculator

investigations


279



ResourcesKnowledge/Skills/Understanding




conclusions?



Grades 7-8


Mathematics

AssessmentsLearning Experiences

Larson Algebra 2

Section 11.4

Students investigate and extend

"The Wave" activity

Do now

Written assessments

Teacher observation


using the graphing calculator

5. Evaluate the use of data in real world

context.

Larson Algebra 2

Chapter 11

Various workbooks

Cooperative learning activities Do now

Written assessments

Teacher observation

4. Use surveys and sampling techniques to

generate data and draw conclusions about

large groups.






Larson Algebra 2

Section 2.6

Do now

Written assessments

Teacher observation

Investigations Do now

Written assessments

Teacher observation

Teacher created problems based on

real world situations


280


Various Workbooks



Grades 7-8






Mathematics


conclusions?


Do now

Written assessments

Teacher observation




and decimals.

Various Workbooks "Dieing for a Four"

investigation: students conduct

and analyze playing a board

game in which they must roll a 4

on the die before taking the first

turn

Do now

Written assessments

Teacher observation


events.


281




Grades 7-8





Mathematics


conclusions?




Larson Algebra 2

Chapter 10







Larson Algebra 2

Chapter 10


Students use the multiplication

rule for independent events and

calculate the theoretical

probability of rolling a sum of 6

with 2 dice

Do now

Written assessments

Teacher observation







Do now

Written assessments

Teacher observation


282




Grades 7-8





Mathematics


conclusions?




Do now

Written assessments

Teacher observation



probabilities.


Various workbooks



expected value.


Do now

Written assessments

Teacher observation

Class discussion


used to solve real life problems

Students will play a variety of

probability games


283




Grades 7-8



Mathematics




conclusions?







3 class officers from a 23 student class);

Factorial notation; Concept of combinations

(e.g., number of possible delegations of 3 out

of 23 students).

Larson Algebra 2

Chapter 10

Various Workbooks

- Investigation when students

explore the placements of jigsaw

puzzle pieces to determine

placement possibilities

-Students determine the number of

handshakes in a social setting

- Students analyze a simulated

lottery game to determine

probability of winn

Do Now

Written assessments

Teacher observation


284




Grades 7-8



Mathematics




conclusions?


Students use Venn diagrams to

solve problems

Do Now

Written assessments

Teacher observation



different contexts.

Various workbooks



Written assessments

Teacher observation



Various workbooks



285




Grades 7-8



Mathematics











Limitations of computers.


Various workbooks

Cooperative learning activities Do now

Written assessments

Teacher observation


conclusions?



286




Grades 7-8


mathematics?








Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all

investigations, activities and

class discussions

Do now

Written assessments

Teacher observation

Resources






Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




problems.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


287




Grades 7-8


mathematics?







difficulty.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


288



mathematics?





Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Larson Algebra 2

Chapters 1 - 14

Various workbooks









Grades 7-8

Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources



Larson Algebra 2

Chapters 1 - 14

Various workbooks



289



mathematics?

Learning Experiences AssessmentsKnowledge/Skills/Understanding







Grades 7-8

Resources

Ongoing through all


class discussions

Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks



290




Grades 7-8




Resources

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions


mathematics?


C. Connections





Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation





Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


291




Grades 7-8




Resources


mathematics?


C. Connections


Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


292




Grades 7-8




Resources

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions


mathematics?


D. Reasoning



solutions.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


293




Grades 7-8




Resources


mathematics?


D. Reasoning


Do now

Written assessments

Teacher observation




Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions





Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation



valid.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


294




Grades 7-8


mathematics?













Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

Resources



problems.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


295




Grades 7-8


mathematics?








phenomena.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation


296




Grades 7-8




Resources

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions


mathematics?


F. Technology




Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation




Do now

Written assessments

Teacher observation



and their graphs.

Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

4.5.F 8th Grade Advanced Algebra

297




Grades 7-8




Resources


mathematics?


F. Technology


Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation



Larson Algebra 2

Chapters 1 - 14

Various workbooks


Ongoing through all


class discussions

Do now

Written assessments

Teacher observation

4.5.F 8th Grade Advanced Algebra

298

Theresa Kane McKell 2003Carson-Dellosa Publishing

Company, Inc.

Geometry

Algebra

Sara Freeman

Dolciani, Brown, and Cole

2004

1986

Milliken

Houghton Mifflin

8th Grade Advanced Algebra

Resources



Grades 7-8


Algebra 2Ron Larson, Laurie Boswell,



Publishing Company2011

Author(s)

Clever CountingLappan, Fey, Fitzgerald, Friel, and

PhillipsPrentice Hall 2002

GeometryMary Lee Vivian, Tammy Bohn-

Voepel, and Margaret ThomasMcGraw Hill 2003

Nasco 2002



Jossey-Bass 2003

Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999

Dale Seymour 1987

Geo Joke Worksheets Christine A. Koers

Algebra Warm-Ups Scott McFadden

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla

Skills for Success - Algebra

8th Grade Advanced Algebra Resources

299


Resources



Grades 7-8


Dolciani, Sorgenfrey, Brown, and

Kane1986Houghton Mifflin

McGraw Hill 2003

AlgebraMary Lee Vivian and Margaret

Thomas

Algebra and Trigonometry

GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000

Algebra Puzzlers Theresa Kane McKell Frank Schaffer Publications 1998

Algebra IIChad Helgeson and Margaret

Thomas


McGraw Hill 2003


Navigating through ProbabilityShaughnessy, Barrett, Billstein,

Kranendonk, and Peck


Teachers of Mathematics, Inc.2004

80 Activities to Make Basic Algebra Easier Robert S. Graflund Walch Publishing 2001



Preparing for the New Jersey GEPA - Grade 8 David J. Glatzer and Joyce Glatzer Amsco School Publications, Inc. 2005


300


Resources



Grades 7-8


Kuta Software - Infinite Algebra 1, Infinite Algebra 2 Kuta Software LLC 2010, 2011


Navigating through Data AnalysisBurrill, Franklin, Godbold, and

Young



Navigating through GeometryDay, Kelley, Krussel, Lott, and

Hirstein






301

-----

12

Polynomials

5 6

2 6


Pacing Guide

Larson Algebra 2



Grades 7-8


Linear Equations

1 8


3 5


a Line

Exponents and Exponential Models

5, 6, 7 8


-----

Quadratics

4

8th Grade Advanced Algebra Pacing Guide

302


Pacing Guide

Larson Algebra 2



Grades 7-8



----- -----

Probability and Discrete Math

10, 11 7

Rational Expressions

8 11

Radical Expressions

6 8

8th Grade Advanced Algebra Pacing Guide

303

Algebra 2 Curriculum

304








Grades 7-8


A. Number Sense

AssessmentsKnowledge/Skills/Understanding Learning Experiences

Quiz 1.1-1.2, Unit Test 11. Extend understanding of the number

system to all real numbers.

Students graph real numbers on a

number line and problem solve

using algebraic models

Larson Algebra 2

Section 1.1

Resources

Quiz 1.1-1.2, Unit Test 1


Larson Algebra 2

Section 1.1

2. Compare and order rational and irrational

numbers.

Written classwork

Students use linear equations to

solve real life problems such as

how much fuel a car consumes

over various distances

3. Develop conjectures and informal proofs of

properties of number systems and sets of

numbers.

Larson Algebra 2

Chapter 1

4.1.A 8th Grade Algebra 2

305




Students use exponents to solve

finding the per capita GDP of

Denmark


Ongoing throughout

investigations

1. Extend understanding and use of operations

to real numbers and algebraic procedures.



Grades 7-8

4. Understand and apply the laws of exponents

to simplify expressions involving numbers

raised to powers.

Larson Algebra 2

Section 5.1

Quiz 6.1-6.3, Unit Test 6,


Direct instruction

- Students use a graphing

calculator to perform matrix

operations


- Students use matrices to find

the number of calories burned

Resources

Quiz 1.1-1.2, Unit Test 1Larson Algebra 2

Chapter 1

Quiz 6.1-6.3, Quiz 6.4-6.6,

Unit Test 6, Quiz 7.1-7.2,


2. Develop, apply, and explain methods for

solving problems involving rational and

negative exponents.

3. Perform operations on matrices.

· Addition and subtraction

· Scalar multiplication

Larson Algebra 2

Section 3.5, 3.6



Knowledge/Skills/Understanding Assessments




Larson Algebra 2

Chapter 6

4.1.B 8th Grade Algebra 2

306






Resources

3. Recognize the limitations of estimation,


estimation, and determine whether the error

is within tolerance limits.

Larson Algebra 2

Section 2.6

Students employ the skill of

estimation in prediction of

outcomes when solving real-life

mathematical problems

Teacher observation

Student solutions to practice

exercises





Grades 7-8

C. Estimation

4.1.C 8th Grade Algebra 2

307




1. Draw perspective views of 3D objects on

isometric dot paper, given 2D representations

(e.g. nets or projective views).

Teacher created resources Students write a system of linear

equations to model real-life

situations

Teacher observation


exercises



Grades 7-8






and physical world?




308




Learning Experiences Assessments

b. Outcome of extending iterative process

indefinitely

Larson Algebra 2

Chapter 12

Students use real-life problem

solving (e.g. finding the balance

of an account; using an

exponential model to study and

analyze endangered species)

Teacher observation

Whole class discussions of

examples


problems

1. Generate and analyze iterative geometric

patterns.

a. Fractals (e.g. Sierpinski's Triangle)

Larson Algebra 2

Chapter 12

Students apply complex numbers

to fractal geometry

Teacher observation


exercises



Grades 7-8

Resources





and physical world?



309




Larson Algebra 2

Chapter 3

Students use linear systems to

solve the real-life problem of

choosing the least expensive

long distance phone system

b. Midpoint and slope of a line segment Larson Algebra 2

Chapter 9

Students use the distance and

midpoint formulas in finding the

diameter of a broken dish




d. Lines with the same slope are parallel Larson Algebra 2

Chapters 2 and 3

Students examine systems with

many or no solutions



c. Finding the intersection of two lines

AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources

1. Use coordinates in geometry to represent

and verify properties of lines.

a. Distance between two points

Larson Algebra 2

Chapter 9

Students derive the distance

formula



and physical world?



Grades 7-8





310




AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources


and physical world?



Grades 7-8




e. Lines that are perpendicular have slopes

whose product is -1

Larson Algebra 2

Chapter 2

Students examine and analyze

real-life examples of slope (e.g.

slope as a geometrical use; slope

as a rate of change)



311








Resources

Appropriate use throughout

lessons

Do Now

Written Assessments

Teacher Observation




miles).

Larson Algebra 2

Chapters 1 - 14


lessons

Do Now

Written Assessments

Teacher Observation

Larson Algebra 2

Chapters 1 - 14


lessons


and physical world?



Grades 7-8





Do Now

Written Assessments

Teacher Observation


Larson Algebra 2

Chapters 1 - 14




equals 12’1”).

4.2.D 8th Grade Algebra 2

312




Resources


and physical world?



Grades 7-8








5/7 = 0.714285714285...

= 0.714285

Larson Algebra 2

Chapters 1 - 14




situation.

Larson Algebra 2

Chapters 1 - 14



Larson Algebra 2

Chapters 1 - 14

Do Now

Written Assessments

Teacher Observation


lessons

Do Now

Written Assessments

Teacher Observation


lessons

Do Now

Written Assessments

Teacher Observation


lessons


313




Resources


and physical world?



Grades 7-8





Do Now

Written Assessments

Teacher Observation



two.

Larson Algebra 2

Chapters 1 - 14


lessons


314





b. Estimation of area, perimeter, volume, and

surface area.

Larson Algebra 2

Chapters 1 and 5

Cooperative learning Teacher observation

Student solutions to class

exercises and homework

problems


and physical world?

1. Use a variety of strategies to determine

perimeter and area of plane figures and

surface area and volume of 3D figures.

a. Finding which shape has minimal (or

maximal) area, perimeter, volume, or surface

area under given conditions using graphing

calculators, dynamic geometric software,

and/or spreadsheets.

Larson Algebra 2

Chapter 5

Graphing calculator

Students use the graph of

polynomial functions to solve

real-life problems such as

maximizing the volume of a box

Teacher observation


exercises and homework

problems





Grades 7-8


4.2.E 8th Grade Algebra 2

315


c. Sums of finite and infinite geometric series.

b. Sums of finite arithmetic series. Larson Algebra 2

Chapter 12



Class discussion of calculator

activity



Teacher created materials Investigation Cooperative activity

Class discussion

Do Nows

Teacher observation


exercises

Larson Algebra 2

Chapter 12


Students evaluate and write

recursive rules for sequences.

Conclusions drawn from

activity

Student written explanations



Grades 7-8

Resources


Assessments

A. Patterns


1. Use models and algebraic formulas to

represent and analyze sequences and series.

a. Explicit formulas for nth terms.

Larson Algebra 2

Chapter 12

Students evaluate and write

recursive rules for sequences


2. Develop an informal notion of limit.


316








Grades 7-8

Resources


Assessments

A. Patterns



Cooperative work/graphic

organizers

Unit Test 11

3. Use inductive reasoning to form

generalizations.

Larson Algebra 2

Chapter 12

Students use mathematical

induction to prove statements

about all positive integers


317


1. Understand relations and functions and

select, convert flexibility among, and use

various representations for them, including

equations or inequalities, tables and graphs.

Larson Algebra 2

Chapters 1 - 14

- Students use piecewise

functions to model real-life

quantities

- Students graph and solve

systems of linear equations and

linear inequalities

- Students write quadratic

functions given characteristics of

their graphs

- Students analyze the graph of a

polynomial function

- Students graph and write

equations of circles


equations of ellipses


equations of hyperbolas

Unit Test 1


Quiz 3.1-3.2, Quiz 3.4, Unit

Test 3

Quiz 5.1-5.3,Unit Test 5



Quiz 10.1-10.3, Quiz 10.4-

10.5, Unit Test 10





Resources





Grades 7-8



318






Resources





Grades 7-8


b. Domain and range Larson Algebra 2

Chapters 2, 4, 5, 6, 7, 8, 9

Students use a graphing

calculator to find and draw

statistical graphs (e.g. NBA foul

shooting percentages).

Do Now

Teacher observation

Classwork activities

2. Analyze and explain the general properties

and behavior of functions of one variable,

using appropriate graphing technologies.

a. Slope of a line or curve

Larson Algebra 2

Chapter 2

Students find slopes of lines and

classify parallel and

perpendicular lines

Teacher observation


problems


319






Resources





Grades 7-8


e. Maximum/minimum Larson Algebra 2

Chapter 4

- Students use technology to find

quadratic models

- Students examine and analyze

turning points corresponding to

local minimum and maximum

values

- Students use rational functions

to find a local minimum

Do Now

Teacher observation


exercises

Students use the graphing

calculator to find the real

solution to equations (e.g.

quadratic equations, polynomial

equations, an equation with an

extraneous solution)

Teacher observation

Solutions to classwork and

homework exercises

d. Continuity Larson Algebra 2

Chapter 2

Direct instruction Teacher observation

Solutions to classwork and

homework exercises

c. Intercepts Graphing calculator


320






Resources





Grades 7-8


g. Intersecting points as solutions of systems of

equations

Larson Algebra 2

Chapter 3

Graphing calculator Teacher observation

Student graphs

f. Estimating roots of equations. Larson Algebra 2

Chapters 2, 4, 8

- Students use technology to

approximate zeros

- Students find the rational

zeroes of a polynomial function


i. Rate of change Larson Algebra 2

Chapter 2


calculator to graph equations of

the form y=f(x)

Teacher observation

Student graphs

Students find and use the

discriminant of quadratic

equations

Student oral and written

solutions

3. Understand and perform transformations

on commonly used functions.

· Effects on linear and quadratic graphs of

parameter changes in equations

Larson Algebra 2

Chapters 2 and 4


321






Resources





Grades 7-8


c. Increasing/decreasing on an interval Larson Algebra 2

Chapters 5 and 7

Graphing calculator activity Do Nows

Teacher observation

Students solutions to practice

exercises

b. Symmetry Larson Algebra 2

Chapter 9

Direct instruction Teacher observation


examples

4. Understand and compare the properties of

classes of functions, including exponential,

polynomial, rational, and trigonometric

functions.

a. Linear vs. non-linear

Larson Algebra 2

Chapters 2, 4, 5, 6, 14

- Students evaluate/graph

polynomial functions

- Students graph and use

exponential growth functions

- Students evaluate and graph

logistic growth functions


equations of parabolas





322


Resources

- Exploration


Unit Test 2

Quiz 8.1-8.3

Unit Test 8

Assessments

- Students write linear equations

- Students write direct variation

equations by analyzing real-life

mathematical models

Larson Algebra 2

Chapters 1 and 8

c. Absolute value Larson Algebra 2

Chapters 1 and 2





b. Direct and inverse variation

1. Use functions to model real-world

phenomena and solve problems that involve

varying quantities.

a. Linear, quadratic, exponential, periodic

(sine and cosine), and step functions (e.g.,

price of mailing a first class letter over the

past 200 years)

Larson Algebra 2

Chapters 2, 4, 7, 14

Graphing calculator



Grades 7-8


C. Modeling

Quiz 2.4-2.5

Unit Test 2

Quiz 9.1-9.3

Unit Test 9

Students use absolute value in

real-life situations (e.g. Path of a

golf ball; graph functions of the

path of sunlight)


Unit Test 1

Unit Test 2


323


Resources AssessmentsKnowledge/Skills/Understanding Learning Experiences






Grades 7-8


C. Modeling


- Exploration


Do Nows

Class discussion of examples

and exploration

Teacher observation

Unit Test 1, Unit Test 2

Quiz 3.3-3.4

Unit Test 3, Unit Test 5

e. Same function can model a variety of

phenomena

Larson Algebra 2

Chapters 2 and 4

f. Growth/decay and change in the natural

world

Larson Algebra 2

Chapter 7

Graphing Calculator

d. Expressions, equations and inequalities Larson Algebra 2

Chapter 1

- Exploration


Students examine and analyze

models of exponential decay.

(e.g. Descending value of an

automobile.) Students analyze

models with power functions

Quiz 8.1-8.3

Unit Test 8


324


Resources AssessmentsKnowledge/Skills/Understanding Learning Experiences






Grades 7-8


C. Modeling


Teacher observation

Oral and written explanations

Larson Algebra 2

Chapter 1

Students evaluate functions in

real-life models (E.g. Domain

and range of the Piccard/Jones

balloon flight; Boston Marathon

finishers as related to age;

domain and range examining cap

sizes)

2. Analyze and describe how a change in an

independent variable leads to change in a

dependent one.

g. Applications in mathematics, biology, and

economics (including compound interest)

Larson Algebra 2

Chapters 1 - 14

Students solve real-life models

mathematically (e.g. Number of

households owning a VCR; US

GDP and logistic growth; focal

lengths)

Teacher observation

Student written work and

solutions to examples


325


1. Evaluate and simplify expressions.

a. Add and subtract polynomials

Larson Algebra 2

Chapter 5

Students use polynomials in real-

life situations (E.g. Finding net

farm income; finding total

revenue from the sale of

softbound books; ratio of heat

release to size of a long-distance

runner; value of gold mined in a

year)

Quiz 6.1-6.3

Unit Test 6






Resources




Grades 7-8

D. Procedures

c. Divide a polynomial by a monomial Larson Algebra 2

Chapter 8

Direct instruction Quiz 9.4-9.6

Unit Test 9

b. Multiply a polynomial by a monomial or

binomial

Larson Algebra 2

Chapter 5

Direct instruction Quiz 5.1-5.3

Unit Test 5

Quiz 6.1-6.3

Unit Test 6


326







Resources




Grades 7-8

D. Procedures

Quiz 1.3-1.5

Unit Test 1

Quiz 3.1-3.2

Unit Test 3

c. All types of equations using graphing,

computer, and graphing calculator techniques

Larson Algebra 2

Chapters 1 - 14

Graphing calculator

2. Select and use appropriate methods to solve

equations and inequalities.

a. Linear equations - algebraically

Larson Algebra 2

Chapter 1

Direct instruction


- Exploration



Quiz 5.1-5.3, Quiz 5.4-5.6,

Unit Test 5



Quiz 10.1-10.3, Quiz 10.4-

10.5, Unit Test 10

b. Quadratic equations - factoring (when the

coefficient of x^2 is 1) and using the quadratic

formula

Larson Algebra 2

Chapter 4

Students factor with: special

patterns; monomials first;

finding zeros of a quadratic

function; solving quadratic

inequalities.

Quiz 5.1-5.3

Quiz 5.4-5.6

Unit Test 5


327







Resources




Grades 7-8

D. Procedures

3. Judge the meaning, utility, and

reasonableness of the results of symbol

manipulations, including those carried out by

technology.

Larson Algebra 2

Chapters 1 - 14

Incorporated in all real-life

models

Teacher observation



328




2. Analyze data using technology, and use

statistical terminology to describe conclusions.

a. Measures of dispersion: variance, standard

deviation, outliers

Larson Algebra 2

Chapter 11

Graphing calculator


calculator to find statistics and

draw statistical graphs (e.g. The

number of calories in a

sandwich)

Teacher observation

Discussion of exploration


conclusions?



b. Correlation coefficient

Learning Experiences Assessments

1.Estimate or determine lines of best fit (or

curves of best fit if appropriate) with

technology, and use them to interpolate within

the range of data.

Larson Algebra 2

Chapters 2 and 4

Exploration

Larson Algebra 2

Chapter 2

Direct Instruction Quiz 2.4-2.5

Unit Test 2


Mathematics



Grades 7-8

Teacher observation


Resources


329





conclusions?




Mathematics



Grades 7-8

Resources

c. Normal distribution (e.g., approximately

95% of the sample lies between two standard

deviations on either side of the mean)

Larson Algebra 2

Chapter 11

Exploration Teacher observation



330


Teacher observation



conclusions?


Students use area to find

probability

Unit 12 Tests



Grades 7-8


Mathematics



B. Probability

2. Use concepts and formulas of area to

calculate geometric probabilities.



and computers) and theoretical models, and

solve problems using these models.

Various workbooks Cooperative learning

Larson Algebra 2

Chapter 10


1. Calculate the expected value of a

probability based game, given the

probabilities and payoffs of the various

outcomes, and determine whether the game is

fair.

Larson Algebra 2

Chapter 10

Direct instruction Unit 12 Tests


331



conclusions?




Grades 7-8


Mathematics



B. Probability


Students explore randomly

selecting two cards from a

standard 52 count deck

Unit 12 Tests

Exploration Unit 12 Tests

Unit 12 TestsExploration

Unit 12 TestsStudents use two six-sided dice

to find the probability of a given

event

4. Determine probabilities in complex

situations.

a. Conditional events

Larson Algebra 2

Chapter 10



probabilities.

Larson Algebra 2

Chapter 10

c. Dependent and independent events

b. Complementary events Larson Algebra 2

Chapter 10

Larson Algebra 2

Chapter 10


332



conclusions?




Grades 7-8


Mathematics



B. Probability


Unit 12 TestsStudents use length (video

cassette recording-probability of

over-recording)

6. Understand and use the "law of numbers"

(that experimental results tend to approach

theoretical probabilities after a large number

of trials).

Larson Algebra 2

Chapter 10


333



2. Apply the multiplication rule of counting in

complex situations, recognize the difference

between situations with replacement and

without replacement, and recognize the

difference between ordered and unordered

counting situations.

Larson Algebra 2

Chapter 10

Students use permutations to

count the number of ways an

event happens

Unit 12 Test

3. Justify solutions to counting problems. Larson Algebra 2

Chapter 10

Real world problem solving Unit 12 Test


conclusions?


1. Calculate combinations with replacement

and without replacement.

Larson Algebra 2

Chapter 10

Direct instruction Unit 12 Test



Grades 7-8



Mathematics




334




conclusions?




Grades 7-8



Mathematics



Students use the binomial

theorem to discover the

relationship between Pascal's

triangle and the coefficients of a

binomial expansion

Unit 12 Test4. Recognize and explain relationships

involving combinations and Pascal's Triangle,

and apply those methods to situations

involving probability.

Larson Algebra 2

Chapter 10


335



thinking to represent and solve practical

problems.

· Circuits that include every edge in a graph

· Circuits that include every vertex in a graph

Various workbooks - Exploration


Teacher made tests


conclusions?




Grades 7-8



Mathematics




- Exploration


Included in probability2. Explore strategies for making fair decisions.

a. Combining individual preferences into a

group decision (e.g., determining winner of a

election or selection process)

Various workbooks


336



conclusions?




Grades 7-8



Mathematics




b. Determining how many Student Council

representatives each class gets when the

classes have unequal sizes (apportionment)

Teacher created resources Exploration Do Now


337


A. Problem Solving

Teacher observation

Student written explanations

Unit Test 3

Quiz 5.5-5.6

Unit Test 5

Larson Algebra 2

Chapters 1 - 14

Incorporated in all mathematical

content


and in other contexts.

a. Open-ended problems

Larson Algebra 2

Chapters 1 - 14


content

b. Non-routine problems Larson Algebra 2

Chapters 1 - 14


content

c. Problems with multiple solutions



Assessments



Larson Algebra 2

Chapters 1 - 14


content.

Teacher observation


ResourcesKnowledge/Skills/Understanding Learning Experiences





Grades 7-8


mathematics?




338


A. Problem Solving



AssessmentsResourcesKnowledge/Skills/Understanding Learning Experiences



Grades 7-8


mathematics?




difficulty.

Larson Algebra 2

Chapters 1 - 14


content

Teacher observation


exercises



Larson Algebra 2

Chapters 1 - 14


content

Continual student to student

feedback

Teacher to student feedback

Student self reflection




problems.

Larson Algebra 2

Chapters 1 - 14


content.

Students use of problem

solving strategies in oral and

written work

Larson Algebra 2

Chapters 1 - 14

Quiz 2.1-2.3, Quiz 2.4-2.5,

Unit Test 2, Quiz 3.1-3.2,

Unit Test 3, Unit Test 4, Quiz

5.4-5.6, Unit Test 5


content

d. Problems that can be solved in several ways


339




Larson Algebra 2

Chapters 1 - 14


content

Student explanation and

mathematical reasoning in

written work

B. Communication






mathematics?


Student to student oral and

written work

Teacher observation




Larson Algebra 2

Chapters 1 - 14


content

Clarity of mathematical logic

in student oral and written

work

Teacher observation


mathematical thinking.

a. Reading and writing

Larson Algebra 2

Chapters 1 - 14

Teacher observation based on

whole class and small group

discussions



Grades 7-8

b. Discussion, listening, and questioning Larson Algebra 2

Chapters 1 - 14


content


content




340


B. Communication






mathematics?




Grades 7-8





Larson Algebra 2

Chapters 1 - 14


content

Student use of mathematical

language in oral and written

work

Teacher observation


341


Student written and oral work

Assessments



numbers, algebra, and geometry).



Larson Algebra 2

Chapters 1 - 14

Integrated throughout problem

solving examples

Teacher observation


explanations

Larson Algebra 2

Chapters 1 - 14



Grades 7-8





Larson Algebra 2

Chapters 1 - 14


solving examples


C. Connections

Do Nows

Teacher observation



solving examples

Resources


mathematics?






342


Assessments



Grades 7-8


C. Connections

Resources


mathematics?





Teacher observation

Class discussions




Larson Algebra 2

Chapters 1 - 14


solving examples

Teacher observation


explanations



Larson Algebra 2

Chapters 1 - 14


solving examples



Larson Algebra 2

Chapters 1 - 14

Art, music, economics, etc.,

history incorporated throughout

mathematical models, examples

and problem solving

Teacher observation; Student

use of abstract math models

to solve "science," "social

studies," "art" and "music"

models


343


Teacher observation; Oral

and written explanations

D. Reasoning



Larson Algebra 2

Chapters 1 - 14




Larson Algebra 2

Chapters 1 - 14


content


content





Larson Algebra 2

Chapters 1 - 14


content

Teacher observation; Student

oral and written work



solutions.

Larson Algebra 2

Chapters 1 - 14





Grades 7-8



mathematics?






content


344


D. Reasoning



Grades 7-8



mathematics?






content

Teacher observation

Student oral and written work



valid.

Larson Algebra 2

Chapter 1


content



Teacher observation

Student oral and written work

b. Verifying conjectures using informal

reasoning or proofs

Larson Algebra 2

Chapter 6


content


conjectures.

a. Counterexamples as a means of disproving

conjectures

Larson Algebra 2

Chapters 8 and 9


345


Assessments


content

Teacher observation


exercises

Teacher observation


exercises



Grades 7-8



mathematics?





Larson Algebra 2

Chapters 1 - 14


content

Teacher observation


exercises

Larson Algebra 2

Chapters 1 - 14

E. Representations

Larson Algebra 2

Chapters 1 - 14


content


record, and communicate mathematical ideas.

a. Concrete representations (e.g., base-ten

blocks or algebra tiles)

c. Symbolic representations (e.g., a formula)

b. Pictorial representations (e.g., diagrams,

charts, or tables)


346


Assessments



Grades 7-8



mathematics?





E. Representations

Teacher observation


exercises



phenomena.

Larson Algebra 2

Chapters 1 - 14


content

Teacher observation


exercises

Larson Algebra 2

Chapters 1 - 14



problems.

Larson Algebra 2

Chapters 1 - 14


content

Teacher observation


exercises


content

d. Graphical representations (e.g., a line

graph)


347





Larson Algebra 2

Chapters 5 and 10


content

Do Now

Written Assessments

Teacher Observation



and their graphs.

Larson Algebra 2

Chapter 5


content

Do Now

Written Assessments

Teacher Observation




Larson Algebra 2

Chapters 1 - 14


content

Do Now

Written Assessments

Teacher Observation

Resources



Grades 7-8


mathematics?





F. Technology

4.5.F 8th Grade Algebra 2

348





Grades 7-8


mathematics?





F. Technology



Larson Algebra 2

Chapters 1 - 14


content

Do Now

Written Assessments

Teacher Observation



Larson Algebra 2

Chapters 1 - 14


content

Do Now

Written Assessments

Teacher Observation

4.5.F 8th Grade Algebra 2

349

Resources


Company, Inc.2003Skills for Success - Algebra Theresa Kane McKell

8th Grade Algebra 2



Grades 7-8

Larson Algebra 2Ron Larson, Laurie Boswell,



Publishing Company2011


GeometryMary Lee Vivian, Tammy Bohn-

Voepel, and Margaret ThomasMcGraw Hill 2003

Clever CountingLappan, Fey, Fitzgerald, Friel,

and PhillipsPrentice Hall 2002



Geo Joke Worksheets Christine A. Koers Nasco 2002

Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999

Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003

Algebra Warm-Ups Scott McFadden Dale Seymour 1987

Algebra Dolciani, Brown, and Cole Houghton Mifflin 1986

Geometry Sara Freeman Milliken 2004

8th Grade Algebra 2 Resources

350

Resources

8th Grade Algebra 2



Grades 7-8


Steck-Vaughn/Berrent Company 2000




Navigating through ProbabilityShaughnessy, Barrett, Billstein,

Kranendonk, and Peck




GEPA Success in Mathematics - Level H Richard Crowe



GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000

Algebra IIChad Helgeson and Margaret


Houghton Mifflin


McGraw Hill

1986

1998

2003

Algebra and Trigonometry

Algebra Puzzlers

Algebra

Dolciani, Sorgenfrey, Brown,

and Kane

Theresa Kane McKell

Mary Lee Vivian and Margaret

Thomas


351

Resources

8th Grade Algebra 2



Grades 7-8


Kuta Software - Infinte Algebra 1, Infinite

Algebra 2Kuta Software LLC 2010, 2011

Algebra 2Barbara Sandall and Melfried

OlsonMark Twain Media 2005

Algebra 2 Sara Freeman Milliken 2002

Joke Worksheets for Algebra 2 and Precalculus Christine A. Koers NASCO 2002

Algebra 2 Word Problems Anita Harnadek The Critical Thinking Company 2001



Navigating through Data AnalysisBurrill, Franklin, Godbold, and

Young



Navigating through GeometryDay, Kelley, Krussel, Lott, and

Hirstein




352

3


10

Linear Equations and Functions

Equations and Inequalities1 6


5


4

Larson Algebra 2

Pacing Guide

Matrices



Grades 7-8

8th Grade Algebra 2

2 6

4

----- -----

Quadratic Functions5

9

Polynomials and Polynomial Function6 10

Powers, Roots, and Radicals7

8th Grade Algebra 2 Pacing Guide

353


Larson Algebra 2

Pacing Guide



Grades 7-8

8th Grade Algebra 2


----- -----

79

Quadratic Relations and Conic Sections10 8

Exponential and Logarithmic Functions8 9

Rational Equations and Functions

8th Grade Algebra 2 Pacing Guide

354

mathematics curriculum grades 7-8€¦ · mathematics curriculum grades 7-8 the following textbooks...

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