7th grade advanced mathematics curriculum · 7th grade advanced mathematics curriculum. course...

7th Grade Advanced Mathematics Curriculum Course Description: In this class, instructional time will focus on four critical areas: (1) formulating and reasoning about expressions and equations, including modeling with a linear equations, and solving linear equations and inequalities; (2) deepening the understanding of a proportion and its relationship to an equation; (3) analyzing two- and three-dimensional space and figures using angle, similarity, and congruence; (4) comparing data distributions and populations, using probability models to draw informal inferences about populations. Scope and Sequence:

Time Frame Unit

30 Days (27 + 3 Buffer Days) The Number System

56 Days (53 + 3 Buffer Days) Expressions & Equations

23 Days (22 + 1 Buffer Day) Statistics and Probability

59 Days (54 + 5 Buffer Days) Geometry

Board Approved: July 23, 2015 2 | Page Revised: April, 2016 MLS Alignment: April, 2017

Curriculum Revision Tracking Changes made in April, 2016:

● Overall sequence of units was changed, with Geometry moving to Unit 4 and Statistics and Probability moving to Unit 3.

● Unit 1: o Pacing adjusted from 34 days to 30 days o Removed Topics 3 and 4

● Unit 2: o Pacing adjusted from 59 to 56 days o Combined Topic 4 with Topic 6 o Topic 8 contains combined lessons o Switched the order of Topics 10 and 11

● Unit 3: o Pacing adjusted from 55 to 59 days o Switched the order of Topics 23, 24, 25, and 26

● Unit 4: o Pacing adjusted from 24 to 23 days o Combined Topics 15 and 16


Unit 1: The Number System

Subject: Mathematics Grade: 7th Accelerated Name of Unit: Number System Length of Unit: 34 days (33 plus 1 buffer day) Overview of Unit: Students will develop an understanding of fractions, decimals, and percents as different representations of rational numbers. Students will extend their knowledge of addition, subtraction, multiplication, and division of rational numbers using properties for each. Through the application of these properties students will explain and interpret the rules for adding, subtracting, multiplying, and dividing integers. They will use arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will extend their mastery of properties of operations to develop an understanding of integer exponents and to work with numbers written in scientific notation. Priority Standards for unit:

● 7.NS.A.3 Solve problems involving four arithmetic operations with rational numbers. ● 7.RP.A.3 Solve problems involving ratios, rates, percentages and proportional

relationships. ● 7.EEI.B.3 Solve multi-step problems posed with rational numbers.

a. Convert between equivalent forms of the same number. b. Assess the reasonableness of answers using mental computation and estimation

strategies. Supporting Standards for unit:

● 8.NS.A.1 Explore the real numbers system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or

repeats. c. Convert decimals which repeat into fractions and fractions into repeating

decimals. d. Generate equivalent representations of rational numbers.

● 7.NS.A.1 Apply and extend previous understandings of numbers to add and subtract rational numbers.

a. Add and subtract rational numbers. b. Represent addition and subtraction on a horizontal or vertical number line. c. Describe situations and show that a number and its opposite have a sum of 0

(additive inverses). d. Understand subtraction of rational numbers as adding the additive inverse. e. Determine the distance between two rational numbers on the number line is the


absolute value of their difference. f. Interpret sums and differences of rational numbers.

● 7.NS.A.2 Apply and extend previous understandings of numbers to multiply and divide rational numbers.

a. Multiply and divide rational numbers. b. Determine that a number and its reciprocal have a product of 1 (multiplicative

inverse). c. Understand that every quotient of integers (with non-zero divisor) is a rational

number. d. Convert a rational number to a decimal. e. Understand that all rational numbers can be written as fractions or decimal

numbers that terminate or repeat. f. Interpret products and quotients of rational numbers by describing real-world

contexts. ● 8.NS.A.2 Estimate the value and compare the size of irrational numbers and approximate

their locations on a number line. ● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role

in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.

● ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.

Standard Unwrapped Concepts

(Students need to know)

Unwrapped Skills (Students need to be

able to do)

Bloom’s Taxonomy

Levels Webb's DOK

7.NS.A.3

problems involving the four arithmetic operations

with rational numbers. Solve Apply 3

7.RP.A.3

problems involving ratios, rates, percentages and

proportional relationships. Solve Apply 3

7.EE.B.3 multi-step problems posed

with rational numbers Solve Apply 3

7.EE.B.3 between equivalent forms

of the same number. Convert Understand 2

7.EE.B.3

the reasonableness of answers using mental

computation and estimation strategies Assess Evaluate 3


Essential Questions: 1. What types of problems can you solve by adding, subtracting, multiplying and dividing

the different types of rational numbers? 2. How can you use distance on the number line to describe situations? 3. How do you multiply and divide rational numbers? 4. What is an irrational number? 5. How do you compare irrational numbers? 6. What types of problems can be solved using proportional relationships and percents?

Enduring Understanding/Big Ideas:

1. You can solve real-world problems that involve adding, subtracting, multiplying and dividing all kinds of positive and negative fractions, integers, and decimals.

2. A number and its opposite have a sum of 0 and are called additive inverses. The distance between two numbers on the number line is the absolute value of their difference.

3. Rational numbers can be multiplied and divided by using properties of operations and the Distributive Property. Every quotient of integers with a nonzero divisor is a rational number.

4. An irrational number is a number that cannot be written as a quotient of two integers. 5. Irrational numbers can be compared using approximations and locations on the number

line. 6. You can use proportional relationships and percents to solve problems including simple

interest, gratuities and commissions, percent increase and decrease, and percent error. Unit Vocabulary:

Academic Cross-Curricular Words Content/Domain Specific

opposites distance

operations estimate

ratio gratuity

commission reasonableness

Topic 1 Absolute Value

Opposites Rational Numbers

Topic 2

Complex Fractions Reciprocals

Topic 3

Repeating Decimal Terminating Decimal

Topic 4

Repeating Decimal Terminating Decimal


Irrational Numbers Perfect Square Real Numbers Square Root

Topic 9 Balance Interest

Interest Rate Principal

Simple Interest Percent Decrease Percent Increase

Percent Of Change Markdown

Markup

Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)


digits Topic 1: Adding and Subtracting Rational Numbers

Standard Topic & Section Suggested # of Days

Notes

7.NS.A.1e 1.1: Rational Numbers, Opposites, and Absolute Value

1 day

7.NS.A.1a 7.NS.A.1b 7.NS.A.1c 7.NS.A.1f

1.2: Adding Integers 1.3: Adding Rational Numbers

1 day Do ALL of Lesson 1.2 and ONLY Part 2 of Lesson 1.3 (key concept not needed on Lesson 1.3 either). Include a vertical number line. For example, real world (temp. gauge) and mathematical example (y-axis).

7.NS.A.1a 7.NS.A.1b 7.NS.A.1d 7.NS.A.1f

1.4: Subtracting Integers 1.5: Subtracting Rational Numbers

1 day Do ALL of Lesson 1.4 and ONLY Part 2 & 3 of Lesson 1.5 (key concept not needed on Lesson 1.5 either).

7.NS.A.1a 7.NS.A.1b 7.NS.A.1c 7.NS.A.1d 7.NS.A.1f

Supplement Material for Review of Lesson 1.2, 1.3, 1.4, and 1.5

1 day white board practice or extra practice

7.NS.A.1e 1.6: Distance on a Number Line 1 day

7.NS.1 1.7: Problem Solving/Review Day for Topic 1

1 day Use this day as needed for problem solving and/or review day

Topic 1 Test 1 day


digits Topic 2: Multiplying and Dividing Rational Numbers


Notes

7.NS.A.2a 7.NS.A.2b

2.1: Multiplying Integers 2.2: Multiplying Rational Numbers

1 day Lesson 2.1: Number line does not need to be stressed much Lesson 2.2: Do all of Part 1. Do not do the number line on Part 2, but do the examples. Do not do Part 3.

7.NS.A.2a 7.NS.A.2c

2.3: Dividing Integers 2.4: Dividing Rational Numbers

1 day Lesson 2.3: Only do the “Got It” on Part 1, do all of Part 2 & 3 Lesson 2.4: Do all of parts 2-3, but do not do the Key Concept

7.NS.A.3 2.5: Operations with Rational Numbers

1 day

7.NS.A.3 7.EEI.B.3

2.6: Problem Solving 1 day

Review for Topic 2 Test 1 day

Topic 2 Test 1 day


digits Topic 3: Decimals and Percents


Notes

8.NS.A.1 7.NS.A.2e

3.1: Repeating Decimals 3.2: Terminating Decimals

1 day 3.1: Skip 2nd “Got It” on Part 3, Reinforce the idea of part = percent X whole and that the part can be bigger than the whole.

7.RP.A.3 3.5: Fractions, Decimals, and Percents

1 day Moved this out of order to ensure understanding of conversions before working with the percent equation in 3.3 and 3.4

7.RP.A.3 3.3: Percents Greater than 100 1 day

7.RP.A.3 3.4: Percents Less than 100 1 day

7.RP.A.3 3.6: Percent Error 1 day You can skip Part 3 if needed.

7.NS.A.3 7.EEI.B.3 7.RP.A.3

3.7: Problem Solving and Topic 3 Review

1 day

Topic 3 Test 1 day


digits Topic 9: Percents


Notes

7.RP.A.3 9.1: The Percent Equation 1 day

7.RP.A.3 9.2:Using the Percent Equation 1 day

7.RP.A.3 9.3: Simple Interest 1 day

9.4: Compound Interest--DO NOT TEACH

7.RP.A.3 9.5: Percent Increase and Decrease 1 day

7.RP.A.3 9.6: Markups and Markdowns 1 day

Review for Test 1 day

Topic 9 Test 1 day


Unit 2: Expressions and Equations

Subject: Mathematics Grade: 7th Accelerated Name of Unit: Expressions and Equations Length of Unit: 59 days (56 plus 3 buffer days) Overview of Unit: Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions as special linear equations, understanding the constant of proportionality is the slope and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that the input or x-coordinate changes by an amount A, and the output or y-coordinate changes by an amount m x A. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Priority Standards for unit:

● 8.EEI.C.7 Solve linear equations in one variable. a. Create and identify linear equations with one solution, infinitely many solutions

or no solutions. b. Solve linear equations and inequalities with rational number coefficients,

including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.

● 7.RP.A.2 Recognize and represent proportional relationships between quantities. a. Determine when two quantities are in a proportional relationship. b. Identify and/or compute the constant of proportionality (unit rate). c. Explain what a point (x,y) on the graph of a proportional relationship means in

terms of the situation. d. Recognize that the graph of any proportional relationship will pass through the

origin. ● 7.EEI.B.4 Write and/or solve linear equations and inequalities in one variable.

a. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers.

b. Write and/or solve two-step equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers, and interpret the meaning of the solution in the context of the problem.

c. Write, solve and/or graph inequalities of the form px + q > r or px + q < r, where p, q, and r are rational numbers.

● 8.EEI.A.1 Know and apply the properties of integer exponents to generate equivalent expressions.


● 8.EEI.B.5 Graph proportional relationships a. Interpret the unit rate as the slope of the graph. b. Compare two different proportional relationships.

● 8.EEI.B.6 Apply concepts of slope and y-intercept to graphs, equations, and proportional relationships.

a. Explain why the slope (m) is the same between any two distinct points in a non-vertical line in the Cartesian coordinate plane.

b. Derive the equation y = mx for a line through the origin and the equation y =mx + b for a line intercepting the vertical axis at b.

Supporting Standards for unit:

● 7.EEI.A.1 Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.

● 7.EEI.A.2 Understand how to use equivalent expressions to clarify quantities in a problems.

● 8.EEI.B.3 Solve multi-step problems posed with rational numbers. a. Convert between equivalent forms of the same number. b. Assess the reasonableness of answers using mental computation and

estimation strategies. ● 8.EEI.A.4 Use scientific notation to solve problems.

a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

● 8.EEI.A.2 Investigate concepts of square and cube roots. a. Solve equations of the form x^2 = p and x ^ 3 = p, where p is a positive

rational number. b. Evaluate square roots of perfect squares less than or equal to 625 and cube

roots of perfect cubes less than or equal to 1000. c. Recognize the square roots of non-perfect squares are irrational.

● 7.GM.A.1 Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing at a different scale.

● 7.NS.A.2 Apply and extend previous understandings of numbers to multiply and divide rational numbers.

a. Multiply and divide rational numbers b. Determine that a number and its reciprocal have a product of 1 (multiplicative

inverse). c. Understand that every quotient of integers (with non-zero divisor) is a rational

number. d. Convert a rational number to a decimal. e. Understand that all rational numbers can be written as fractions or decimal


numbers that terminate or repeat. f. Interpret products and quotients of rational numbers by describing real-world

contexts. ● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role


● ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.

● ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.


● CREATIVE COMMUNICATOR.6: Students communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals.




able to do)

Bloom’s Taxonomy

Levels Webb's DOK

8.EEI.C.7

linear equations and inequalities and pairs of

simultaneous linear equations Solve Apply 2

8.EEI.C.7a

linear equations with one solution, infinitely many solutions or no solutions. Create Create 3

8.EEI.C.7a

linear equations with one solution, infinitely many solutions or no solutions. Identify Remember 1

8.EEI.7b

linear equations and inequalities with rational

number coefficients, including equations and

inequalities whose solutions require

expanding expressions using the distributive Solve Apply 2


property and combining like terms

8.EEI.B.5 proportional relationships Graph Understand 2

8.EEI.B.5 the unit rate as the slope of

a graph Interpret Analyze 2

8.EEI.B.5 two different proportional

relationships Compare Analyze 2

7.RP.A.2 proportional relationships between quantities. Recognize Remember 1

7.RP.A.2 proportional relationships between quantities Represent Understand 1

7.RP.A.2a when two quantities are in a proportional relationship Determine Understand 2

7.RP.A.2b and/or compute the constant of proportionality (unit rate) Identify Apply 2

7.RP.A.2c

what a point (x,y) on the graph of a proportional relationship means in terms of the situation Explain Understand 2

7.RP.A.2d

that the graph of any proportional relationship will

pass through the origin. Recognize Remember 1

8.EEI.B.6

concepts of slope and y-intercept to graphs,

equations and proportional relationships Apply Apply 1

8.EEI.B.6a

why the slope (m) is the same between any two

distinct points on a non-vertical line in the

Cartesian coordinate plane. Explain Understand 2

8.EEI.B.6b

the equation y=mx for a line through the origin and the equation y=mx + b for

a line intercepting the vertical axis at b Derive Create 2

7.EEI.B.4 linear equations and

inequalities in one variable Write Understand 2

7.EEI.B.4 linear equations and

inequalities in one variable Solve Apply 2


7.EEI.B.4a

equations of the form x+p=q and px=q in which p and q

are rational numbers. Write Understand 2

7.EEI.B.4a

equations of the form x+p=q and px=q in which p and q

are rational numbers Solve Apply 2

7.EEI.4b

two-step equations of the form px + q =r and p(x + q)=r, where p, q and r are

rational numbers, and interpret the meaning of the solution in the context of the

problem. Write Understand 2

7.EEI..4b

two-step equations of the form px + q =r and p(x + q)=r, where p, q and r are

rational numbers, and interpret the meaning of the solution in the context of the

problem. Solve Apply 2

7.EEI.4c

Inequalities of the form px+q > r or px + q < r, where p, q, and r are rational numbers Write Understand 2

7.EEI.4c

Inequalities of the form px+q > r or px + q < r, where p, q, and r are rational numbers Solve Apply 2

7.EEI.4c

Inequalities of the form px+q > r or px + q < r, where p, q, and r are rational numbers Graph Apply 2

8.EEI.A.1

the properties of integer exponents to generate

equivalent expressions. Know Remember 1

8.EEI.A.1

the properties of integer exponents to generate equivalent expressions Apply

Essential Questions:

1. How can you determine if an equation has one solution, infinitely many solutions, or no solution?

2. How can you use unit rate and slope of a graph to compare proportional relationships? 3. How can you determine proportionality? 4. How can equations and inequalities be used to solve real-world problems?


5. How can rewriting an expression help you when solving problems? Enduring Understanding/Big Ideas:

1. You can transform an equation into simpler forms to determine if it has one solution, infinitely many solutions, or no solution.

2. By using unit rate and slope of two proportional relationships you can compare situations. 3. Proportionality can be determined by graphing or finding equivalent ratios in a table. 4. Equations and inequalities can be used to represent real-world situations and to solve for

an unknown variable. 5. Rewriting an expression in different forms can shed light on the problem and how the

quantities in it are related. Unit Vocabulary:


accuracy infinitely many

expanding represent identify explain

Topic 5 cube root

perfect cube Negative Exponent Property

Zero Exponent Property

Topic 6 Scientific Notation

Topic 7

equivalent ratio ratio

terms of a ratio rate

unit price unit rate

Topic 8

proportional relationship constant of proportionality

proportion scale

scale drawing

Topic 10 coefficient constant

simplify an algebraic expression


Topic 11 Addition Property of Equality Division Property of Equality

isolate a variable Multiplication Property of Equality

Subtraction Property of Equality

Topic 12 infinitely many solutions

no solution

Topic 13 Addition Property of Inequality

inequality solution of an inequality

solution set Subtraction Property of Inequality

Division Property of Inequality Multiplication Property of Inequality

equivalent inequalities

Topic 14 linear equation

slope slope of a line

y-intercept

Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook)


digits Topic 5: Integer Exponents


Notes

8.EEI.A.2 5.1: Perfect Squares, Square Roots, and Equations of the form 𝒙𝒙𝟐𝟐 = 𝒑𝒑 5.2: Perfect Cubes, Cube Roots, and Equations of the form 𝒙𝒙𝟑𝟑 = 𝒑𝒑

1 day Combine these 2 lessons.

8.EEI.A.1 5.3: Exponents and Multiplication 1 day

8.EEI.A.1 5.4: Exponents and Division 1 day

8.EEI.A.1 5.5: Zero and Negative Exponents 1 day

8.EEI.A.1 5.6: Comparing Expressions with Exponents

1 day


Topic 5 Test 1 day


digits Topic 4: Rational and Irrational Numbers Topic 6: Scientific Notation


Notes

4.1: Expressing Rational Numbers with Decimal Expansions--DO NOT TEACH

8.NS.A.1 4.2: Exploring Irrational Numbers 1 day Discuss the definition of a rational number. Include extra practice with Part 3 concepts in homework.

8.NS.A.2 4.3: Approximating Irrational Numbers

1 day Part 3 is challenging, possibly do extra practice with this section.

8.NSA.2 4.4: Comparing and Ordering Rational and Irrational Numbers

1 day

8.EEI.A.4 6.1: Exploring Scientific Notation 1 day

8.EEI.A.4 8.EEI.A.3

6.2: Using Scientific Notation to Describe Very Large Quantities

1 day Skip the “Got It” on Part 2

6.3: Using Scientific Notation to Describe Very Small Quantities

1 day

8.EEI.A.4 6.4: Operating with Numbers Expressed in Scientific Notation

1 day


Topic 6 Test 1 day


digits Topic 7: Ratios and Rates


Notes

7.RP.A.2 7.1: Equivalent Ratios 0 Review in warm-up

7.RP.A.2b 7.2: Unit Rates 1 day Lots of practice on Part 3

7.RP.A.2b 7.NS.A.2c

7.3: Ratios with Fractions 1 day Good for fractions sense needed in Algebra. Stress multiplying by the common denominator and cross-reducing (Key Concept)

7.RP.A.2b 7.NS.A.2c

7.4: Unit Rates with Fractions 1 day Teach using Extremes over Means OR method used in the lesson (dividing fractions by multiplying by reciprocal)


Topic 7 Test 1 day


digits Topic 8: Proportional Relationships

Note: Standard 7.RP.2d is only in 8.6 Problem Solving. Therefore, if you do not plan on teaching the Problem Solving section, you will need to supplement opportunities for 7.RP.2d in the other sections.


Notes

7.RP.A.2a 8.1: Proportional Relationships and Tables 8.2 Proportional Relationships and Graphs

1 day (0,0) and (1,r) – be sure to discuss what they mean in a table and on a graph.

7.RP.A.2b 7.RP.A.2c

8.3: Constant of Proportionality 8.4: Proportional Relationships and Equations

1 day Be sure to show the students y = mx + b

7.GM.A.1 8.5: Maps and Scale Drawings 1 day

Test Review Day 1 day

Topic 8 Test 1 day


digits Topic 14: Proportional Relationships, Lines, and Linear Equations


Notes

8.EEI.B.5 8.EEI.B.6

14.1: Graphing Proportional Relationships 14.2 Linear Equations: y = mx

1 day

8.EEI.B.5 14.3 The Slope of a Line 1 day

8.EEI.B.5 14.4: Unit Rates and Slope 1 day

8.EEI.B.6 14.5: The y-intercept of a Line 1 day

8.EEI.B.6 14.6: Linear Equations: y=mx+b 1 day


Topic 14 Test 1 day


digits Topic 10: Equivalent Expressions


Notes

7.EEI.A.1 7.EEI.A.2

10.1: Expanding Algebraic Expressions

1 day

7.EEI.A.1 7.EEI.A.2

10.2: Factoring Algebraic Expressions

1 day

7.EEI.A.1 7.EEI.A.2

10.3: Adding Algebraic Expressions 1 day

7.EEI.A.1 7.EEI.A.2

10.4: Subtracting Algebraic Expressions

1 day

White board practice over all types 1 day


Topic 10 Test 1 day


digits Topic 11: Equations


Notes

7.EEI.B.4a 11.1: Solving Simple Equations 11.2: Writing Two-Step Equations

1 day Review all but Part 3 of 11.1 in warm-ups, teach Part 3 of 11.1 and practice, then teach 11.2

7.EEI.B.4a 8.EEI.C.7b

11.3: Solving Two-Step Equations 1 day Finish 11.2 if needed and teach 11.3, only do Got It on Part 2 of 11.3

8.EEI.C.7b 12.2: Solving Equations with Variables on Both Sides

1 day

7.EEI.B.4a 8.EEI.C.7b

11.4: Solving Equations Using the Distributive Property AND 12.3: Solving Equations Using the Distributive Property

1 day Do some of both lessons together. They are teaching the same concept combining previous concepts.

8.EEI.C.7a 12.4: Solutions: One, None, or Infinitely Many

1 day


Topic 11 Test 1 day


digits Topic 13: Inequalities


Notes

7.EEI.B.4b 13.1: Solving Inequalities with Addition and Subtraction 13.2 Solving Inequalities with Multiplication and Division

1 day Make sure that students know the 5 types of inequalities, graphing the different types of inequalities, and how to graph an inequality that has the variable on the right side (reverse it). Focus on flipping the inequality symbol when multiplying or dividing by a negative number.

7.EEI.B.4b 13.3 Solving Two-Step Inequalities 1 day

7.EEI.B.4b 13.4: Solving Multi-Step Inequalities 1 day

Review Day 1 day

Topic 13 Review on computers 1 day

Topic 13 Test 1 day


Unit 3: Statistics and Probability

Subject: Mathematics Grade: 7th Accelerated Name of Unit: Statistics and Probability Length of Unit: 24 days (22 plus 2 buffer days) Overview of Unit: Students work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Priority Standards for unit:

● 7.DSP.C.5 Investigate the probability of chance events. a. Determine probabilities of simple events. b. Understand that the probability of a chance event is a number between 0 and 1

that expresses the likelihood of the event occurring. ● 7.DSP.C.8 Find probabilities of compound events using organized lists, tables, tree

diagrams, and simulation. a. Represent the sample space of a compound event. b. Design and use a simulation to generate frequencies for compound events.

● 7.DSP.B.4 Compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population.

● 7.DSP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population.

a. Understand that a sample is a subset of a population. b. Understand that generalizations from a sample are valid only if the sample is

representative of the population. c. Understand that random sampling is used to produce representative samples

and support valid inferences. Supporting Standards for unit:

● 7.DSP.C.6 Investigate the relationship between theoretical and experimental probabilities for simple events.

a. Predict outcomes using theoretical probability. b. Perform experiments that model theoretical probability. c. Compare theoretical and experimental probabilities.

● 7.DSP.B.3 Analyze different data distributions using statistical measures. ● 7.DSP.C.7 Explain possible discrepancies between a developed probability model and

observed frequencies.


a. Develop a uniform probability model by assigning equal probability to al outcomes, and use the model to determine probabilities of events.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

● 7.DSP.A.2 Use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristics of interest.

● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.








able to do)

Bloom’s Taxonomy

Levels Webb's DOK

7.DSP.C.5 the probability of chance

events. Investigate Understand 2 7.DSP.C.5 probabilities of simple events. Determine Apply 1

7.DSP.C.5

that the probability of a chance event is a number

between 0 and 1 that expresses the likelihood of the

event occurring. Understand Understand 3

7.DSP.C.8

the probabilities of compound events using organized lists,

tables, tree diagrams and simulations. Find Apply 1

7.DSP.C.8 sample the space of a

compound event Represent Analyze 2 7.DSP.C.8 a simulation to generate Design Create 3


frequencies for compound events

7.DSP.C.8

a simulation to generate frequencies for compound

events Use Create 3

7.DSP.B.4

the numerical measures of center, measures of frequency

and measures of variability from two random samples to

draw inferences about the population Compare Analyze 2

7.DSP.A.1

that statistics can be used to gain information about a

population by examining a sample of the population Understand Understand 1

7.DSP.A.1a that a sample is a subset of a

population Understand Understand 1

7.DSP.A.1b

that generalizations from a sample are valid only if the

sample is representative of the population Understand Understand 1

7.DSP.A.1c

that random sampling is used to produce representative samples and support valid

inferences Understand Understand 1 Essential Questions:

1. How can you determine the likelihood an event will occur? 2. Suppose you want to know the characteristics of a larger group of people or things. How

can you draw conclusions about the entire group without checking every member of the group?

3. How can you compare the characteristics of two groups of people or things? 4. How do you measure the probability of more than one event? 5. Can you use probability to predict future events? How confident can you be in your

predictions? Enduring Understanding/Big Ideas:

1. A probability close to 0 indicates an unlikely event; a probability of ½ indicates neither a likely nor unlikely (equally likely) event, and a probability close to 1 indicates a likely event.


2. You can draw conclusions about an entire group by sampling the group for information. There are three types of sampling: convenience, systematic, and random. The key is to ensure you have a representative sample.

3. Using measures of center, such as median and mean, you can compare characteristics of two groups of people or things.

4. You can find the number of outcomes of a multi-step process by finding the product of the number of possible outcomes of each step of the process.

5. When all outcomes of an action are equally likely, you can use theoretical probability to make predictions. Otherwise you can collect data and use experimental probability to predict future events.

Unit Vocabulary:


Mean Range

Population Subject Action Event

Outcome

Topic 15 Bias

Biased Sample Inference

Invalid Inference Population

Representative Sample Sample of a Population

Subject Valid Inference

Convenience Sampling Systematic Sampling

Simple Random Sampling

Topic 16 Interquartile Range

Mean Median Quartile Range

Comparative Inference Mean Absolute Value

Topic 17

Probability Of an Event Action Event

Outcome Sample Space

Simulation


Theoretical Probability Probability Model

Uniform Probability Model

Topic 18 Compound Events Dependent Events

Independent Events Counting Principle

Resources for Vocabulary Development: Use quality tools


digits Topic 15: Sampling

Topic 16: Comparing Two Populations


Notes

7.DSP.A.1 7.DSP.A.2

15.1: Populations and Samples 15.2: Estimating a Population

1 day

7.DSP.A.1 7.DSP.A.2

15.3 : Convenience Sampling 15.4: Systematic Sampling 15.5 Simple Random Sampling

1 day Combine all 3 lessons and cut where needed. All slides of all 3 lessons are not needed. Cut and combine for one day lesson/homework.

7.DSP.A.1 7.DSP.B.4

16.1: Statistical Measures 1 day

7.DSP.A.1 7.DSP.B.3 7.DSP.B.4

16.2: Multiple Populations and Inferences

1 day

7.DSP.B.4 16.3: Using Measures of Center 1 day

7.DSP.B.4 16.4: Using Measures of Variability 1 day

7.DSP.B.3 7.DSP.B.4

16.5: Exploring Overlap in Data Sets 1 day

7.DSP.B.4 16.6: Problem Solving and Review of Topic 16

1 day

Topic 16 Test 1 day


digits Topic 17: Probability Concepts


Notes

7.DSP.C.5 7.DSP.C.6

17.1: Likelihood and Probability 1 day

7.DSP.C.6 7.DSPC.7a 7.DSP.C.7b

17.2: Sample Space 1 day

7.DSP.C.6 17.3: Relative Frequency and Experimental Probability

1 day

7.DSP.C.6 7.DSP.C.7a

17.4: Theoretical Probability 1 day

7.DSP.C.7a 7.DSP.C.7b

17.5: Probability Models 1 day

7.DSP.C.7 17.6: Problem Solving and Review of Topic 17

1 day

Topic 17 Test 1 day


digits Topic 18: Compound Events


Notes

7.DSP.C.8b 18.1: Compound Events 18.2: Sample Spaces

1 day

7.DSP.C.8a 7.DSP.C.8b

18.3: Counting Outcomes 1 day

7.DSP.C.6 7.DSP.C.8a

18.4: Finding Theoretical Probabilities 1 day

7.DSP.C.8c 18.5: Simulation with Random Numbers

1 day Skip 18.6

7.DSP.C.7 7.DSP.C.8a 7.DSP.C.8b 7.DSP.C.8c

18.7: Problem Solving and Review Day 1 day

Topic 18 Test 1 day


Unit 4: Geometry

Subject: Mathematics Grade: 7th Accelerated Name of Unit: Geometry Length of Unit: 55 days (53 plus 2 buffer days) Overview of Unit: Students continue their work with area, solving problems involving area and circumference of a circle and surface area of three-dimensional objects. Students will reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students complete their work on volume by solving problems involving cones, cylinders, and spheres. Priority Standards for unit:

● 7.GM.B.5 Use angle properties to write and solve equations for an unknown angle. ● 8.GM.A.2 Understand that two-dimensional figures are congruent if a series of rigid

transformations can be performed to map the pre-image to the image. a. Describe a possible sequence of rigid transformations between two congruent

figures. ● 8.GM.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-

dimensional figures using coordinates. ● 7.GM.B.6 Understand the relationship between area, surface area and volume.

a. Find the area of triangles, quadrilaterals, and other polygons composed of triangles and rectangles.

b. Find the volume and surface area of prisms, pyramids and cylinders. Supporting Standards for unit:

● 8.GM.A.5 Explore angle relationships and establish informal arguments. a. Derive the sum of the interior angles of a triangle. b. Explore the relationship between the interior and exterior angles of a triangle. c. Construct and explore the angles created when parallel lines are cut by a

transversal.


d. Use the properties of similar figures to solve problems. ● 7.GM.A.2 Use a variety of tools to construct geometric shapes.

a. Determine if provided constraints will create a unique triangle through construction.

b. Construct special quadrilaterals given specific parameters. ● 8.GM.A.4 Understand that two-dimensional figures are similar if a series of

transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.

a. Describe a possible sequence of transformations between two similar figures. ● 8.GM.A.1 Verify experimentally the congruence properties of rigid transformations.

a. Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations.

b. Investigate if orientation is preserved under rigid transformations. ● 7.GM.A.3 Describe two-dimensional cross sections of pyramids, prisms, cones and

cylinders. ● 7.GM.A.4 Understand concepts of circles.

a. Analyze the relationships among circumference, the radius, the diameter, the area and Pi in a circle.

b. Know and apply the formulas for circumference and area of circles to solve problems.

● 8.GM.C.9 Solve problems involving surface area and volume. a. Understand the concept of surface area and find surface area of pyramids. b. Understand the concepts of volume and find the volume of pyramids, cones and

spheres. ● ISTE-EMPOWERED LEARNER 1: Students leverage technology to take an active role







Standard

Unwrapped Concepts (Students need to know)


able to do)

Bloom’s Taxonomy

Levels Webb's DOK

7.GM.B.5

angle properties to write and solve equations for an

unknown angle Use Apply 3

8.GM.A.2

that two-dimensional figures are congruent if a

series of rigid transformations can be

performed to map the pre-image to the image Understand Apply 2

8.GM.A.2

a possible sequence of rigid transformations between

two congruent figures Describe Analyze 2

8.GM.A.3

the effect of dilations, translations, rotations, and

reflections on two-dimensional figures using

coordinates Describe Evaluate 3

7.GM.B.6

the relationship between area, surface area and

volume Understand Understand 2

7.GM.B.6

the area of triangles, quadrilaterals and other polygons composed of triangles and rectangles Find Apply 2

7.GM.B.6

the volume and surface area of prisms, pyramids and

cylinders Find Apply 2 Essential Questions:

1. Intersecting lines form angles. How can you best describe relationships between those angles?

2. What makes a circle a circle? What does it mean to talk about the size of a circle? 3. How much information do you need to be able to draw a unique figure? 4. In what ways can you measure a three-dimensional figure? Are some measurements more

useful in certain situations than others?


5. What does it mean for two figures to be identical? How can you be sure they are identical?

Enduring Understanding/Big Ideas:

1. The sum of the measures of two complementary angles is 90 degrees. The sum of the measures of two supplementary angles is 180 degrees. The measures of vertical angles are equal.

2. The set of points in a plane that are the same distance from another point define a circle. The radius, diameter, circumference, and area of a circle are all related; you can use them to talk about the size of a circle. You can cut a circle into wedges and approximate a parallelogram that will have the same area as the circle, and then you can relate the formulas for area.

3. You can use a ruler and a protractor or technology to accurately draw a figure. You need a minimum of three pieces of information (about side lengths or angles) to draw a unique triangle. Slices made parallel to a prism face are identical in size and shape to that face.

4. You can measure a three-dimensional figure by its volume--the amount of space inside the figure. You can measure a three-dimensional figure by its surface area--the sum of the areas of each face. You can use what you know about the volume of a right rectangular prism to find the volume of any right prism.

5. Two figures are identical if you can map one to the other by a sequence of rigid motions, such as translations, reflections, and rotations. A rigid motion changes the position of a figure, but not its size or shape. When figures are congruent, all the matching angles and sizes are congruent.

Unit Vocabulary:


scale image

reflection height plane

wedges approximate

Topic 19

acute Angle angle

obtuse angle right angle

straight angle vertex of an angle

adjacent angles complementary angles supplementary angles

vertical angles

Topic 23 congruent figures


Topic 24 dilation

enlargement reduction

scale factor similar figures

Topic 22

lateral area of a prism surface area of a cube surface area of a prism

volume of a cube volume of a prism

Topic 25

alternate interior angles corresponding angles

transversal deductive reasoning

exterior angle of a triangle remote interior angles

Topic 20 center of a circle

circle diameter

radius circumference of a circle

Pi area of a circle

Topic 21

included angle included side

Topic 23

image rigid motion

transformation translation

line of reflection reflection

angle of rotation center of rotation

rotation


Topic 26 base cylinder

height lateral area

lateral surface right cylinder surface area

volume base cone

height lateral area

lateral surface right cone

slant height surface area

vertex radius sphere

surface area volume of a sphere

Resources for Vocabulary Development: Use quality tools


digits Topic 19: Angles


Notes

7.GM.A.2 19.1: Measuring Angles 1 day May need students to use actual protractors if time permits.

7.GM.A.2 7.GM.B.5

19.2: Adjacent Angles 1 day

7.GM.A.2 7.GM.B.5

19.3: Complementary Angles 19.4: Supplementary Angles

1 day Both sections are very similar. One uses 90 the other 180. Combine in one day.

7.GM.A.2 7.GM.B.5

19.5: Vertical Angles 1 day


Topic 19 Test 1 day


digits Topic 20: Circles


Notes

7.GM.A.2 7.GM.A.4

20.1: Center, Radius, and Diameter 1 day

7.GM.A.2 7.GM.A.4

20.2: Circumference of Circles 1 day Use 227

when called for.

7.GM.A.2 7.GM.A.4

20.3: Area of Circles 1 day Explain what it means to leave pi in answers.

7.GM.A.4 20.4: Relating Area and Circumference of Circles

1 day

7.GM.A.4 Review Day 2 days Great enrichment problems for this topic. (Problem Solving)


Topic 20 Test 1 day


digits Topic 21: 2-Dimensional and 3-Dimensional Shapes


Notes

7.GM.A.2 21.1: Geometry Drawing Tools 1 day This lesson could be adapted through Geogebra.

7.GM.A.2

21.2: Drawing Triangles with Given Conditions.

1 day This lesson could be adapted through Geogebra. It also may help to keep a running list of congruency statements on the board. This lesson stresses SSS and SAS.

7.GM.A.2

21.3: Drawing Triangles with Given Conditions Day 2.

1 day Students add AAS to their list and learn AAA does not produce congruent triangles.

7.GM.A.2 Extra Practice with Drawing Triangles with Given Conditions

1 day

7.GM.A.3 21.4: 2-D slices of right rectangular prisms 21.5: 2-D slices of right rectangular pyramids

1 day Combine 2 lessons.

21.6 Problem Solving/Topic 21 Review day

1 day

Topic 21 Test 1 day


digits Topic 22: Surface Area and Volume


Notes

7.GM.B.6 22.1: Surface Area of Right Prisms 2 days Use the formula SA=LA+2B. Students need to insert the formula for the B from memorization.

7.GM.B.6 22.2: Volumes of Right Prisms 1 day Use the formula V=Bh

7.GM.B.6 22.5: Problem Solving 1 day Do this so students can see applications

Review for Topic 22 1 day

Topic 22 Test 1 day


digits Topic 26: Surface Area and Volume


Notes

8.GM.C.9 26.1: Surface Area of Cylinders 1 day

8.GM.C.9 26.2: Volumes of Cylinders 1 day

8.GM.C.9 26.3: Surface Area of Cones 1 day .

8.GM.C.9 26.4: Volumes of Cones 1 day

8.GM.C.9 26.5: Surface Area of Spheres 1 day .

8.GM.C.9 26.6: Volumes of Spheres 1 day

8.GM.C.9 26.7: Problem Solving/ Test Review 1 day

Topic 26 Test 1 day


digits Topic 23: Congruence

Topic 24: Similarity


Notes

8.GM.A.1a 8.GM.A.1b 8.GM.A.1c 8.GM.A.3

23.1: Translations 1 day

8.GM.A.1a 8.GM.A.1b 8.GM.A.1c 8.GM.A.3

23.2: Reflections 1 day

8.GM.A.1a 8.GM.A.1b 8.G.M.A1c 8.GM.A.3

23.3: Rotations 1 day

8.GM.A.2 23.4: Congruent Figures 1 day

8.GM.A.3 24.1: Dilations 1 day

8.GM.A.4 24.2: Similar Figures 1 day

8.GM.A.2 Review for Test 1 day Topic 23.5 - Great enrichment problems for this topic.

Topic 23/24 Test 1 day


digits Topic 25: Reasoning in Geometry


Notes

8.GM.A.5 25.1: Angles, Lines, and Transversals

1 day

8.GM.A.5 25.2: Reasoning and Parallel Lines 1 day

8.GM.A.5 25.3: Interior Angles of Triangles 1 day Example 3 involves algebra from earlier topics. Lesson is pretty easy until this point.

8.GM.A.5 25.4: Exterior Angles of Triangles 1 day

8.GM.A.3 8.GM.A.4 8.GM.A.5

25.5: Angle-Angle Triangle Similarity

1 day

8.GM.A.5 25.6: Problem Solving 1 day Great enrichment and extra practice for this topic.

Topic 25 Test Review 1 day

Topic 25 Test 1 day


Unit of Study Terminology Appendices: All Appendices and supporting material can be found in this course’s shell course in the District’s Learning Management System. Assessment Leveling Guide: A tool to use when writing assessments in order to maintain the appropriate level of rigor that matches the standard. Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student’s 21st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities.

7th grade advanced mathematics curriculum · 7th grade advanced mathematics curriculum. course...

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