Instructional Week 4: January 25-29
Grade 7 ISTEP+
Focus Topic: Proportional Relationships
Paced Standards:
7.AF.9: Identify real-world and other mathematical situations that involve proportional relationships.
Write equations and draw graphs to represent proportional relationships and recognize that these
situations are described by a linear function in the form y = mx, where the unit rate, m, is the slope of
the line.
PS: 1, 2, 3, 4, 5, 6, 7, and 8 +
Key Vocabulary
Proportional relationship: two quantities vary directly with one and other.
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.AF.9
1. Coffee costs $18.96 for 3 pounds.
a. What is the cost for one pound of coffee?
$6.32 cost per pound
b. At this store, the price for a pound of coffee is the same no matter how many pounds you buy. Let x be
the number of pounds of coffee and y be the total cost of x pounds. Draw a graph of the relationship
between the number of pounds of coffee and the total cost.
c. Where can you see the cost per pound of coffee in the graph? What is it?
The cost per pound is at the point (1, 6.32)
As the slope of the line: $6.32 per pound.
2.
The table below shows the cost of gum packs. Represent this relationship using a graph and equation. Be
sure to define your variables and label your axes.
x = Number of packs of gum
y = cost in dollars
Equation: y = 1.5 x
Be sure and explain that the graph should not include negative x or y values based on the definition of
each variable. You cannot have a negative number of packs of gum.
3.
Emmanuel reads 2 pages every 3 minutes.
a. Write an equation that shows the relationship between the number of pages he reads (p) and the
number of minutes he spends reading (m).
p = 2/3 m
b. Draw a graph of the relationship between the number of pages Emmanuel reads versus the total
minutes. Be sure and label the axes.
c. Mark on the graph where it shows how many minutes Emmanuel read if he read 16 pages.
24 minutes
Resources for 7.AF.9
http://www.onlinemathlearning.com/variation-algebra-2.html
http://www.ck12.org/algebra/Applications-Using-Direct-Variation/
https://www.illustrativemathematics.org/content-standards/tasks/101
Process Standards to Emphasize with Instruction of 7.AF.1
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 4 Assessment
ISTEP+ Grade 7
Name______________________________
(7.AF.9). 1. Crystal and Hayden were at track practice. The track is 2/5 kilometers around.
 Crystal ran 1 lap in 2 minutes.
 Hayden ran 3 laps in 5 minutes.
a. Construct a table for the number of laps and the number of kilometers.
Number of Laps
Number of Kilometers
b. How many minutes does it take Crystal to run one kilometer? What about Hayden?
c. How far does Crystal run in one minute? What about Hayden?
d. Who is running faster? Explain your reasoning.
(7.AF.9) 2. The cost of filling up a tank of gas is modeled by the equation y = 1.97x at the Speedway Gas
Station, where x is the number of gallons of gas purchased and y is the total cost of the gas.
a. How much will 13 gallons of gas cost?
b. Interpret the slope of the line.
c. How many gallons of gas can be purchased for $27.58?
Instructional Week 4 Assessment Key
ISTEP+ Grade 7
(7.AF.9) 1. 8 points total, 2 points per section. Use the ISTEP+ Constructed Response Rubric. Answers will vary.
a.
Number of Laps
1
2
3
4
5
Number of Kilometers
2/5
4/5
6/5
8/5
2
b. Crystal
Hayden:
c. Crystal: She runs 1 lap in 2 minutes so she runs ½ lap in 1 minute. Since 1 lap is 2/5 km. ½ lap is 1/5
km. So she runs 1/5 km in one minute.
Jayden runs 1 lap in 5/3 minutes, he will run 3/5 laps in 1 minute. Since Hayden runs 1 km in 25/6
minutes, he will run 6/25 km in 1 minutes.
d. Hayden runs the same distance in less time than Crystal, so Hayden is running faster than Crystal.
(7.AF.9) 2. 6 points total, 2 points per section. Use the ISTEP+ Constructed Response Rubric. Answers will vary.
a. $25.61 for 13 gallons of gas
b. The slope of the line is 1.97 which is the cost of one gallon of gas.
c. 14 gallons of gas
All constructed response problems will be graded using the ISTEP+ Content Rubric.