Unit 3 Lesson 3 - GaDOE Inspire

​Classifying Proportion and Non-Proportion Situations

GaDOE Inspire - Unit 3 Lesson 3

Learning Goals

• I can determine if two quantities are in a proportional relationship.

• I can determine the unit rate in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.

Getting Things in Proportion - Pre-questions

The next couple of slides will check your thought process on creating proportional relationships.

It is okay if you do not know the answers, just try!

Multiple Choice

Leon has $40. $1 can buy him 12 Mexican Pesos.

How many Mexican Pesos can Leon buy with his $40?

Be prepared to explain your thought process.

• 40

• 48

• 480

• 450

Multiple Choice

Minna has a cell phone plan that costs $15 per month plus free texts plus $0.20 per minute of call time.

Minna made 30 minutes of calls this month and 110 texts. How much did she have to pay the phone company?

Be prepared to explain your reasoning.

• $21

• $125.20

• $100

• $25

Getting Things in Proportion

Not every proportion is direct and obvious.

Sometimes you have to take a list of things, word problems, or numbers and create proportions out of them to solve issues.

Using unit rates, you can make proportions easier to create. Remember, creating a unit rate requires you to make the denominator equal to 1. Example: 6 cookies per 1 box, or 6:1 (cookies to boxes)

Getting Things in Proportion - Leon's Question

Leon has $40. $1 can buy him 12 Mexican Pesos. How many Pesos can he buy with his $40?

If $1 can buy him 12 Mexican Pesos and he has $40, what should we do?

To solve this, multiply 12 Mexican Pesos by 40 because for every dollar, he can buy 12 Pesos. 40*12 = 480 Mexican Pesos. Our unit rate is 12 Pesos per $1, or 12:1.

Getting Things in Proportion - Leon's Question

What is an equation we could set up for this question?

We could set this up as ($40 / $1) * 12.
($40 / $1) = $40
$40 * 12 = 480 Mexican Pesos

Multiple Choice

What if Leon had $50? How many Pesos could he purchase? Remember, our unit rate is 12:1, or 12 Pesos per $1.

Be prepared to explain your answer.

• 520

• 480

• 560

• 600

Getting Things in Proportion - Minna's Question

Minna has a cell phone plan that is $15 per month plus free texts plus $0.20 per minute of call time. She made 30 minutes of calls this month and 110 texts. How much does she have to pay the phone company?

Getting Things in Proportion - Minna's Question

To solve this multiply $0.20 by the 30 minutes of call time and add $15. Since texts are free, you do not have to worry about adding that at all. What is our equation?

$15 + ($0.20 * 30).
$15 + ($6)
$21 is how much Minna owes the phone company.

Getting Things in Proportion - Minna's Question

Our proportional setup is as follows...

$0.20 per 1 minute of phone call, then add $15 for total cost.

Using this proportional relationship, let's try to solve another problem on the next slide.

Multiple Choice

If Minna made 100 minutes of phone calls this month, how much would she owe the phone company? Remember, our proportional relationship is $0.20 per 1 minute of call time, plus $15 for the total.

Be prepared to explain your reasoning.

• $40

• $25

• $27

• $35

Direct Proportions

A direct proportion is a relationship where two quantities increase or decrease by the same ratio.

The graph of the relationship is a straight line through the origin (0,0). This is the typical proportional relationship.

Direct Proportions - Properties

• One quantity is a multiple of the other. Ex: 2:1

• If the first quantity is zero, the second quantity is zero.

• If you double one quantity, the other also doubles.

Direct Proportions - Examples

• Your wage is $20 per hour. Working 2 hours earns you $40. Working 4 hours earns you $80. When you double the hours, the total earned doubles. Your unit rate is $20:1.

• You can make 4 pancakes with 1 box of batter. Making 8 pancakes requires 2 boxes of batter. When you double the pancakes, the boxes of batter doubles. Your unit rate is 4:1.

Multiple Choice

I purchase 12 pencils for $6. What is my cost if I purchase 6 pencils?

Use unit rate and direct proportions properties to answer this.

• $2

• $6

• $3

• $4

Questions?

Time for practice.