1. Lesson 7.1.1 – Teacher Notes Standard:
7.RP.A.2d Recognize and represent proportional relationships between quantities.
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.
Full mastery can be expected by the end of the chapter.
Lesson Focus:
The focus of the lesson is for students to understand how to read a graph, paying close attention to unit rate. Students will also need to apply knowledge of unit rate. If you decide to use the toys, it is a good idea to only use one toy per table.
(7-2, 7-3, and 7-7)
I can explain what a point (x, y) on a graph of a proportional relationship means in terms of the situation.
Calculator: No
Literacy/Teaching Strategy: Teammates Consult and Whiparound (7-1); Huddle (Struggling learners); Walk and Talk (Closure)

2. Lesson 7.1.1
Example.
On a field trip, every chaperone is assigned 12 students. Is the student to chaperone ratio proportional?
If you use a table to demonstrate, you would need several ratios to start.
Next, find the simplified ratios and compare
them. Are they the same?
Yes, they are proportional.
You can determine if a relationship is proportional by looking at a table of values or the graph.
How?
Table
If all the ratios of numbers in the table are equivalent, the relationship is proportional.
Graph
If the graph of the numbers forms a straight line through the origin (0,0), the relationship is proportional.
Chaperones 1 2 3 4 5
Students 12 24 36 48 60
12 1
24 2 = 12 1
36 3 = 12 1
48 4 = 12 1
60 5 = 12 1

3. Try this:
The local pizza place sells a plain pie for $10. Each topping costs an additional $ Is the cost of pizza proportional to the number of toppings purchased?
Toppings 1 2 3 4
Cost ($)
11.50
13.00
14.50
16.00
Ratios:
cost .
toppings
Since the ratios are not equivalent, the relationship is not proportional.

4. 1) Is the relationship shown in the table proportional?
Yes No
Year 1 2 4 5
Income
$22,000
$44,000
$88,000
$110,000
2) Is the relationship shown in the table proportional?
Yes No x 2 5 6 9 y 7
17.5 21
34.5
Answer: Yes
3) Is the relationship shown in the table proportional?
Yes No x 1 2 6 9 y 5 11 31 46

5. 4) Is the relationship shown in the table proportional?
Yes No x 1 2 4 7 y 8 16 35
Answer: No
5) Is the relationship shown in the table proportional?
Yes No x 2 4 6 8 y -3
-10
-15
-20

6. Example.
On a field trip, every chaperone is assigned 12 students. Is the student to chaperone ratio proportional?
Chaperones 1 2 3 4 5
Students 12 24 36 48 60
Remember:
Table
If all the ratios of numbers in the table are equivalent, the relationship is proportional.
Graph
If the graph of the numbers forms a straight line through the origin (0,0), the relationship is proportional.
Chaperones
Students 6 12 18 24 30 36 42 48 54 60
How can we tell if the graph is proportional????

7. 7) Is the relationship shown in the graph proportional?
Example.
Draw a graph to represent the relationship. Is the relationship proportional?
7) Is the relationship shown in the graph proportional?
Yes No
Teachers
Students 5 10 15 20 25 30 35 40 45 50 6) 10 X Y 1
5.5 2 7 3
8.5 4 10 9 8 7 6 5 4 3 2 1
Yes No

8. 9) Is the relationship shown in the graph proportional?
Yes No
Yes No
Hours
Salary ($) 5 10 15 20 25 30 35 40 45 50
Answer: Yes

9. 10) Is the relationship shown in the graph proportional?
Yes
Yes No No
Answer: Yes

10. Constant of Proportionality
We can find the constant of proportionality from a table of values, equation and a graph.
In a table, simplify any one of the ratios.
Return to Table
of Contents
The constant of proportionality is a
constant ratio (unit rate) in any
proportional relationship.
We use the letter k to represent the
constant of proportionality.
Equations:
y = kx or k = y x
Chaperones 1 2 3 4 5
Students 12 24 36 48 60

11. Find the constant of proportionality:
12)
13) X Y 2
1.5 5
3.75 10
7.5 12 9
Apples (lbs) 2
2.5 3
3.5 4
Cost ($)
3.96
4.95
5.94
6.93
7.92
k = 𝑦 𝑥 = = 0.75
14)
15)
16) X Y 3
4.5 4 6 5
7.5 8 12 9
13.5 X Y 2
2.5 3
3.75 4 5 9
11.25 X Y 50 3 75
4.5
100 6
140
8.4
k = 𝑦 𝑥 = = 1.25
k = 𝑦 𝑥 = = 0.06

12. In an equation, write the equation in the form y = kx. Examples:
Find the constant of proportionality: e d a b f g c h i
17) Find the constant
of proportionality.
18) Find the constant
of proportionality.
19) Find the constant
of proportionality.
y = 12.9x
y = 0.45x
k = 12.9
k = 0.45
k = 1 9

13. Find the constant of proportionality.
In a graph, choose a point (x, y) to find and simplify the ratio. (2, 24)
21)
20)
k = 𝑦 𝑥 = = 8
22) 4 8 12 16 20 24 28 32 36 40
k = 𝑦 𝑥 = = 1.666…

14. 23) Find the constant of proportionality.
Answer: k = 8
(7.5, 2.5)
(4, 0.5)

15. Writing Equations For Proportions
Return to Table
of Contents
Writing Equations For Proportions
The constant of proportionality and the unit rate are equivalent.
We can use the constant of proportionality to help write equations using proportional relationships.
By transforming the equation from: to y = kx, we can
write an equation that can be applied to various situations.
*Remember: x is the independent variable and y is the dependent variable. This means that a change in x will effect y.

16. EXAMPLE
You are buying Jersey Tomatoes for a cost of 2 pounds for $ Write an equation to represent the proportional relationship.
Let c = cost
p = pounds
Determine the unit rate:
k = $1.99 per pound
Write an equation to relate the two quantities:
c = kp
c = 1.99p
TRY THIS:
At the candy store, you purchase 5 lbs for $ Write an equation to represent the proportional relationship.
Let c = cost
p = pounds
Determine the unit rate:
k = $4.49 per pound
Write an equation to relate the two quantities:
c = kp

17. Write an equation that represents the proportional relationship.
TRY THIS:
25) Write an equation to represent the proportional relationship shown in the table.
Let g = gallons
m = miles
m= 24.7g
Write an equation that represents the proportional relationship.
26) The total cost (c) of grapes for $1.40 per pound(p)
A) c = 1.4p
B) p = 1.4c
Gallons 10 15 20 25
Miles
247
370.5
494
617.5
Write an equation that represents the proportional relationship.
27)
Shirts 5 15 25 35
Cost
$57.50
$172.50
$287.50
$402.50
A) s = 11.5c
B) c = 11.5s
C) c = 0.09s
D) s = 0.09c