grade 7 big ideas 2017-2018 sy - philasd.org e.g., by testing for equivalent ratios in a table or...

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

Grade 7 Big Ideas 2017-2018 SY

Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4

Dat

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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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Cyc

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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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Big Ideas 1: Integers 2: Rational Numbers 3.1, 3.2*: Expressions and Equations *Note: The 3.2 Lesson Extension does not include PA eligible content for 7th grade and so can be done following the PSSA.

Big Ideas 3.3 – 3.5: Expressions and Equations 4: Inequalities 5: Ratios and Proportions 6.1 – 6.4: Percents

Big Ideas 6.5 – 6.7: Percents 7: Constructions and Scale Drawings 8: Circles and Area 9: Surface Area and Volume

Big Ideas 10: Probability and Statistics Remediate and Extend

A benchmark cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken in the first week 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 ........................................................................................................................................................................... 4

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

Benchmark Cycle 2 Scope and Sequence ........................................................................................................................................................................... 9

Benchmark Cycle 3 Standards ........................................................................................................................................................................................... 12

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 15

Cycle 4 Standards .............................................................................................................................................................................................................. 19

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 21

Document Information Page ............................................................................................................................................................................................ 26


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.2.2.7.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.

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

Chapter 1: Integers

Suggested Dates

Section Lesson Title Lesson Goal(s) Eligible Content

9/5

– 9

/26

2 D

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+ 4

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1.1 Integers and Absolute Value - Define the absolute value of a number - Find absolute values of numbers - Solve real-life problems

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

1.2 Adding Integers - Add integers - Show that the sum of a number and its opposite is 0 - Solve real-life problems

M07.A-N.1.1.1

1.3 Subtracting Integers - Subtract Integers - Solve real-life problems

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

1.4 Multiplying Integers - Multiply integers - Solve real-life problems

M07.A-N.1.1.3

1.5 Dividing Integers - Divide Integers - Solve real-life problems

M07.A-N.1.1.3


Chapter 2: Rational Numbers

Suggested Dates


9/2

7 –

10

/12

2 D

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+ 3

Day

s 2.1 Rational Numbers - Understand that a rational number is an integer divided by an integer - Convert rational numbers to decimals

Preparing for: M07.A-N.1.1.1

2.2 Adding Rational Numbers - Add rational numbers - Solve real-life problems

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

2.3 Subtracting Rational Numbers - Subtract rational numbers - Solve real-life problems

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

2.4 Multiplying and Dividing Rational Numbers

- Multiply and divide rational numbers - Solve real-life problems

M07.A-N.1.1.3


Chapter 3: Expressions and Equations

Suggested Dates


10

/13

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3.1 Algebraic Expressions - Apply properties of operations to simplify algebraic expressions - Solve real-life problems

M07.B-E.1.1.1 M07.B-E.2.1.1

3.2 Adding and Subtracting Linear Expressions

- Apply properties of operations to add and subtract linear expressions - Solve real-life problems

M07.B-E.1.1.1

3.3 Solving Equations Using Addition or Subtraction

- Write simple equations - Solve equations using addition or subtraction - Solve real-life problems

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

3.4 Solving Equations Using Multiplication or Division

- Solve equations using multiplication or dividion - Solve real-life problems

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

3.5 Solving Two-Step Equations - Solve two-step equations - Solve real-life problems

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

Benchmark 1 Window: 11/1 – 11/17




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


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.

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

M07.A-R.1.1.2 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.

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.1.1.3 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.

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.



Chapter 4: Inequalities

Suggested Dates


11

/02

– 1

1/2

2

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4.1 Writing and Graphing Inequalities - Write and graph inequalities - Use substitution to check whether a number is a solution to an inequality

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

4.2 Solving Inequalities Using Addition or Subtraction

- Solve inequalities using addition or subtraction - Solve real-life problems

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

4.3 Solving Inequalities Using Multiplication or Division

- Solve inequalities using multiplication or division - Solve real-life problems

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

4.4 Solving Two-Step Inequalities - Solve multi-step inequalities - Solve real-life problems

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


Chapter 5: Ratios and Proportions

Suggested Dates


11

/27

– 1

2/2

2

2 D

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5.1 Ratios and Rates - Find ratios, rates and unit rates - Find ratios and rates involving ratios of fractions

M07.A-R.1.1.1

5.2 Proportions

- Use equivalent ratios to determine whether two ratios form a proportion - Use the Cross Products Property to determine whether two ratios form a proportion

M07.A-R.1.1.2

5.2 Extension

Graphing Proportional relationships - Use graphs to determine whether two ratios form a proportion - Interpret graphs of proportional relationships

M07.A-R.1.1.2

5.3 Writing Proportions - Write proportions - Solve proportions using mental math

M07.A-R.1.1.4

5.4 Solving Proportions

- Solve proportions using multiplication or the Cross Products Property - Use a point on a graph to write and solve proportions

M07.A-R.1.1.6

5.5 Slope - Find the slopes of lines - Interpret the slopes of lines as rates

M07.A-R.1.1.5

5.6 Direct Variation - Identify direct variation from graphs or equations - Use direct variation models to solve problems

M07.A-R.1.1.5


Chapter 6: Percents

Suggested Dates


01

/03

– 0

1/2

6

2 D

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+ 3

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6.1 Percents and Decimals - Write percents as decimals - Write decimals as percents - Solve real-life problems

Preparing for: M07.A-R.1.1.6

6.2 Comparing and Ordering Fractions, Decimals, and Percents

- Compare and order fractions, decimals, and percents - Solve real-life problems

Preparing for: M07.A-R.1.1.6

6.3 The Percent Proportion - Use the percent proportion to find parts, wholes, and percents

M07.A-R.1.1.6

6.4 The Percent Equation - Use the percent equation to find parts, wholes, and percents - Solve real-life problems

M07.A-R.1.1.6

6.5 Percents of Increase and Decrease - Find percents of increase - Find percents of decrease

M07.A-R.1.1.6

6.6 Discounts and Markups - Use percent of discounts to find prices of items - Use percents of markups to find selling prices of items

M07.A-R.1.1.6

6.7 Simple Interest - Use the simple interest formula to find interest earned or paid, annual interest rates and amounts paid on loans

M07.A-R.1.1.6

Benchmark 2 Window 01/26 – 02/13








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.


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

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.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.



Chapter 7: Constructions and Scale Drawings

Suggested Dates

Section Lesson Title Lesson Objective(s) Eligible Content

01

/30

– 0

2/2

3

2 D

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+ 2

.5 D

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7.1 Adjacent and Vertical Angles - Identify adjacent and vertical angles - Find angle measures using adjacent and vertical angles

M07.C-G.2.1.1

7.2 Complementary and Supplementary Angles

- Classify pairs of angles as complementary, supplementary, or neither - Find angle measures using complementary and supplementary angles

M07.C-G.1.1.1 M07.C-G.1.1.2

7.3 Triangles

- Construct triangles with given angle measurements - Construct triangles with given side lengths* *Note: Construction is not assessed on the PSSA. Students must be familiar, however, with angles in triangles and the Triangle Inequality Theorem.

M07.C-G.1.1.1 M07.C-G.1.1.2

7.3 Extension

Angle Measures of Triangles - Understand that the sum of the angle measures of any triangle is 180o - Find missing angle measures in triangles

M07.C-G.1.1.1

7.4

Quadrilaterals

- Understand that the sum of the angle measures of any quadrilateral is 360o - Find missing angle measures in quadrilaterals - Construct quadrilaterals* *Note: Construction is not assessed on the PSSA. Students must be familiar, however, with angles in quadrilaterals.

M07.C-G.1.1.1 M07.C-G.2.2.2

7.5 Scale Drawings

- Use scale drawings to find actual distances - Find scale factors - Use scale drawings to find actual perimeters and areas - Recreate scale drawings at a different scale

M07.C-G.1.1.1

Supplemental Lesson

Angles formed by Parallel Lines Cut by a Transversal

M07.C-G.2.1.2


Chapter 8: Circles and Area

Suggested Dates


02

/26

– 0

3/0

9

2 D

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3 D

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8.1 Circles and Circumference

- Describe a circle in terms of radius and diameter - Understand the concept of pi - Find circumferences of circles and perimeters of semicircles

M07.C-G.2.2.1

8.3 Areas of Circles - Find areas of circles and semicircles M07.C-G.2.2.1

8.4 Areas of Composite Figures

- Find areas of composite figures by separating them into familiar figures - Solve real-life problems

M.07.C-G.2.2.2


Chapter 9: Surface Area and Volume

Suggested Dates


03

/12

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4/1

3

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SSA

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9.1 Surface Areas of Prisms

- Use two-dimensional nets to represent three-dimensional solids - Find surface areas of rectangular and triangular prisms - Solve real-life problems

M.07.C-G.2.2.2 Preparing for

M.07.C-G.1.1.4

9.2 Surface Areas of Pyramids - Find surface areas of regular pyramids - Solve real-life problems


M.07.C-G.1.1.4

9.3 Surface Areas of Pyramids - Find surface areas of cylinders


M.07.C-G.1.1.4

9.4 Volumes of Prisms - Find volumes of prisms - Solve real-life problems


M.07.C-G.1.1.4

9.5 Volumes of Pyramids - Find volumes of pyramids - Solve real-life problems


M.07.C-G.1.1.4

9.5 Extension

Cross Sections of Three-Dimensional Figures

- Describe the intersections of planes and solids M.07.C-G.1.1.4

Math PSSA 4/16 – 4/20


Chapter 10: Probability and Statistics

Suggested Dates

Section Lesson Title Lesson Objective Eligible Content

04

/23

– 0

5/0

8

2 D

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Per

Les

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+ 2

Day

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10.1 Outcomes and Events - Identify and count the outcomes of experiments M07.D-S.3.1.1 M07.D-S.3.2.2

10.2 Probability - Understand the concept of probability and the relationship between probability and likelihood - Find probabilities of events

M07.D-S.3.1.1

10.3 Experimental and Theoretical Probability

- Find relative frequencies - Use experimental probabilities to make predictions - Use theoretical probabilities to find quantities - Compare experimental and theoretical probabilities

M07.D-S.3.2.1


Cycle 4 Standards


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


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

Chapter 10: Probability and Statistics

Suggested Dates

Section Lesson Title Lesson Objective Eligible Content

05

/10

– 0

6/0

1

2 D

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+ 2

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10.4 Compound Events - Use tree diagrams tables, or a formula to find the number of possible outcomes - Find probabilities of compound events

M07.D-S.3.2.3

10.5 Independent and Dependent Events

- Identify independent and dependent events - Use formulas to find probabilities of independent and dependent events

M07.D-S.3.1.1 M07.D-S.3.2.2 M07.D-S.3.2.3

10.5 Extension

Simulations Not Assessed

in PA

10.6 Samples and Populations - Determine when samples are representative of populations - Use data from random samples to make predictions about populations

M07.D-S.1.1.1 M07.D-S.1.1.2

10.6 Extension

Generating Multiple Samples - Use multiple samples to make predictions about populations M07.D-S.1.1.1 M07.D-S.1.1.2

10.7 Comparing Populations - Use measures of center and variation to compare populations - Use random samples to compare populations

M07.D-S.1.1.1 M07.D-S.1.1.2

8.2 Perimeters of Composite Figures - Find perimeters of composite figures Not Assessed in

PA


6/04 – 6/12 7 Days

Remediate and Extend by Preparing for Grade 8

Option 1: 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 2: 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 3: 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://philadelphiafed.org/education/teachers/lesson-plans

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


PA Core Standards and Eligible Content by Cycle

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

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).

X

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

X

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

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


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 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.

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

X

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


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 of Eligible Content if Chapters 1-10 Are Taught




100% 85.5% 83% 81.5%

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].

grade 7 big ideas 2017-2018 sy - philasd.org e.g., by testing for equivalent ratios in a table or...

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