7 Math Curricul… · Web viewSolve word problems leading to equations of the form . px + q = r...

Unit Title: Proportional RelationshipsGrade Level: 7

Timeframe: Marking Period 1

Essential Questions

(1) Can we become confident in our knowledge of quantities, units, and values of measuring that are used in relationships?(2) Can we become effective and efficient at representing relationships in all four traditional representations—tables, symbols, graphs, and narratives?(3) Can we become effective and efficient at asking and answering typical mathematical questions? (4) Can we become effective and efficient at talking about relationships given in any representation?(5) Can we become effective and efficient at reading and understanding others’ relationships and questions given in any representation?(6) Can we become effective and efficient at identifying patterns in relationships, and create simultaneous ones for any variation of quantities?(7) Can we become effective and efficient at creating equations and expressions given any scenario?

New Jersey Student Learning Standards

Standards/Cumulative Progress Indicators (Taught and Assessed):

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. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

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.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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

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

CAR © 2009

or vertical number line diagram.a) Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.b) Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a

number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.c) Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line

is the absolute value of their difference, and apply this principle in real-world contexts.d) Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations,

particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

c) Apply properties of operations as strategies to multiply and divide rational numbers.d) Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

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

21st Century Skills Standard and Progress Indicators:

CRP4. Communicate clearly and effectively and with reason.CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

Instructional Plan ReflectionDiagnostic AssessmentGrade 7 Math – Cumulative Assessment

SLO - SWBAT Student Strategies Formative Assessment Activities and Resources Reflection

CAR © 2009

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. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Do Now – Count around the room. Make combinations. [5 minutes]

Direct Instruction/Modeling

Small Group Instruction

Constructed responses from the Type 2-3 Bank and Carnegie Learning

PARCC Released Items

Performance Tasks

Standards Based Problems Aligned to Touchpoint and End of Unit Assessment

Exit Ticket - Standards Based Problems Aligned to Touchpoint and End of Unit Assessment

7.RP.1 – Touchpoint

Standards Based Constructed Response ExampleThe table shows distances run by Jeremy and Mateo in particular amounts of time.

Part A What is Jeremy’s running rate, in miles per hour?

Part B What is Mateo’s running rate, in miles per hour?

Part C Jeremy and Mateo both plan to run 7 miles. They will run at their rates given in the table. How many hours apart should they start so that they finish at the same time?

Constructed Response ResourcesEdConnect 7.RP.1 - Type 2-3 Bank

Questions 1-9

Carnegie Learning Course 2

PARCC Released Items#30

https://prc.parcconline.org/system/files/Grade%2007%20Math

%20-%20Item%20Set.pdf

Performance Task ResourcesIllustrative Mathematics

Performance Tasks 7.RP.1https://

www.illustrativemathematics.org/content-standards/7/RP/A/ 1

PMI Math Labshttps://njctl.org/courses/math/7th-grade/ratios-proportions/

Direct Instruction ResourcesEngageNY Lessons 7.RP.1

https://www.engageny.org/search-site?search=7.RP. 1

Learnzillion Lesson Plans Proportional Reasoning Lessons 3-9

https://learnzillion.com/resources/64233-proportional-

reasoning

PMI SMART Presentations https://njctl.org/courses/math/7th-

grade/ratios-proportions/

CAR © 2009

https://njctl.org/courses/math/7th-grade/ratios-proportions/


https://learnzillion.com/resources/64233-proportional-reasoning



https://www.engageny.org/search-site?search=7.RP.




https://www.illustrativemathematics.org/content-standards/7/RP/A/



https://prc.parcconline.org/system/files/Grade%2007%20Math%20-%20Item%20Set.pdf



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






Performance Tasks




Standards Based Constructed Response ExampleThe baseball coach of Freeville High School wants to purchase 25 T-shirts for the boys’ team and 20 T-shirts for the girls’ team. On ShopWithUs.com’s website, the boys’ T-shirts will cost $100 and the girls’ T-shirts will cost $80.

Part A. Plot the cost and number of T-shirts for each team in the graph below. Use the points you plotted to find out if the cost per T-shirt is the same for the boys’ team and the girls’ team. Assume the prices are constant across a range of orders. Explain your answer.

Part B. Use the graph to determine the constant of


Questions 1-14


PARCC Released Items#3, 7, 11, 14, 26





www.illustrativemathematics.org/content-standards/7/RP/A/ 2

PMI Math Labshttps://njctl.org/courses/math/7th-grade/ratios-proportions/


https://www.engageny.org/search-site?search=7.RP. 1

Learnzillion Lesson Plans Proportional Reasoning Lessons 3-9


reasoning



CAR © 2009
















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.

proportionality.

Part C. Write an equation using the constant of proportionality to find, C, the cost of a set of x number of T-shirts. Use the equation to fill in the table below.

Use words, numbers, and/or pictures to show your work.

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,




Constructed responses from the Type 2-3 Bank and Carnegie

7.EE.4 – Touchpoint

Standards Based Constructed Response ExampleTom has a summer job that pays $7.25 per hour. Out of his earnings, he buys a bus pass for $12.50 each week.

Part A Tom worked 27 hours the first week. What was Tom’s pay the first week, not counting taxes, after he paid for a bus pass? Show or explain your work.

Part B Write an inequality that can be used to determine the number of hours (h) Tom must work each week in order to make at least $240.00 each week not, counting taxes, after he paid for a bus pass.

Constructed Response ResourcesEdConnect 7.EE.4 - Type 2-3 Bank

Questions 1-18


PARCC Released Items#10, 13




Performance Tasks 7.EE.4

CAR © 2009




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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

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

Learning PARCC Released

Items Performance

Tasks Standards Based

Problems Aligned to Touchpoint and End of Unit Assessment


Part C Solve the inequality in Part B for hand identify the minimum number of whole hours Tom must work in order to make at least $240.00 each week, not counting taxes, after he paid for a bus pass. Show or explain your work.

https://www.illustrativemathematics.org/content-standards/7/EE/B/4

PMI Math Labshttps://njctl.org/courses/math/7th-grade/equations-inequalities-7th-

grade/

Direct Instruction ResourcesEngageNY Lessons 7.EE.4

https://www.engageny.org/search-site?search= 7.ee.4

Learnzillion Lesson Plans Proportional Reasoning Lesson 8


reasoning

Learnzillion Lesson Plans Solving Equations Lessons 6-7; 9-14

https://learnzillion.com/resources/64238-solving-equations

PMI SMART Presentations https://njctl.org/courses/math/7th-grade/equations-inequalities-7th-

grade/

CAR © 2009

https://njctl.org/courses/math/7th-grade/equations-inequalities-7th-grade/








https://www.engageny.org/search-site?search=6.ee.6








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. 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.

a) Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b) Understand p + q as the number






Performance Tasks


7.NS.1 – Touchpoint

Standards Based Constructed Response ExampleAs part of a science project, Wendy recorded the average daily temperature in New York for six days.

Part A. Complete the table below to calculate the change in the average temperature from the previous day. Indicate whether the change is an

increase or decrease in the average

Constructed Response ResourcesEdConnect 7.NS.1 - Type 2-3 Bank

Questions 11-16; 19-33


PARCC Released Items#1, 9, 15




Performance Tasks 7.NS.1https://www.illustrativemathematics.org/content-standards/7/NS/A/1

PMI Math Labshttps://njctl.org/courses/math/7th-

grade/numbers-and-operations-7th-grade/

Direct Instruction ResourcesEngageNY Lessons 7.NS.1

CAR © 2009

https://njctl.org/courses/math/7th-grade/numbers-and-operations-7th-grade/



https://www.illustrativemathematics.org/content-standards/7/NS/A/1






located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c) Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d) Apply properties of operations as strategies to add


temperature.

Part B. Between which two days was the change in the average temperature the greatest? By how much did it decrease or increase?

Part C. What was the change in the average temperature from Tuesday to Wednesday?

Part D. Represent the change in the average temperature from Thursday to Friday on the number line.


https://www.engageny.org/search-site?search=7.ns.1

Learnzillion Lesson Plans Grade 7 Unit 4

https://learnzillion.com/resources/64236-rational-number-

operations-addition-and-subtraction

PMI SMART Presentations

https://njctl.org/courses/math/7th-grade/numbers-and-operations-

7th-grade/

CAR © 2009




https://learnzillion.com/resources/64236-rational-number-operations-addition-and-subtraction





and subtract rational numbers.

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b) Understand that integers can be divided, provided






Performance Tasks




Standards Based Constructed Response ExampleSewing Project

James is working on project. James is working on a sewing project. The fabric store

Keeps cloth in rolls that are yards wide.

Part A

James needs square yards of yellow cloth for his project. He needs to tell the store clerk the length of the cloth he needs.

Find the length of the cloth James needs in yards.

Part B

James cuts a piece of yellow cloth in the shape of a

rectangle that is the width and the length of the original piece.

Find the dimensions of the piece that he cuts.


Questions 21-50






Performance Tasks 7.NS.2https://

www.illustrativemathematics.org/content-standards/7/NS/A/2




https://www.engageny.org/search-site?search=7.NS.2

Learnzillion Lesson Plans Grade 7; Unit 5

https://learnzillion.com/resources/64237-rational-number-

operations-multiplication-and-division

CAR © 2009

https://learnzillion.com/resources/64237-rational-number-operations-multiplication-and-division














that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

c) Apply properties of operations as strategies to multiply and divide rational numbers.

d) Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

What fraction of the area of the original piece is the area of the new piece?

Part C

James buys some blue cloth. The width of the blue

cloth is and the length is yards.

Convert the length of the blue cloth to decimal form. Show your work.

Is the decimal form a rational number? Explain why or why not.

Part D

James paid $3.50 per yard for blue cloth that he purchased.

Write the price of the blue cloth and the length of the blue cloth as improper fractions.

Determine the total price of the blue cloth by finding the product of the two improper fractions. State your answer as a decimal, rounding to the nearest tenth, if necessary.

Determine the total price of the blue cloth by finding the product of the price per yard and the

decimal form of If necessary, round the

decimal form of to the nearest hundredth.



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Are the prices equivalent? Explain why or why not.

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






Performance Tasks




Standards Based Constructed Response ExampleJavier made some purchases by check and recorded them in his checkbook. His checkbook has columns to write the check number, date, a description, the amount of the payment or deposit, and the balance (the amount left in his account). For example, on May 8 Javier bought $63.97 worth of groceries at Food Market using check 421. He entered in this information in his checkbook and subtracted the purchase amount of $63.97 from his starting balance of $452.38, as shown below.

Part A. The list below shows the purchases and deposits he made during a two-week period after


Questions 1-15





Performance Task Resources Illustrative Mathematics

Performance Tasks 7.NS.3https://www.illustrativemathematics.org/content-standards/7/NS/A/3







CAR © 2009















May 8. Fill in the checkbook to show each transaction and the balance after each one.

May 10—Deposited $237.04 from his paycheck

May 11—Bought 2 movie tickets for $11.25 each (check 422)

May 13—Paid gym membership fee of $29.00 (check 423)

May 16—Deposited $50.00 check from Grandma

May 17—Sent $25.00 check to charity (check 424)

May 18—Paid $39.99 for phone bill (check 425)

May 20—Paid $44.21 for gas (check 426)

May 21—Paid his share of pizza delivery, which cost $34.24 and was split 4 ways (check 427)

Part B. Javier wants to buy a new stereo system and 2 new speakers for his room. The stereo system costs $375 and each speaker costs $79.99. Does Javier have enough in his checking account after the May 21 transaction to make this purchase? Explain.

Use words, numbers and/or pictures to show your work.

Summative Assessment

Grade 7 Math – End of Unit 1 Assessment in EdConnect

CAR © 2009

Unit Title: Measuring, Representing our measuring, and Reading others’ representations of measuring Grade Level: 7


Essential Questions

(1) Can we become confident in our knowledge of quantities, units, and values of measuring that are used in relationships?(2) Can we become effective and efficient at representing relationships in all four traditional representations—tables, symbols, graphs, and narratives?(3) Can we become effective and efficient at asking and answering typical mathematical questions? (4) Can we become effective and efficient at talking about relationships given in any representation?(5) Can we become effective and efficient at reading and understanding others’ relationships and questions given in any representation?



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. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

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

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.

CAR © 2009

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.



Instructional Plan ReflectionDiagnostic AssessmentGrade 7 Math – Cumulative AssessmentGrade 7 Math – End of Unit 1 AssessmentUnit 1 Touchpoints

SLO - SWBAT Student Strategies Formative Assessment Activities and Resources Reflection7.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






Performance


Standards Based Constructed Response ExamplesAt a department store, sweaters are on sale for 30% off the original price. Scarves are not on sale and cost $2.10 each, but for every two scarves purchased, the shopper receives one free.

Part A One sweater has a sale price of $10.50. Another sweater has a sale price of $12.60. What was the total original price for these two sweaters? Show all your work and explain your answer.

Part B The sales tax on clothing is 8%. What is the total cost for both sweaters from Part A, plus six scarves, including tax? Show all your work and explain your answer.

Tom has a summer job that pays $7.25 per hour. Out of his earnings, he buys a bus pass for $12.50 each


Questions 1-14





Performance Task ResourcesIllustrative Mathematics Performance Tasks 7.EE.3

https://www.illustrativemathematics.org/

content-standards/7/EE/B/3

CAR © 2009







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. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Tasks Standards Based

Problems Aligned to Touchpoint and End of Unit Assessment


week.

Part A Tom worked 27 hours the first week. What was Tom’s pay the first week, not counting taxes, after he paid for a bus pass? Show or explain your work.

Part B Write an inequality that can be used to determine the number of hours (h) Tom must work each week in order to make at least $240.00 each week not, counting taxes, after he paid for a bus pass.

Part C Solve the inequality in Part B for hand identify the minimum number of whole hours Tom must work in order to make at least $240.00 each week, not counting taxes, after he paid for a bus pass. Show or explain your work.


grade/


https://www.engageny.org/search-site?search=7.EE.3



reasoning-with-percents


grade/

CAR © 2009




https://learnzillion.com/resources/64235-proportional-reasoning-with-percents








7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.






Performance Tasks




Standards Based Constructed Response ExamplesMike went to the store to buy some shirts. The price of the shirts he wanted to buy was $45 each. The store was offering the following on all shirts at that price:

Buy 1 shirt and get any 2 shirts 40% off.

Mike decided to buy the 3 shirts. If the sales tax on his purchase was 8.25%, how much money did he save by buying the shirts at the discounted price?

Because the Moon has a weaker gravitational pull than Earth, objects on the Moon weigh less than they would on Earth. An astronaut who weighs 185 pounds on Earth weighs only 31 pounds on the Moon.

Part A. If another astronaut weighs 175 pounds on Earth, about how much would they weigh on the Moon?

Part B. A rock weighs 60 pounds on the Moon. About how much would the rock weigh on Earth?

Part C. By what percentage does the weight of the astronaut decrease on the Moon, compared to their weight on Earth?

Part D. By what percentage does the weight of the astronaut increase on Earth, compared to their weight on the Moon?



Questions 1-16


PARCC Released Items#18; 24





www.illustrativemathematics.org/content-standards/7/RP/A/3




https://www.engageny.org/search-site?search=7.RP.3



reasoning-with-percents



CAR © 2009










https://www.illustrativemathematics.org/content-standards/7/RP/A/3






7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."






Performance Tasks




Standards Based Constructed Response ExampleA floral shop charges $7 for a vase and $1.75 per flower for their custom arrangements.

Part A Write an expression to represent the cost of a custom arrangement with f number of flowers.

Part B What effect does changing the cost per flower have on the expression?

Part C If a customer bought 2 custom arrangements with the same number of flowers in each arrangement, explain how the expression would need to be changed to represent the customer’s total cost.

Part D If a customer bought a custom arrangement for $28, how many flowers were in the arrangement? Show or explain your work.

Constructed Response ResourcesEdConnect 7.EE.2- Type 2-3 Bank

Questions 1-4







content-standards/7/EE/A/2


grade/



Learnzillion Lesson Plans Solving Equations



grade/

CAR © 2009











https://www.illustrativemathematics.org/content-standards/7/EE/A/2






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






Performance Tasks




Standards Based Constructed Response ExampleMcKenna has $30. She wants to save at least $95 to buy a digital camera. McKenna will save $4 per week.

Part A Write an inequality that represents this situation. Let n represent the number of weeks that McKenna saves $4.

Part B Solve the inequality.

Part C What is the least number of whole weeks McKenna will need to save $4 per week in order to save at least $95?


Questions 1-3; 6


PARCC Released Items#4; 16






grade/



Learnzillion Lesson Plans Solving Equations



https://njctl.org/courses/math/7th-grade/equations-inequalities-7th-

grade/

CAR © 2009

















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.






Performance Tasks



7.G.4 – Touchpoint

Standards Based Constructed Response ExampleAbby drew a map of her rectangular bedroom.

Abby drew a larger version of the map using a ratio of 1 to 4.

Part A The length of Abby’s bed is 6 inches on the larger map. In inches, what is the length of the bed, x, on Abby’s original map?

Part B In square inches, what is the area of Abby’s bedroom on the larger map?

Part C The area of Abby’s rug is 0.4375 square inches on the original map. In square inches, what is the area of Abby’s rug on the larger map?

Constructed Response ResourcesEdConnect 7.G.4 - Type 2-3 Bank

Questions 8-12





Performance Task ResourcesIllustrative Mathematics Performance Tasks 7.G.4


content-standards/7/G/B/4


grade/2d-geometry/

Direct Instruction ResourcesEngageNY Lessons 7.G.4

https://www.engageny.org/search-site?search=7.g.4

Learnzillion Lesson Plans 2-D Figures

https://learnzillion.com/resources/64243-2-d-figures


https://njctl.org/courses/math/7th-grade/2d-geometry/

CAR © 2009









https://www.illustrativemathematics.org/content-standards/7/G/B/4






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.






Performance Tasks




Standards Based Constructed Response ExampleIn order to select boxes for its products, a company is considering the volumes and costs of two box options. For both options, the cost per square foot for the box material is $1.05. The dimensions of the boxes, in feet, are shown in the table.

Length Width HeightBox X 6 4 2Box Y 6 5 3

Part A

One of the company's products is a skateboard. The skateboard is packaged without wheels, so it is not very tall, but it has a large base. The company needs to determine if the box options can hold the skateboards. What is the area of the largest face of each box?

Part B

The company also sells wheels for its skateboards. The company needs to determine which box option can hold more wheels. What is the volume of each box?

Part C

The company needs to determine how much it would save by selecting the less-expensive box. Write and solve an equation that represents the difference between the cost of the material for Box X and the cost of the material for Box Y.


Questions 15-26


Performance Task Resources Illustrative Mathematics Performance Tasks 7.G.6



grade/2d-geometry/

https://njctl.org/courses/math/7th-grade/geometry/



Learnzillion Lesson Plans 2-D Figures


Learnzillion Lesson Plans 3-D Shapes

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Unit Title: StatisticsGrade Level: 7


Essential Questions

(1) Can we become effective and efficient at identifying what a statistical question is which a question about a population?(2) Can we become effective and efficient representing statistical values?(3) Can we become effective and efficient answering and answering questions about central tendencies, variability, outliers and adding or subtracting data points?(4) Can we become effective and efficient about talking statistical values?(5) Can we become effective and efficient about reading statistical values?



7.SP.A.1Understand 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.

7.SP.A.2Use 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. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Draw informal comparative inferences about two populations.

7.SP.B.3Informally 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. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.


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http://www.corestandards.org/Math/Content/7/SP/B/4/


http://www.corestandards.org/Math/Content/7/SP/A/2/


7.SP.A.1Understand 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.






Performance Tasks



7.SP.1 – Touchpoint

Standards Based Constructed Response ExampleA school board wants to conduct a survey about the mode of transportation students use to get to school. There are a total of 300 students at the school.

Part A. Identify the sample and determine the population for this survey.

Part B. The school board has determined two methods to do the survey.

Method 1: Survey every 10th student from the list of the school directory.

Method 2: Survey the first 30 students who enter the school.

Identify the type of sampling used in each survey method.

Part C. Which survey method should the school board use and why?

Part D. In the survey the school board conducted, 12 out of 30 students said they rode their bikes to school. Based on this result, about how many students at the school do not ride their bikes to school?


Constructed Response ResourcesEdConnect 7.SP.1 - Type 2-3 Bank

Questions 1-5





Performance Task ResourcesIllustrative Mathematics Performance Tasks 7.SP.1


content-standards/7/SP/A/1


grade/statistics-probability/

Direct Instruction ResourcesEngageNY Lessons 7.SP.1

https://www.engageny.org/search-site?search=7.SP.1


https://learnzillion.com/resources/64242-sampling-inferences-and-comparing-

populations



7.SP.A.2 Do Now – Count around 7.SP.2 – Touchpoint Constructed Response Resources

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https://njctl.org/courses/math/7th-grade/statistics-probability/


https://learnzillion.com/resources/64242-sampling-inferences-and-comparing-populations







https://www.illustrativemathematics.org/content-standards/7/SP/A/1







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. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

the room. Make combinations. [5 minutes]





Performance Tasks



Standards Based Constructed Response ExampleTamara is interested in finding out which letters of the alphabet are most common as first letters of people’s names.

Tamara conducted a survey and recorded the initials of the first names of 116 males and 104 females of all ages. She made the chart below to show her findings.

EdConnect 7.SP.2 - Type 2-3 BankQuestions 1-4







content-standards/7/SP/A/2







populations



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Part A. What are the five most common initials for male names? For female names?

What percentage of the male names start with J? Give your answer to the nearest 0.1 percent.

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What percentage of the female names start with M? Give your answer to the nearest 0.1 percent.

Part B. There are about 155,000,000 males and 160,000,000 females in the United States. If Tamara’s survey is representative of the whole country, about how many males have a name that starts with J? About how many females have a name that starts with M? Show your work. Give your answers to the nearest hundred thousand.

Part C. Find the population of your city. Use the results of Tamara’s survey to estimate the number of people in the city with J names.

Part D. Tamara wonders how the first letters of names compare with the first letters of words in general. She has the idea of counting the number of pages for each letter in a dictionary. Her results are below.

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7.SP.B.3Informally 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. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.






Performance Tasks




Standards Based Constructed Response Example

Julie wants to compare the heights of two types of tomato plants, Type A and Type B, for her vegetable garden. She thinks the mean height of Type A plants will be greater than the Type B, but she doesn’t know how much greater. She also wants to know about the variability of the heights of each plant type. She uses the data she collects to generate the list below.

Part A. Create two dot plots using the same scale to help Julie compare her data sets.

Part B. Julie observes that there is some overlap in the sets. Calculate the mean height of each of these tomato plants. Round your answers to the nearest whole number. What is the difference in the mean height of these tomato plants?

Part C. Compare the variability of the sets. Look at the mean heights and the variability of the sets to make a comparison statement about the two sets.



Questions 1-2




content-standards/7/SP/B/3







populations



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https://www.illustrativemathematics.org/content-standards/7/SP/B/3




7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.






Performance Tasks




Standards Based Constructed Response ExampleRhonda recorded a random sample for the state English test scores of 40 7th graders and 40 8th graders. A score of 4 is the highest score and a score of 0 is the lowest score.

Rhonda claimed that 8th graders performed better than 7th graders on the state English test.

Part A Use two measures of center (mode and median) to justify Rhonda’s claim that 8th graders performed better than 7th graders on the state English test. Be sure to name and include the values


Questions 1-6




content-standards/7/SP/B/4







populations



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of the measures used.

Part B Use a measure of center (mean) to show that Rhonda’s claim is notvalid. Be sure to name and include the values of the measures used. Show or explain your work.

Part C Which grade had less variability in its scores? Be sure to name and include the values of the measures used. Show or explain your work.



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Unit Title: Probability Models and Geometric Reasoning

Grade Level: 7


Essential Questions

1. Can we become confident in our knowledge of quantities, units, and values used in experiments we find in probability models?2. Can we become effective and efficient at creating probability models?3. Can we become effective and efficient at representing probability models?4. Can we become effective and efficient at asking and answering questions about probability models?5. Can we become effective and efficient at talking about probability models and questions asked about probability models?6. Can we become effective and efficient at reading and understanding others’ probability models and questions asked about probability their 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. 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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7. SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

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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. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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. 21st Century Skills Standard and Progress Indicators:




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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.






Performance Tasks




Standards Based Constructed Response Example A bag contains eight congruent pyramids: 5 red, 2 blue, and 1 black. Pyramids are randomly drawn from the bag and are not replaced.

Part A What color is most likely to be drawn from the bag on the first draw? Explain why you know your answer is correct.

Part B What is the probability, in simplest fraction form, of drawing a blue pyramid from the bag on the first draw? Show or explain your work.

Part C What is the minimum number of pyramids you must draw from the bag, without looking at the color, to guarantee that you have drawn at least 1 red pyramid? Explain your answer.


Questions 1-2



Performance Tasks 7.SP.5https://

www.illustrativemathematics.org/content-standards/7/SP/C/5





Learnzillion Lesson Plans Grade 7; Units 8-9

https://learnzillion.com/resources/64240-probability-of-

simple-events


compound-events



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https://learnzillion.com/resources/64241-probability-of-compound-events



https://learnzillion.com/resources/64240-probability-of-simple-events







https://www.illustrativemathematics.org/content-standards/7/SP/C/5



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.

For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.






Performance Tasks




Standards Based Constructed Response Example A fruit juice company uses a machine to fill juice bottles. On average, the machine makes an error in the amount of juice it adds to 1 out of every 40 bottles.

Part 1. On average, how many errors would the machine make if it filled 600 bottles with juice?

The company is going to purchase a second machine. This machine makes 1 error out of every 125 bottles.

Part 2. How many fewer errors would the new machine make than the first machine if each of them fill 1,000 bottles with juice?

The company can add a device to the second machine that will identify mistakes and fix them. The device will fix 98% of the mistakes the machine makes. Each mistake the device fixes will save the company about $0.25.

Part 3. How many bottles of juice on average could be filled by the second machine before a total of 10 mistakes are not fixed by the device?

Part 4. The device costs $500. How many bottles of juice would be filled by the second machine before the savings from the device would equal its cost?


Questions 1-10














simple-events


compound-events

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7. SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the






Performance Tasks




Standards Based Constructed Response ExampleThe school band has 64 students. The number of students who play each instrument is shown in the table.

One student from the band will be selected at random to announce the order of the musical


Questions 1-12











simple-events

https://learnzillion.com/

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probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

compositions for a concert. Part A What is the probability that the student selected will be a flute player? Give your answer as a fraction reduced to lowest terms. Show or explain your work. Part B How much more likely is it that a clarinet player will be selected than a trombone player? Give your answer as a fraction reduced to lowest terms. Show or explain your work. Part C Which two combined instrument sections are as likely to have a student selected as the trumpet section is to have a student selected? Show or explain your work.

resources/64241-probability-of-compound-events



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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






Performance Tasks




Standards Based Constructed Response ExampleJack plays basketball for his school team. When Jack attempts free throws, on average he makes 75% of his attempts and misses 25% of his attempts. Suppose Jack attempts 12 free throws. To find the probability that Jack will make at least 9 of the 12 attempts, a simulation modeling his free throws using random numbers from 1 to 4 is created. Numbers 1, 2, and 3 represent attempts Jack makes and number 4 represents attempts Jack misses. The results of the simulation are shown below.

Part A. Complete the last column of the simulation to


Questions 1-11














simple-events


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the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

find the baskets he makes.

Part B. Calculate the experimental probability that Jack scores at least 75% of his baskets.

Part C. Charlie also plays basketball for the school team. When Charlie shoots free throws, he usually makes 60% of the baskets he shoots.

Design a simulation using random numbers to estimate the probability that Charlie will make 9 of the next 15 baskets he shoots. Be sure to explain what numbers you would use and how you would calculate the experimental probability.


compound-events

PMI SMART Presentationshttps://njctl.org/courses/math/7th-


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7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.






Performance Tasks




Standards Based Constructed Response ExampleJay is trying to make a reusable corner triangular shelf. He evaluates different lengths for the sides of the triangle as follows.

Part A. Jay decides to make a triangular shelf with sides 4 centimeters (cm), 4 cm, and 10 cm long. Use a ruler to draw the three measures and explain whether Jay could build such a shelf.

Part B. Jay also makes a triangular shelf ABC with side length

Determine how many possible Jay can construct using these measures. Use a compass and ruler to construct the possible triangular designs Jay can make.

Part C. Jay is not satisfied with the shelves he has made so far. He decides to make a triangular shelf with all equal angles that can be of any side length. Use a compass and ruler to construct the design Jay has decided to make and label it.



Questions 1-9







content-standards/7/G/A/2

PMI Math Labshttps://njctl.org/courses/math/7th-grade/drawing-geometric-figures/


https://www.engageny.org/search-site?search=7.G.2

Learnzillion Lesson Plans Scale Drawings

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https://www.illustrativemathematics.org/content-standards/7/G/A/2






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.






Performance Tasks




Standards Based Constructed Response ExampleThe map shows intersections of 4 streets. Jackson Avenue and Jefferson Street are straight lines. Jefferson Street and Washington Boulevard intersect at a right angle.

Part A What is the measure of the angle formed by Washington Boulevard and Jackson Avenue NE?

Part B What is the measure of the obtuse angle formed by Jefferson Street and Jackson Avenue SW?

Part C What is the measure of the angle formed by Jackson Avenue SW and Lincoln Avenue?


Questions 1-4




content-standards/7/G/B/5


grade/2d-geometry/



Learnzillion Lesson Plans from Grade 7 Units 11, 12, & 14https://learnzillion.com/

resources/64468-7th-grade-math


grade/2d-geometry/

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https://learnzillion.com/resources/64468-7th-grade-math

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Grade 7 Math – End of Unit 4 Assessment in EdConnectGrade 7 Math – Cumulative AssessmentDiagnostic Assessment

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