Instructional Week 3: January 20-22
Grade 7 ISTEP+
Focus Topic: Proportional Relationships
Paced Standards:
7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations, such
as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions
within and across measurement systems, percent increase and decrease, and percent error.
PS: 1, 2, 3, 4, 5, 6, 7, and 8 +
Key Vocabulary
Proportional Relationship-when two ratios are equal, they are said to have a proportional relationship.
Gratuities-payment due for service
Commission-payment calculated on the basis of a percentage of the goods sold.
Connection to other 7th grade Standards
7.C.5: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units.
Prerequisite/Foundational Standards
6.NS.9: Understand the concept of a unit rate and use terms related to rate in the context of a ratio
relationship.
6.NS.10: Use reasoning involving rates and ratios to model real-world and other mathematical problems
(e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or
equations).
Teacher Background: Samples Problems for 7.C.6
1. Carol has two cats Rover and Bobo. Rover eats 3.4 a can of cat food each day and Bobo eats ½ of a can of cat
food each day. Cat food costs $5.00 for three cans. It is only sold in 3 can packs.
How much does it cost Carol for a 60-day supply of cat food for her two cats? Show your work.
Extension: Find the cost of cat food for the 29-day supply, a 30-day supply, and a 31-day supply.
Total cans of cat food per month
3.4 + .5 = 3.9 cans/day
3.9 x 60 = 234 cans/month
$5 =
x ;
3cans 234cans
x=$390.00
2. Dan and Alan take turns cutting the grass. Their lawn is 60 yards long and 40 yards wide.
a. What is the area of the yard?
Dan takes an hour to cut the lawn using an old mower.
b. How many square yards does Dan cut in a minute?
Alan only takes 40 minutes using a new mower.
c. How many square yards does Alan cut in a minute?
d. One day they both cut the grass together. How long do they take?
a. 60 x 40 = 2, 400 yards
b. 2400 yd2 = x
; x = 40 yd2/min
60 min
1 min.
c. 2400 yd2 = x
; x = 60 yd2/min
40 min
1 min
d. 40 + 60 = 2400/x ; x =24 min.
3. Jose and Rosie are shopping for sneakers. They see this special offer.
Jose and Rosie both want to find out how much they will save.
Jose says,”20% of $44 is $8.80. That’s a good saving.”
Rosie says, “I think the sneakers are reduced by $11.”
Who is right?________________________________________________
Explain what each person has done to figure out there answer and say what mistake led to the wrong
answer.
Explain why, if the price of somethings is increased by 10% and the new price is reduced by 10% the final
price is less than the original price.
Jose - 44 x 0.2= $8.80 saving
Rosie - $11 savings
Jose is correct. He has correctly calculated the saving by multiplying $44 by 0.20 to show that the savings is
$8.80. Rosie seemed to have divided $44 by 4.
Increase the price by 10% ( 44 X 1.1 = $48.40), then decrease by 10% ( 48.40x .9= $43.56 )
4. Last year, Kim earned $8 per hour at her job. This year, Kim earns $10 per hour at her job. What is the
percent of increase, in dollars earned per hour, from last year to this year?
(10-8)/8 x 100= 25; 25 % increase
Resources for 7.C.6
 This activity provides an opportunity for students to practice calculating tip and tax:
https://www.illustrativemathematics.org/content-standards/tasks/106

These videos provide tutorials for multiple proportion processes. Search “percent” or “proportion” and scroll
down.
http://www.virtualnerd.com/tutorials/?id=Alg1_4_4

MathPlayground.com
http://www.mathplayground.com/percent_shopping.html
http://www.mathplayground.com/mathatthemall2.html

This provides an opportunity for online practice:
http://www.quia.com/cb/55701.html
Process Standards to Emphasize with Instruction.
PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively.
PS.3: Construct a viable argument and critique the reasoning of others.
PS.4: Model with mathematics.
PS.5: Use appropriate tools strategically.
PS.6: Attend to precision.
PS.7: Look for and make use of structure.
PS.8: Look for and express regularity in repeated reasoning.
Instructional Week 3 Assessment
ISTEP+ Grade 7
Name______________________________
(7.C.6) 1. The taxi fare in Gotham City is $2.40 for the first ½ mile and additional mileage charged at the rate of $0.20 for
each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
a.
b.
c.
d.
2 miles
2.3 miles
2.8 miles
3.3 miles
(7.C.6) 2. It takes Tina 10 hours to pick forty bushels of apples. Kayla can pick the same amount in 12 hours. How long will
it take if they work together?
a.
b.
c.
d.
3 hours
4.54 hours
5.45 hours
22 hours
(7.C.6) 3. Hector and Jamal work at the mall at “Video Games R US”. Hector earned $67.50 and Jamal earned
$72.50 on their last paycheck. They decide they want to buy video games. The games are on sale for
15% off for a Valentine’s Day special, plus they each receive a 20% employee discount. There is a 7% state sales
tax. Each video game originally cost $33.00.
Both Hector and Jamal think they can buy three video games each.
a. Show how Hector and Jamal would calculate the cost of buying three video games? Be sure and show all
work.
b. Will both Hector and Jamal be able to purchase three video games? Explain.
Instructional Week 3 Assessment Key
ISTEP+ Grade 7
(7.C.6) 1. D
(7.C.6) 2. C
(7.C.6) 3. 4 points total. Use the ISTEP+ Constructed Response Rubric. Answers will vary.
a. 99(0.85) = 84.15
84.15(0.8) = 67.32
67.32(1.07) =72.03
cost of three video games whose price is reduced by 15%
cost of three video games on sale with employee discount
total cost of three video games with sales tax
b. Only Jamal could afford to buy three video games. His check was for $72.50 and the three video games
including sale price, employee discount and sales tax is $72.03. Hector doesn’t have enough money.
All constructed response problems will be graded using the ISTEP+ Content Rubric.