PARCC Grade 7 Mathematics Lesson 17: Performance · PDF fileLesson 17: PBA Ratio and ... Students will compute unit rates associated with ratios of fractions. ... Lesson 17: PBA Ratio

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Lesson 17: PBA Ratio and Proportional Relationships Page 1 © 2015 Standards Solution Holding, LLC. All Rights Reserved.

Rationale

Students’ understanding of the multiplicative reasoning used with proportions continues

from 6th grade. Students determine if two quantities are in a proportional relationship

from a table. Fractions and decimals could be used with this standard. Students expand

their understanding of proportional reasoning to solve problems that are easier to solve

with cross-multiplication. Students understand the mathematical foundation for cross-

multiplication.

Goals

To provide opportunities to analyze and represent proportional relationships.

Objectives

Students will compute unit rates associated with ratios of fractions.

Students will recognize and represent proportional relationships between quantities.

Students will decide whether two quantities are in a proportional relationship by testing

for equivalent ratios.

Standard

7.RP.2 Recognize and represent proportional relationships between quantities.

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.

a. Identify the constant of proportionality (unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of proportional relationships.

b. 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.

c. 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.RP.3 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.

Materials

Performance-Based Assessment – Task 1 and/or Task 2 (attached)

Journal

PARCC Grade 7 Mathematics

Lesson 17: Performance-Based Assessment

Ratio and Proportional Relationships


Class Folder Labeled: Lesson 17: Performance-Based Assessment – Ratio and

Proportional Relationships. (At the end of the lesson, place the class papers in the folder.

If students used “scratch” paper, please have students attach the “scratch” paper to their

Mathematics Items handout.)

Procedure

Say, “This year, you will be taking the math PARCC Assessment. It will test all of the

things you have learned this year in math in order to find out if you have mastered the

concepts or if you still need more practice. Today we will be learning about what you will

need to know for the test. You will determine what is easy for you and what is challenging

for you. We will then work on a plan for improving the areas which are difficult for you

right now.”

Assign students to groups of 2 or 3. Give them the Performance-Based Assessment. Tell

students that this is an example of what a Performance-Based Assessment may look like.

Review the directions for the Tasks. Instruct students to record their answers on the

assessment.

Ask students to work in pairs and discuss each Task. Each student should complete their

own assessment. Remind students to use clear explanations in their justification of their

answers.

While the students are working, circulate the room and monitor students’ approaches.

Note patterns of difficulty and/or errors.

When students have finished, ask them to share their answers to the questions.

Assessment or Check for Understanding

Journal writing: in the last 2-3 minutes of class, students should record what they learned

about themselves regarding test taking strategies and the content of the CCSS.

Follow-up

During any Performance-Based Assessment mathematics lesson, engage students in a

discussion of why one task was less challenging and another task more challenging.

PARCC Technology Tips

PARCC equation editors are provided as the answer boxes for responses that include

math, utilizing special mathematical functions. In this lesson, a written response is needed

and the Open Response Equation Editor is provided. It is possible to respond with a

combination of words and math.

It is suggested that letters, numbers, and punctuation symbols from the standard keyboard

be used. Any part of the response that indicates mathematical processes can be described

using the function keys provided in the Open Response Equation Editor. When the

pointer (curser) hovers over a function key, the name of the function appears as a pop-up.

It is NOT possible to create diagrams, models and/or step-by-step solution processes in a

vertical format (such as solving with an algorithm).


Task #1 (PARCC 7.C.4; 7.C.6.1)

Sam described the constant of proportionality as: “The number of candy bars (c)

times the cost of each candy bar is the total cost in dollars (d).”

Complete the equation to represent this constant of proportionality when the

cost of each candy bar is $1.50.

= 1.50 ( )

Complete the ratio table to represent the proportional relationship of candy

bars(c) to cost in dollars (d). Drag and drop the correct selections into the

chart.

candy bars

(c)

0

1

3

2

3

cost in

dollars (d)

0

$1.50

$2.00

$3.00




1

2 $0.50 8

3

4

3

$1.00

Choose

d

c

Choose

d

c

$0.75 3


Connie has $90 to spend. She needs to buy 75 candy bars. The regular price of each

candy

bar is $1.50.

Which of the special pricing offers described below can she use to get 75

candy bars and spend $90 or less?

Select each offer that she can use.

A. 30% off of the regular price

B. BOGO (buy one at regular price, get one free)

C. buy one, get 50% of the second one

D. buy three, get a fourth one free

E. buy two, get the third one free


Task # 2 (PARCC 7.C.4; 7.C.7.1)

Part A

The cost of each candy bar is $1.50.

Sam represented the number of candy bars to the total cost in the graph below.

Does the graph represent the same constant of proportionality as indicated by

the unit rate?

Explain your reasoning.

Enter your answer and explanation in the space provided.





Part B

Sam wants to give candy bars to his 30 classmates on his birthday. Sam has $40.00

to spend on candy bars. The cost of each candy bar is $1.50.

Does Sam have enough money to buy each classmate one candy bar?

Explain how you determined your answer using math or words.

Enter your answer and your explanation or process in the space provided.


# _1_

Score Description

3

Student response includes each of the following 3 elements:

Correct selection in the drop down menu to complete the equation

Correct selections to complete the table

Correct selections of available offers, A, B, and E

Sample Student Response:

d = 1.50c

candy

bars

©

0

1

3

2

3

cost in

dollars

(d)

0

$1.50

$2.00

$3.00

30% off of the regular price

buy one at regular price, get one free

buy one, get 50% of the second one

buy three, get a fourth one free

buy two, get the third one free

2 Student Response includes 2 of the 3 elements.


0 Student Response is incorrect or irrelevant.

1

2

$0.50

4

3

$1.00

x


# _2_ Part A

Score Description

2


Correct answer, the graph does represent the same constant proportionality as the unit rate

Valid explanantion that demonstrates understanding of ratio reasoning.


Yes, the graph does represent the same constant proportionality as the unit rate.

The graph of ratios equivalent to the unit rate forms a straight line through the origin.



# _2_ Part B

Score Description

2


Correct answer, no

Valid explanantion that reflects conceptual understanding of ratio reasoning


No, Sam does not have enough money to buy 30 candy bars. He only has $40 and he needs

$45 to buy 30 candy bars that cost $1.50 each.

The ratio of 1 candy bar to cost is 1 1

2 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 to 1 candy bar. To findhe equivalent ratio for

30 candy bars I multiplied the numerator and denominator by 30. 1 1

2 (30) = 45. Sam would

need $45 to buy 30 candy bars.



Documents

PARCC Grade 7 Mathematics Lesson 17: Performance · PDF fileLesson 17: PBA Ratio and ... Students will compute unit rates associated with ratios of fractions. ... Lesson 17: PBA Ratio