Illustrative Mathematics
7.RP Art Class, Variation 1
Alignment 1: 7.RP.A.2
The students in Ms. Baca's art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if
the blue and yellow paint are in the same ratio.
The table below shows the different mixtures of paint that the students made.
Yellow
. Blue
C
D
E
2 parts
3 parts
4 parts
6 parts
3 parts
6 parts
6 parts
9 parts
A
B
1 part
2 part
a. How many different shades of paint did the students make?
b. Some of the shades of paint were bluer than others. Which mixture(s) were the bluest? Show work or explain how you know.
Number ofblue parts
c. Carefully plot a point for each mixture on a coordinate plane like the one that is shown in the figure. (Graph paper might help.)
Number of yellow parts
d. Draw a line connecting each point to (0,0). What do the mixtures that are the same shade of green have in common?
Name
Date
Parker is planning to drive from Nashville to Atlanta in his car. Parker started to fill out
the table below showing how far in miles he can travel for each gallon of gas he uses.
2
56
Gallons
Miles
4
168
8
224
10
Use the information in Parker's table to answer the questions below.
a. Complete the table for Parker. Assume the relationship in the table is proportional.
b. Based on the table, how many miles per gallon did Parker's car get? Explain your reasoning
in words.
c. Write an equation that Parker can use to find the distance (d) he can drive on any number of
gallons of gas (g).
d. When Parker's tank is full, it holds 20 gallons. How far can Parker drive on a full tank of gas?
Task
Milan Middle is having a dance in a week. As of today, 4 boys and 3 girls have purchased tickets.
a. After 2 days of sales, 6 girls have purchased tickets with a goal of 24 by the end of the week. Predict
how many boys have purchased tickets. Explain how you determined your answers.
B .If we meet our goal of 24 girls, how many boys will be attending the dance?
c. Develop the table below and explain the pattern.
# of boys
# of girls
d. Predict how many weeks we would need to sell tickets if we want 36 girls to attend.
7.RP.1 7.RP.2a practices 1,4,6,7,8
7.EE.2 Task • zxpre,;sions and E 110 iCHIS
Saving Money
instruction
Common Core State Standard
Use properties of operations to generate equivalent expressions.
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 + 0.5a = 1.0511 means that "increase by 5%" is the same as "multiply by 1.05."
Task Overview
Background
Understanding that dil 'I
can result in equivalent expressions is
an important building block in algebra. Sometimes rewriting an expression in an equivalent form
can result in a problem that is easier to solve. This task helps students discover relationships between
different . forms of an expression in real-world examples using money. In the first part, students will
investigate interest rates (which result in increase by a percent) and in the second part, students
investigate sales rates (which result in decrease by a percent).
Prior to this task, students should have experience with converting percentages to decimal
numbers, multiplying by decimal numbers, and writing algebraic expressions from verbal
descriptions.
The task also provides practice with:
•
multiplying with decimal values
•
calculating percentages
•
writing algebraic expressions from verbal descriptions
Implementation Suggestions
Students may work individually, in pairs, or in small groups to complete one or both parts of the task.
Some students may benefit from the use of calculators for the evaluation portion of this task.
introduction
introduce the task by asking students if they have a savings account to help them save the money they
make or receive as gifts. Do they earn interest on the account? Are they involved in the decision of
where the money is invested (in an account, a CD, or other savings plan)? Do they keep track of the
account balance? What do they know about interest rates?
O Walch Education
Ell
Common Core State Standards Transition Tasks for Mathematics, Grade 7
TEE.2 Task • E r
1"r"
Saving Money
Instruction
When introducing Part 2, ask students if anyone has a family business. How are the prices set?
Are there ever sales designed to help move merchandise? Is anyone involved with any aspects of the
business?
Begin the task by having students recall the difference between an algebraic expression and an
algebraic equation (an equation has an equal sign). If necessary, discuss how the students might
determine if two expressions are equivalent (substitute a value into each expression and see if the
result is the same). Review how verbal expressions translate into mathematical operations (for
example, "increased by" means add to and "reduction amount" means subtractfrom). Determine
whether students will work individually or in pairs and make the appropriate groupings.
Monitoring/Facilitatin.g the Task
Ask questions and prompt student thinking so that they:
•
Use variables to represent unknown amounts.
•
Accurately rewrite percentages as decimal numbers.
•
Remember the rules of multiplying decimal numbers.
•
Think about reasonable answers. in a savings account, should the amount at the end of the
interest period be more or less than the initial amount? At a store, should the sale prices be
more or less than the original price?
•
Determine if two expressions are equivalent.
•
Represent an algebraic expression in verbal form.
Debriefing the Task
•
Upon completion of the task, students should share their results.
•
Ask students to explain how they determined if they should be adding or subtracting the
percentages. Encourage a discussion around reasonableness of answers.
•
Ask students to discuss how they determined that a variable should be used ("an amount")
and how they decided which variable to use.
•
Ask students to describe how they determined that two expressions are equivalent. How is
that shown? (by the use of an equal sign between the two expressions)
•
Ask students to share any difficulties they had with this task. Encourage them to describe how
they addressed those difficulties.
26
Common Core State Standards Transition Tasks for Mathematics, Grade 7
0 Walch Education
71EE2 Task • E: mssions
ExatioH,,s
Saving Money
Instruction
Answer Key
1. 0.02x
2. Multiply the amount invested by 0.02 and add the result to the original amount invested.
3.
+ 0.02x
4. 1.02x
5. The expressions are equivalent. Sample answer: Suppose you invest $200.
200 + 0.02(200) = 204
1.02(200) = 204
The amounts are equal.
6. x + 0.2x = 1.02x, Sample answer: A savings account with a 2% interest rate yields the same
amount as multiplying the amount invested by 1.02.
7. Use the expression 0.10x, for which x is the original price of any item. Multiply the price by
0.10, and the result is the amount by which the price will be reduced.
8. Multiply the original price by 0.10 and subtract the result from the original price.
9. x— 0.10x
10. 0.90x
11. Evaluate each expression using the same original price and confirm that the results are the
same.
Differentiation
Some students may benefit from the use of calculators during this task. Some students may find it
helpful to use one of the online instruction/review tools prior to completing the task.
Students who complete the task early could research various interest rates and calculate earnings
of a certain amount invested.
Technology Connection
Students could use one of the online tools prior to completing the task.
II
Walch Education
Common Core State Standards Transition Tasks for Mathematics, Grade 7
7EE2 Task •
Saving Money
ski s andL. 41
n
Instruction
Choices for Students
Following the introduction, offer students the opportunity to research and use their own interest
rates for the first part of the task. Similarly, they could set their own sales rate for the second part of
the task. You might ask them to find advertised interest rates or sales in the newspaper.
Meaningful Context
This task uses the real-world example of a savings account. Many students have a college fund or
other savings account and could track their own interest earnings. The second part of the task uses
the real-world example ()kale prices. Students should be aware of various ways to represent sale
prices or interest rates.
Recommended Resources
•
Algebra Tiles
WWW I ch.cont/rr/CCTIG7AloebraTiles
• alent.
Students can use this interactive tool to determine which expressions are equiv
•
Equivalent Expressions
WWW aidismilLy±
u CCITGrEvivExpEssions
This applet uses algebra tiles to explore equivalent expressions.
•
Money Rates
www.walch.com irr CCTTGAnterestRates
Look up current daily interest rates for various types of accounts.
28
Common Core State Standards Transition Tasks for Mathematics, Grade 7
Walch Education
NAME:
7.EE.2 Task •
Saving Money
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Part 1
You are planning to open a savings account. You want to shop around to get the best interest rate so
you can earn the most money.
1. The first bank you visit has an interest rate 4'2% per year. Write an algebraic expression to
represent the amount of interest you would earn on an amount of money after one year.
2. How would you determine the total amount of money you would have in your savings account
at the end of one year? Describe fully.
3. Write an algebraic expression to represent the amount you described in problem 2, your total
savings after one year in the account.
4. You visit a different bank that advertises that they will multiply the amount of money that you
have in your savings account by 1.02. Write an algebraic expression to represent this scenario.
continued
29
© Welch Education
Common Core State Standards Transition Tasks for Mathematics, Grade 7
NAME:
71E2 Task • k\xoressithis
Saving Money
5 Compare the two algebraic expressions you wrote. Describe their relationship. Select an amount
of money you think you will have to open your account. Use that amount to evaluate the two
expressions you wrote. How do the amounts compare?
6. Using algebraic notation, develop an equation from the above information. Write a verbal
statement that corresponds to the algebraic notation.
continued
30
Common Core State Standards Transition Tasks for Mathematics, Grade 7
Walch Education
NAME:
7.EE.2 Task •
Saving Money
,rePsions
Part 2
Your mother owns a skateboard shop. You are helping to price items for an upcoming sale. All prices
will be reduced by 10% for the sale.
7. Flow can you determine the amount by which the original price will be reduced for any item?
Describe fully.
8. Ilow can you determine the sale price of an item? Describe fully.
9. Write an algebraic expression to represent the sale price of an item.
10. Think about the expression you wrote. Write another algebraic expression to represent the sale price.
11. How can you determine that the two expressions are equivalent? Describe your reasoning.
0 Watch Education
Common Core State Standards Transition Tasks for Mathematics, Grade 7