Week 23 Day 5: Proportional and Nonproportional

Week 23 Day 5: Proportional and Non Proportional

I can distinguish between proportional and nonproportional relationships.

Do Now Questions

Multiple Choice

Mr. Rogers needs fertilizer for his 1-acre garden. The package suggests 1/2 pound of fertilizer for 1/45 of an acre. How many pounds of fertilizer does Mr. Rogers need for his entire garden?

• 11 1/4

• 22 1/2

• 45

• 90

Multiple Choice

If a dog can eat 1/3 of a bag of food in 1/2 week, how many bags of food can the dog eat in 1 week?

• 1/6

• 2/3

• 3/2

• 5/6

Multiple Choice

If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of the snail, in meters per hour?

• 1/40

• 5/18

• 1 1/2

• 3 3/5

Multiple Choice

Ben drove 4 3/4 hours and used 10 1/2 gallons of gas. How many gallons did Ben use in 1 hour?

• 1 18/42 gallons per hour

• 2 4/19 gallons per hour

• 19/42 gallons per hour

• 42/19 gallons per hour

Proportional and Nonproportional Relationships

What is proportional relationship

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Proportional verses Nonproportional

Proportional Relationship 

• Contains the Origin (0,0)
• Data is linear.
• Constant rate of change.
 Equation will always be: 

 $y=k\ \cdot\ x$  

Multiplicative relationship.

Non-Proportional Relationship

 $0$  

• May or may not contain the origin (0,0)
• Data may or may not be linear
•May or may not have a constant rate of change.
• No Constant of Proportionality
• Equation will never be:

  $y=k\cdot x$  

Multiple Choice

Is the graph proportional or nonproportional?

• proportional

• non proportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes, because the line is pretty.
• No, because the line goes through the origin.
• Yes because the line goes through the origin.
• No, because the graph is non-proportional.

Multiple Choice

A gymnast burns 15 calories a minute.

• Proportional
• Nonproportional

Multiple Choice

Determine whether the number of legs are proportional to the number of spiders. 

• Yes, proportional
• No, non-proportional

Multiple Choice

Why does this graph show a non-proportional relationship?

• It doesn't, it is proportional because it is a straight line

• It goes through the origin

• It does not go through the origin

• It is a straight line

Multiple Choice

Which statement best describes the relationship between x and y in the table?

• Proportional

• Not Proportional

Multiple Choice

Which table shows a car moving at a constant speed?

Multiple Choice

How much does Dan charge per hour for walking dogs?

• $5

• $1

• $20

Multiple Choice

Find the unit rate:  $3.60 for 3 pounds of apples. How much does it cost for 1 pound of apples?

• $1.00 per pound
• $3.60 per pound
• $1.20 per pound
• $1.10 per pound

Multiple Choice

What is the constant of proportionality (in miles per hour) based on the table?

• 45
• 90
• 135
• 2