Grade 7 enVisionmath2.0 2017-2018 SY...Numbers - Add and subtract positive and negative rational numbers - Use number lines to model addition and subtraction as a movement or distance

THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 1

Grade 7 enVisionmath2.0 2017-2018 SY

Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4

Dat

es September 5 - October 31

BM Window Opens November 1 November 2 - January 26 BM Window Opens January 29

January 30 - May 8 BM Window Opens May 9

May 10 - June 12

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l

Teac

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g D

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Total Days: 39 Including 1 Half Day

Total Days: 50 Including 4 Half Days

Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days; Excluding Week of Math PSSA

Total Days: 22 Including 1 Half Day

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enVisionmath2.0 (Pearson) 1: Integers and Rational Numbers 2: Analyze and Use Proportional Relationships

enVisionmath2.0 (Pearson) 3: Analyze and Solve Percent Problems 4: Generate Equivalent Expressions 5-1 – 5-3: Solve Problems Using Equations and Inequalities

enVisionmath2.0 (Pearson) 5-4 – 5-7: Solve Problems Using Equations and Inequalities (cont’d) 8: Solve Problems Involving Geometry + 2 PA Lessons (see below) 6: Use Sampling to Draw Inferences About Populations 7-1 – 7-3: Probability* *Note: Topic 7 will not be assessed on Benchmark 3.

Supplementary Lessons PA-1: Describe Triangle Properties PA-2: Angles, Lines and Transversals.

enVisionmath2.0 (Pearson) 7: Probability Remediate and Extend

Note: A cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken on the first day of the window. This means that though it is fine to give the test later in the window, you should be moving on to new content as of the above listed dates, or you will fall behind.


Table of Contents

Benchmark Cycle 1 Standards ............................................................................................................................................................................................. 3

Benchmark Cycle 1 Scope and Sequence ........................................................................................................................................................................... 5

Benchmark Cycle 2 Standards ............................................................................................................................................................................................. 7

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 10

Benchmark Cycle 3 Standards ........................................................................................................................................................................................... 13

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 17

Cycle 4 Standards .............................................................................................................................................................................................................. 21

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 23

PA Core Standards and Eligible Content ........................................................................................................................................................................... 25

Document Information Page ............................................................................................................................................................................................ 28


Benchmark Cycle 1 Standards

PA Core Standard PA Eligible Content Common Core Standard

CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers.

M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts.

7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a

horizontal or vertical number line diagram. d. Apply properties of operations as strategies to add and subtract rational numbers.

M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical number line.

M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.

CC.2.1.7.D.1Analyze proportional relationships and use them to model and solve real‐world and mathematical problems.

M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

7.RP.2. Recognize and represent proportional

relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

M07.A-R.1.1.4 Represent proportional relationships by equations.

M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.


d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems.

CC.2.2.7.B.3Model and solve real‐world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.

M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a

horizontal or vertical number line diagram.d. Apply

properties of operations as strategies to add and subtract rational numbers.



Benchmark Cycle 1 Scope and Sequence

Topic 1: Integers and Rational Numbers

Suggested Dates

Topic- Lesson

Lesson Title Lesson Objective(s) Eligible Content

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1-1 Relate Integers and Their Opposites

- Understand how integers, their opposites, and absolute values are related - Apply this understanding to models (number lines) and use these to solve real-world problems

M06.A-N.3.2.1 Preparing for: M07.A-N.1.1.1 M07.A-N.1.1.2

1-2 Understand Rational Numbers - Identify rational numbers - Convert rational numbers expressed as fractions to terminating or repeating decimals

Preparing for: M07.A-N.1.1.1

1-3 Add Integers - Add positive and negative integers - Model integer addition in real-life applications

M07.A-N.1.1.1

1-4 Subtract Integers - Understand subtraction of integers as addition the additive inverse, p – q = p + (-q) - Use addition and subtraction rules to solve real-world problems

M07.A-N.1.1.1 M07.A-N.1.1.2

1-5 Add and Subtract Rational Numbers

- Add and subtract positive and negative rational numbers - Use number lines to model addition and subtraction as a movement or distance between rational numbers

M07.A-N.1.1.1 M07.A-N.1.1.2

1-6 Multiply Integers - Multiply positive and negative integers - Use models and mathematical properties to develop a deep understanding of and fluency with multiplying integers

M07.A-N.1.1.3

1-7 Multiply Rational Numbers - Multiply with rational numbers - Apply operations with rational numbers to real-world contexts

M07.A-N.1.1.3

1-8 Divide Integers - Use the relationship between multiplication and division to divide integers - Determine which quotients of integers are equivalent

M07.A-N.1.1.3

1-9 Divide Rational Numbers

- Understand how the signs of integers in multiplication sentence relate to the signs in a related division sentence - Extend their knowledge about multiplying rational numbers and dividing integers to division of rational numbers

M07.A-N.1.1.3

1-10 Solve Problems with Rational Numbers

- Decide which operations to use to solve problems with rational numbers

M07.A-N.1.1.1 M07.A-N.1.1.3 M07.B-E.2.1.1


Topic 2: Analyze and Use Proportional Relationships

Suggested Dates

Topic- Lesson


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2-1 Connect Ratios, Rates and Unit Rates

- Use ratios and rates to describe the relationship between two quantities - Find equivalent ratios and use unit rates to solve multi-step problems

M07.A-R.1.1.1 M07.A-R.1.1.6

2-2 Determine Unit Rates with Ratios of Fractions

- Find unit rates with ratios of fractions - Use unit rates to solve multi-step problems

M07.A-R.1.1.1 M07.A-R.1.1.6

2-3 Understand Proportional Relationships: Equivalent Ratios

- Determine whether quantities are proportional by testing for equivalent ratios

M07.A-R.1.1.2

2-4 Describe Proportional Relationships: Constant of Proportionality

- Use the constant of proportionality to write equations that represent proportional relationships - Use equations to solve problems involving proportional relationships

M07.A-R.1.1.3 M07.A-R.1.1.4

2-5 Graph Proportional Relationships - Use a graph to recognize proportionality - Identify a constant of proportionality from a graph - Interpret a point on a graph of a proportional relationship

M07.A-R.1.1.2 M07.A-R.1.1.3 M07.A-R.1.1.5

2-6 Apply Proportional Reasoning to Solve Problems

- Explain whether a situation represents a proportional relationship - Use representations to find entry points into problems

M07.A-R.1.1.2 M07.A-R.1.1.6

Benchmark 1 Window: 11/1 – 11/17




CC.2.2.7.B.1Apply properties of operations to generate equivalent expressions.

M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.


M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational

numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a

new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by

reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.


M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.

7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by

reasoning about the quantities.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

CC.2.1.7.D.1Analyze proportional relationships and use them to model and solve real‐world and mathematical problems.


7.RP.2. Recognize and represent proportional

relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.


M07.A-R.1.1.4 Represent proportional relationships by equations.

M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.


d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems.



Topic 3: Analyze and Solve Percent Problems

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Topic- Lesson


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3-1 Compare Proportional Relationships

- Understand that equivalent ratios can be used to model percent problems - Analyze percents of numbers in a real-world context

M07.A-R.1.1.2 M07.A-R.1.1.3 M07.A-R.1.1.4 M07.A-R.1.1.5

3-2 Connect Percent and Proportion - Write a proportion to model a percent situation - Use a percent proportion to find an unknown part, whole, or percent

M07.A-R.1.1.4

3-3 Represent and Use the Percent Equation

- Represent proportional relationships using percents - Use the percent equation to represent and solve percent problems

M07.A-R.1.1.4

3-4 Solve Percent Change and Percent Error Problems

- Calculate percent change and percent error - Understand the percent equation and how it leads to the percent change formula

M07.A-R.1.1.6

3-5 Solve Markup and Markdown Problems

- Understand and calculate percent markups and markdowns M07.A-R.1.1.6

3-6 Solve Simple Interest Problems - Understand what simple interest is and how it is calculated - Solve problems involving simple interest

M07.A-R.1.1.6


Topic 4: Generate Equivalent Expressions

Suggested Dates

Topic- Lesson


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4-1 Write and Evaluate Algebraic Expressions

- Write and evaluate algebraic expressions M07.B-E.2.1.1

4-2 Generate Equivalent Expressions - Write equivalent expressions by using properties and by combining like terms - Identify equivalent expressions

M07.B-E.1.1.1

4-3 Simplify Expressions - Identify and combine like terms - Simplify expressions using like terms

M07.B-E.1.1.1

4-4 Expand Expressions - Apply the Distributive Property to expand linear expressions - Use area models to solidify their understanding of the Distributive Property

M07.B-E.1.1.1

4-5 Factor Expressions - Find common factors of linear expressions using the Distributive Property Recognize factoring is the opposite of expanding expressions

M07.B-E.1.1.1

4-6 Add Expressions - Add expressions with rational coefficients using the Commutative and Associative Properties - Add expressions that represent real-world situations

M07.B-E.1.1.1

4-7 Subtract Expressions - Identify the similarity of the procedure between subtracting integers and subtracting linear expressions - Simplify linear expressions involving subtraction

M07.B-E.1.1.1

4-8 Analyze Equivalent Expressions

- Write equivalent expressions by combining like terms, using the Distributive Property, and performing other mathematical operations - Use equivalent expressions to examine relationships between quantities and interpret information in real-world problems

M07.B-E.1.1.1


Topic 5: Solve Problems Using Equations and Inequalities (5-1 – 5-3)

Suggested Dates

Topic- Lesson


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5-1

Write Two-Step Equations

- Analyze word problems to write two-step equations - Interpret the quantities in an equation

M07.B-E.2.2.1 M07.B-E.2.3.1

5-2

Solve Two-Step Equations

- Solve a problem using a two-step equation - Compare algebraic and arithmetic solutions

M07.B-E.2.1.1 M07.B-E.2.2.1

5-3 Solve Equations Using the Distributive Property

- Solve equations using the Distributive Property

M07.B-E.2.1.1 M07.B-E.2.2.1 M07.B-E.2.3.1

5-4 Solve Inequalities Using Addition or Subtraction

- Graph the solution of inequalities on a number line - Solve inequalities using the Addition and Subtraction Properties of Inequality

M07.B-E.2.2.2 M07.B-E.2.3.1

Benchmark 2 Window 01/29 -2/13








M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.

7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems

by reasoning about the quantities.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.


7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

CC.2.3.7.A.2Visualize and represent geometric figures and describe the relationships between them.

M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.


M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures.

NO MATCH

M07.C-G.1.1.3 Use and apply the triangle inequality theorem.

8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures.

7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids

CC.2.3.7.A.1Solve real‐world and mathematical problems involving angle measure, area, surface area, circumference, and volume.

M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi- step problem to write and solve simple equations for an unknown angle in a figure.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).

8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.


M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.

7.G.4. Know the formulas for the area and circumference of a circle and use them to solve

problems; give an informal derivation of the relationship between the circumference and area of

a circle.

M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CC.2.4.7.B.1Draw inferences about populations based on random sampling concepts.

M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation.

7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

CC.2.4.7.B.2Draw informal comparative inferences about two populations.

M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability.

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability

.


CC.2.4.7.B.2Draw informal comparative inferences about two populations.


7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.



Topic 5: Solve Problems Using Equations and Inequalities (5-4 – 5-7)

Suggested Dates

Topic. Lesson


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5-5 Solve Inequalities Using Multiplication or Division

- Write inequalities and solve them using the Multiplication and Division Properties of Inequality - Graph the solutions of inequalities on a number line

M07.B-E.2.2.2 M07.B-E.2.3.1

5-6 Solve Two-Step Inequalities

- Solve an inequality by multiplying or dividing by a negative rational number - Write a two-step inequality to solve a problem - Solve a two-step inequality

M07.B-E.2.2.2 M07.B-E.2.3.1

5-7 Solve Multi-Step Inequalities

- Reinforce skills learned in previous lessons and apply that knowledge to solving multi-step inequalities - Explore the relationship between two-step inequalities and multi-step inequalities - Apply the Distributive Property to simplify and solve multi-step inequalities

M07.B-E.2.2.2 M07.B-E.2.3.1


Unit 8: Solve Problems Involving Geometry

Suggested Dates

Topic- Lesson


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8-1 Solve Problems Involving Scale Drawings

- Use a scale drawing as a representation of actual lengths and area M07.C-G.1.1.1

8-2 Draw Geometric Figures - Draw geometric shapes with given conditions - Name and classify quadrilaterals according to their properties

No PA Alignment

8-3 Draw Triangles with Given Conditions

- Sketch and construct triangles with given conditions - Determine the number of triangles that can be formed given side lengths and angle measures

M07.C-G.1.1.2 M07.C-G.1.1.3

PA-1 Describe Triangle Properties

- Determine measures of interior angles of triangles - Describe a triangle using angle measures and side lengths - Use the Triangle Inequality Theorem to determine whether three side lengths can form a triangle

M07.C-G.1.1.2 M07.C-G.1.1.3

8-4 Solve Problems Using Angle Relationships

- Find the measure of angles using angle relationships - Recognize the relationship between different angles formed by intersecting lines and rays

M07.C-G.2.1.1

PA-2 Angles, Lines and Transversals

- Identify relationships among angles formed by parallel lines and a transversal - Determine the measures of angles formed by parallel lines and a transversal

M08.C-G.2.1.2

8-5 Solve Problems Involving Circumference of a Circle

- Calculate the circumference, radius, or diameter of a circle - Recognize the relationship between the circumference of a circle,

diameter of a circle, and M07.C-G.2.2.1

8-6 Solve Problems Involving Area of a Circle

- Find the area of a circle - Use the area of a circle to find the radius and diameter - Solve problems involving the area of a circle

M07.C-G.2.2.1

8-7 Describe Cross Sections - Describe and sketch cross sections of right rectangular prisms and right rectangular pyramids - Solve problems involving cross sections

M07.C-G.2.1.4

8-8 Solve Problems Involving Surface Area

- Find the surface area of 2-dimensional composite shapes - Find the surface area of 3-dimensional composite shapes

M07.C-G.2.2.2

8-9 Solve Problems Involving Volume

- Calculate the volume of various three-dimensional figures composed of prisms - Solve problems involving the volume of three-dimensional figures

M07.C-G.2.2.2 M07.A-N.1.1.3


Topic 6: Use Sampling to Draw Inferences About Populations

Suggested Dates

Topic- Lesson


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6-1 Populations and Samples - Understand the difference between a population and a sample - Establish whether a sample is representative of a population - Generate random samples that represent the entire population

M07.D-S.1.1.1

6-2 Draw Inferences from Data

- Make qualitative and quantitative inferences from a sample data set - Make estimates about a population based on a sample data set, and assess whether the inferences are valid

M07.D-S.1.1.2

6-3 Make Comparative Inferences About Populations

- Use box plots to compare and make inferences about populations - Use the median and interquartile range (IQR) of data sets to informally compare and make inferences about two populations

M07.D-S.2.1.1

6-4 Make More Comparative Inferences About Populations

- Use the mode, range, mean and mean absolute deviation (MAD) to compare populations

M07.D-S.2.1.1

Math PSSA 4/16 – 4/20


Topic 7: Probability

Suggested Date

Topic- Lesson


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7-1 Understand Likelihood and Probability

- Use probability to describe the likelihood that an event will occur - Relate probability to mathematical fairness

M07.D-S.3.1.1

7-2 Understand Theoretical Probability

- Understand theoretical probability and how it can be used - Use theoretical probability to predict an outcome

M07.D-S.3.1.1 M07.D-S.3.2.2

7-3 Understand Experimental Probability

- Compare theoretical and experimental probability - Use experimental probability to make predictions - Explain difference between theoretical and experimental probability

M07.D-S.3.2.1

Benchmark 3 Window 5/9 – 5/25

*Note: Topic 7(Probability) will not be assessed on Benchmark 3.


Cycle 4 Standards


CC.2.4.7.B.3Investigate chance processes and develop, use, and evaluate probability models.

M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.

7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

M07.D-S.3.2.2 Find the probability of a simple event,

including the probability of a simple event not occurring.

Preparing for 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and

simulation.a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.8. Find probabilities of compound events using

organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language


(e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies

for compound events.


Cycle 4 Scope and Sequence

Topic 7: Probability

Suggested Date

Topic- Lesson


04

/23

– 0

5/1

8

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7-1 Understand Likelihood and Probability

- Use probability to describe the likelihood that an event will occur - Relate probability to mathematical fairness

M07.D-S.3.1.1

7-2 Understand Theoretical Probability

- Understand theoretical probability and how it can be used - Use theoretical probability to predict an outcome

M07.D-S.3.1.1 M07.D-S.3.2.2

7-3 Understand Experimental Probability

- Compare theoretical and experimental probability - Use experimental probability to make predictions - Explain difference between theoretical and experimental probability

M07.D-S.3.2.1

7-4 Use Probability Models - Develop a probability model - Use a probability model to evaluate a situation - Use a probability model to make an estimate

M07.D-S.3.1.1 M07.D-S.3.2.1 M07.D-S.3.2.2

7-5 Determine Outcomes of Compound Events

- Use a tree diagram, a table, or an organized list to represent the sample space for a compound event

M07.D-S.3.2.3

7-6 Find Probabilities of Compound Events

- Organize information about a compound event on a table, a tree diagram, or an organized list - Find the probability of a compound event

M07.D-S.3.2.3

7-7 Simulate Compound Events - Use different tools to simulate a compound event - Model a real-world situation involving a compound event and predict its outcome using a simulation

M07.D-S.3.2.3


5/21 – 6/12 15 Days

Remediate and Extend by Preparing for Grade 8

Option 1: Revisit 3-Act Math

Lessons

(6-8 enV)

Each Topic featured a 3-Act Mathematical Modeling lesson that you may or may not have had time to do with your students. During the remainder of the year, you can revisit key ideas from 6th grade and provide students with opportunities to engage authentically in the Standards for Mathematical Practice through a series of 3-Act Lessons. You can also find more lessons at this link: https://whenmathhappens.com/3-act-math/.

Option 2: Reteach Based on

Common Core-identified focal

areas.

You taught many topics this year. The four below are identified as the most critical for 7th grade. If you want to revisit something, one or more of these topics would be a good idea.

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.EE.A Use properties of operations to generate equivalent expressions. 7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Option 3: Pre-Teach Based on

7th Grade Needs

You can check in with your 8th grade teacher to ask what content you could pre-teach or what content they would like you to revisit. The first two Topics in 8th grade are: 1) Real Numbers

2) Analyze and Solve Linear Equations

You can access the 8th grade Teacher’s Guide and materials online for reference.

Option 4: Financial Literacy

The Federal Reserve Bank of Philadelphia has posted free lesson plans for elementary teachers (including K) on financial literacy at: https://philadelphiafed.org/education/teachers/lesson-plans. Many of these lessons are tied to early children’s literature, as well. In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: https://www.census.gov/schools/activities/math.html.

https://whenmathhappens.com/3-act-math/

https://philadelphiafed.org/education/teachers/lesson-plans

https://www.census.gov/schools/activities/math.html


PA Core Standards and Eligible Content

PA Core Standard PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real-world and mathematical problems.

M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

X


X X


X X

M07.A-R.1.1.4 Represent proportional relationships by equations. X X

M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the

points (0, 0) and (1, r), where r is the unit rate. X X

M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. X X


M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts. X

M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical

number line. X


X


CC.2.2.7.B.1 Apply properties of operations to generate equivalent expressions.

M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. X X

CC.2.2.7.B.3Model and solve

real‐world and mathematical

problems by using and

connecting numerical,

algebraic, and/or graphical

representations.

M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. X

M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. X

M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the

solution set of the inequality. X

CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.


X

CC.2.3.7.A.1 Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.

M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi- step problem to write and solve simple equations for an unknown angle in a figure.

X

M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).

X

M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems

involving area and circumference of a circle(s). Formulas will be provided. X

M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

X


CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them.

M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area. X

M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures. X

M07.C-G.1.1.3 Use and apply the triangle inequality theorem. X

M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures. X

CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts.

M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation. X

M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. X

CC.2.4.7.B.2 Draw informal comparative inferences about two populations.


X

CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models.

M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).

X

M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability. X

M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring. X

M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation. X


Document Information Page

Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle X Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle’s Benchmark. The Benchmark Cycle X Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught.

What is a Cycle?

We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle.

What If I Fall Behind?

We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide.

If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn’t Belong. Rather than pushing to “cover” content, or using test prep resources, content can be infused through short but meaningful structures.

The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes.

Percent if Topics 1-8 Are Taught

Percent if Topics 1-6 and 8 Are Taught



100% 91.2% 80% 71.2%

http://wodb.ca/


Additional Key Considerations in Mathematics

The Standards for Mathematical Practice are: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

You should try to infuse these Standards into your lessons regularly. Rather than thinking of them as a box to check, think about how you are providing students with opportunities to develop as mathematical thinkers and doers.

The Common Core has identified the following as the four critical areas for Grade 7: 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.EE.A Use properties of operations to generate equivalent expressions. 7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations

These do not necessarily reflect what is most tested on the PSSA, but it is the content that is most essential as you prepare students for 8th grade.

The School District of Philadelphia’s Vision for Mathematics Teaching and Learning:

All students think mathematically, and they will be empowered to own, share, and do mathematics.

Our Guiding Principles:

Equitable Discourse Rich + Meaningful Tasks Purpose-Driven Work Questioning and Curiosity Valuing Diverse Thinking

If you have any questions or would like more information, please contact us at [email protected].

Documents

Grade 7 enVisionmath2.0 2017-2018 SY...Numbers - Add and subtract positive and negative rational numbers - Use number lines to model addition and subtraction as a movement or distance