mathematics 7 accelerated curriculum guide · vocab – linear expression session 8 factoring...

MATHEMATICS 7

ACCELERATED

CURRICULUM

GUIDE: Mathematics 7 Accelerated

SPRING 2017

BELLMORE-MERRICK

CENTRAL HIGH SCHOOL DISTRICT

BOARD OF EDUCATION

2016-2017

Janet Goller, President

Nancy Kaplan, Ed.D., Vice President

Marion Blane Lisa Katz

JoAnn DeLauter Nina Lanci

Wendy Gargiulo Gina Piskin

CENTRAL ADMINISTRATION

John DeTommaso

Superintendent of Schools

Mara Bollettieri, Psy.D.

Deputy Superintendent

Kate Freeman

David Seinfeld

Assistant Superintendents

3

MATHEMATICS 7 ACCELERATED

CURRICULUM GUIDE:

Mathematics 7 Accelerated

Authored by:

Anna Aprilakis (Merrick Avenue Middle School)

Katie Zaikowski (Grand Avenue Middle School)

Project Administrator: David T. Gunder

District Chairperson - Mathematics

4

TABLE OF CONTENTS

UNIT PAGE NUMBERS

Introduction 5

Unit 1 - Integers 6

Unit 2 - Rational Numbers 7

Unit 3 - Expressions and Equations 8

Unit 4 - Inequalities 10

Unit 5 - Ratios and Proportions 11

Unit 6 - Percents 13

Unit 7 – Similarity and Scale

Drawings

15

Unit 8 – Circles and Area 16

Unit 9 – Surface Area/Volume 18

Unit 10 – Probability 20

Unit 11 – Statistics 21

Unit 12 – Angles and Triangles 22

Unit 13 – Square Roots and

Pythagorean Theorem

23

5

INTRODUCTION

This curriculum guide was created in response to the restructuring of the Mathematics 7

Accelerated Course. In order to create more opportunities for students in the subject of

mathematics, this course provides an alternate day block schedule which allows for additional

instruction in mathematics.

This curriculum guide contains a yearly overview of the course, divided by unit of study. The

course has been aligned to the Big Ideas textbook series and has sequenced out each unit,

allowing for additional days of instruction/remediation at the discretion of the teacher. Key

vocabulary terms are indicated for each unit in which to emphasize during instruction. With the

introduction of the blocked scheduling, units are divided into sessions rather than lessons as each

day will vary with a single or double period for students.

6

Unit 1 – Integers

Big Ideas Chapter 1

Sessions 1-2 Intro to Integers:

Vocab, Positive vs Negative, Integer Concepts, Absolute Value,

Comparing Integers (with and without a number line)

Vocab: rational, integer, absolute value, additive inverse

Sessions 3-4 Adding Integers

Vocab: additive inverse, commutative property

Sessions 5-6 Subtracting Integers

Session 7 Review

Session 8 Unit 1 Quiz

Sessions 9-10 Multiplying Integers

Including Exponents: ex -23 verse (-2)

3

Session 11 Dividing Integers

Session 12 Order of Operations

Session 13 Evaluating Expression (optional: see BI chapter 1, page 31, ex 3)

Session 14 Review

Session 15 Unit 1 Test

13 Sessions

1 Quiz

1 Test

5 extras

20 total

7

Unit 2 – Rational Numbers

Big Ideas Chapter 2

Sessions 1-2 Intro to Rationals:

Ordering Rationals (with and without a number line), Converting

Fractions to Decimals, Converting Decimals to Fractions

Vocab: rational number, terminating decimal, repeating decimal

Sessions 3-4 Adding Rationals

Including evaluating expressions with rationals (BI chapter 2, page 53,

ex 3)

Session 5 Review


Sessions 7-8 Subtracting Rationals

Including distance between (BI chapter 2, page 61, ex 3)

Sessions 9-10 Multiplying and Dividing Rationals

Vocab: Multiplicative Inverse

Session 11 Review


10 Sessions

1 Quiz

1 Test

3 Extras

15 total

8

Unit 3 – Expressions and Equations

Big Ideas Chapter 3

Session 1 Evaluating Algebraic Expressions (optional in Unit 1)

Session 2 Translating Algebraic Expressions

Sessions 3-5 Identifying Like Terms and Simplifying Algebraic Expressions

Vocab – simplest form, like terms, distributive property

Sessions 6-7 Adding and Subtracting Linear Expressions

Vocab – linear expression

Session 8 Factoring Algebraic Expressions

Vocab – greatest common factor, factoring

Session 9 Multiplying Expressions and Distributing

Vocab – distributive property

Session 10 Review


Sessions 12-13 One-Step Equations

Sessions 14-15 Two-Step Equations

Session 16 Multi-Step Equations – Combining Like Terms

Session 17 Multi-Step Equations – Distributive

Session 18 Multi-Step Equations – Variables on Both Sides

Session 19 Review


9

18 Sessions

1 Quiz

1 Test

3 Extras

----------------------------------------------

23 total

10

Unit 4 –Inequalities

Big Ideas Chapter 4

Session 1-2 Intro to Inequalities:

Writing an Inequality, Graphing an Inequality, Checking Solutions

Vocab- inequality, solution set, graph of an inequality

Sessions 3-5 Solving One-Step Inequalities


Session 7-8 Solving Two-Step Inequalities

Session 9 Solving Multi-Step Inequalities

Session 10 Review


9 Sessions

1 Quiz

1 Test

3 Extras

----------------------------------------------

14 total

11

Unit 5 – Ratios and Proportions

Big Ideas Chapter 5

Session 1 Simplifying Fractions and Finding Equivalent Fractions

Sessions 2-3 Ratios, Rates and Unit Rates:

Finding ratios and rates; finding a rate from a ratio table; finding a rate

from a graph; solving ratio problems

Vocab – ratio, rate, unit rate and complex fraction

Sessions 4-5 Proportions:

Determining if ratios forms a proportion; determine if two quantities form

a proportion; identify a proportional relationship

Vocab – proportion, proportional relationship, cross products

Sessions 6-7 Graphing Proportional Relationships:

Determine if two quantities are proportional; interpreting the graph of a

proportional relationship

Session 8 Review


Sessions 10-11 Writing and Solving Proportions

Sessions 12-13 Slope:

Finding slope of a line; interpreting slope

Vocab - slope

Sessions 14-15 Direct Variation:

Identifying direct variation; writing an equation to represent a line

Vocab – direct variation, constant of proportionality

Session 16 Review


12

15 Sessions

1 Quiz

1 Test

3 Extras

----------------------------------------

20 total

13

Unit 6 – Percent

Big Ideas Chapter 6

Sessions 1-2 Percent Conversions:

Percent to fraction; fraction to percent; percent to decimal; decimal to

percent; fraction to percent and decimal

Sessions 3-4 Comparing and Ordering Fractions, Decimals and Percents

Sessions 5-6 Percent Proportion:

Solving for percent, part and whole

Session 7-8 Percent Equation:

Solving for percent, part and whole

Session 9 Review


Session 11-12 Percent Increase and Decrease:

Vocab – percent change, percent increase, percent decrease, percent

error

Sessions 13-14 Discount and Markup

Vocab – discount, markup

Session 15 Commission and Gratuity

Vocab – commission, gratuity

Session 16-17 Simple Interest

Vocab – simple interest, principal

Session 18 Review


14

17 Sessions

1 Quiz

1 Test

3 Extras

---------------------------------------

22 total

15

Unit 7 – Similarity, Scale Drawings

Big Ideas Chapter 7

Session 1 Identifying Similar Figures

Similar Figures, Corresponding Angles, Corresponding Sides,

Proportion

Session 2 Perimeters and Areas of Similar Figures

Sessions 3-4 Finding Unknown Measures in Similar Figures

(Include word problems such as shadow problems)

Indirect Measurement

Sessions 5-6 Scale Drawings

Scale Drawing, Scale Model, Scale, Scale Factor

Study Tip: Scales are written so that the drawing distance comes first

in the ratio

Session 7 Review


7 Sessions

1 Test

3 Extras

----------------------

11 total

16

Unit 8 – Circles and Area

Big Ideas Chapter 8

Sessions 1-3 Parts Of The Circle,

Arc, Center, Chord, Circumference, Diameter, Radius, π

Circumference of a Circle

- include solving to a given place value and/or leaving answers in terms of

π

- include solving for the radius or diameter when given the circumference

Sessions 4-5 Area of A Circle

- include solving to a given place value and/or leaving answers in terms of

π

- include solving for the radius or diameter when given the area

Sessions 6-8 Applications of Circles

- include word problems, tire rotation questions (circumference)

- include questions when given circumference you have to find area or

when given area you have to find the circumference

- include problems such as when the radius is multiplied by a given factor

what happens to the circumference, area of the circle

Session 9 Unit 8 Quiz 1

Sessions 10-12 Vertical Angles, Supplementary Angles, Complementary Angles with

Algebra

Sessions 13-16 Parallel Lines Cut By A Transversal

Transversal, Interior Angles, Exterior Angles, Alternate Interior

Angles, Alternate Exterior Angles, Corresponding Angles, Same Side

Interior Angles

Session 16 Unit 8 Test review


17

15 Sessions

1 Quiz

1 Test

2 Extras

19 total

18

Unit 9 – Surface Area/Volume

Big Ideas Chapter 9

Session 1 Review of Perimeter and Area

Apothem

Sessions 2-3 3-Dimensional Figures

(Drawing 3-D figures, Vocabulary, Cross Sections)

Edge, Vertex, Face, Base, Net, Cross Section, Solid, Polyhedron,

Lateral Face

Session 4 Surface Area of Prisms

Session 5 (OPTIONAL) Surface Areas of Cylinders

(you may want to start with a brief review of the circle)

Session 6 (OPTIONAL) Surface Areas of Pyramids

Regular Pyramid, Slant Height

Session 7 (OPTIONAL) Surface Areas of Cones

Slant Height

Sessions 8-9 Mixed Review, Real Life Applications, Surface Areas of Composite

Solids

Composite Solid


Session 11 Volumes of Prisms

B = Area of the base

Session 12 Volumes of Cylinders

Session 13 (OPTIONAL) Volumes of Pyramids

Session 14 Volumes of Cones

Session 15 Volumes of Spheres

19

Sessions 16-17 Mixed Review, Real Life Applications, Volumes of Composite Solids

Session 18 Review


13 Sessions

4 Optional Sessions

1 Quiz

1 Test

2 Extras

----------------------

21 total (with optional topics) or 17 total

20

Unit 10 - Probability

Big Ideas Chapter 10

Session 1 Introduction To Probability

Experiment, Outcomes, Favorable Outcomes, Event, Impossible –

Unlikely - As Likely As Not – Likely - Certain), Theoretical

Probability, Experimental Probability, Fair Experiment, Independent

Events, Dependent Events

Session 2 Theoretical Probability

Session 3 Experimental Probability

Session 4 Making Predictions

Session 5 Applications and Activities


Session 7-8 Compound Probability

Independent Events, Dependent Events, Counting Principle

Session 9 Tree Diagrams, Sample Space

Session 10 Simulation (table of random digits)

Session 11 Review


10 Sessions

1 Quiz

1 Test

3 Extras

----------------------

15 Total

21

Unit 11 – Statistics


Session 1 Samples

Data, Survey, Population, Sample, Representative Sample, Random

Sample, Biased Sample

Session 2 Measures of Central Tendency

Mean, Median, Mode, Outlier

Session 3 Choosing The Best Measure

Session 4 Dot Plot and Range

Sessions 6-7 Measures of Variation, Box-and-Whisker Plot (Box Plot)

Range, Interquartile Range (IQR), 5 Number Summary – Minimum,

First Quartile, Median, Third Quartile, Maximum

Session 8 Mean Absolute Deviation (MAD)

Variability

Session 9 Compare Data Sets, Making Predictions

Session 10 Review


10 Sessions

1 Test

3 Extras

----------------------

14 Total

22

Unit 12 – Angles and Triangles


Sessions 1-2 Finding Measures of Angles When Parallel Lines Are Cut By A

Transversal (including algebra)

Sessions 3-4 Angles and Sides of A Triangle, Sum of Interior Angles of a Triangle

(Find missing angle measurements in a triangle including algebra)

Equiangular, Equilateral Triangle, Isosceles Triangle, Scalene

Triangle, Acute Triangle, Obtuse Triangle, Right Triangle

Sessions 5-6 Exterior Angle of A Triangle Theorem

(Find missing angle measurements with exterior angles of a triangle

including algebra)

Session 7 Review


7 Sessions

1 Test

3 Extras

----------------------

11 Total

23

Unit 13 – Square Roots and The Pythagorean Theorem


Sessions 1-2 Finding Square Roots

Sessions 3-4 Finding Cube roots

Sessions 5-6 Approximating Square roots


Sessions 8-9 Pythagorean Theorem, Converse of Pythagorean Theorem, Pythagorean

Triples

Hypotenuse, Legs

Sessions 10-11 Word Problems with Pythagorean Theorem

Session 12 3D Pythagorean Theorem

Session 13 Review


12 Sessions

1 Quiz

1 Test

3 Extras

----------------------

17 Total

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