Learning Target: I can represent ratios using models.


 
Modeling Ratios



Models

Models can provide a picture of ratio relationships.  They can help us solve problems by showing the quantities and items being compared in an organized way.



Types of Models

Some models used in representing ratios include tape diagrams, double number lines, tables and graphs.  These can all be used to show how different quantities are related in a consistent relationship.


Example

Stella's mother shops at a grocery store that sells bulk products.  She can buy macaroni and cheese in a small carton of 4 boxes, medium carton of 8 boxes or large carton of 20 boxes. 

Stella uses a tape diagram to represent these quantities.



If the small carton of macaroni & cheese costs $3.50, and the rate of cost remains constant, how much will the large carton of mac & cheese cost?

Think --

The diagram shows that the large carton is 5 times as large as the small carton.  If the rate of the cost remains constant, the large carton will cost 5 times as much as the small carton.

Solve --

5 × $3.50 = $16.50





Let's Practice Together

1.  At the drug store, bars of Moisture Soap are sold in a package of 6.  Franklin made a double number line to represent the ratio of number of bars of soap per package.



If a customer needed 40 bars of soap, how many packages would need to be purchased?




Your Turn
2.  Stan recorded the number of miles he traveled based on the amount of gas he used in a table.





Based on this information, how far would he travel using 6 gallons of gas?




3.  In West Road Middle School there are 4 fifth grade classes and 4 sixth grade classes.  The ratio of students to teachers is listed in the tables below.

Based on this information, what generalization can be made?
A.  The average student to teacher ratio is lower for grade 5.
B.  The average student to teacher ratio is lower for grade 6.
C.  The student to teacher ratios for grades 5 and 6 are the same.
D.  Since class sizes vary per grade, it is impossible to find the average ratio.





4.  Elijah walked four miles every hour for three hours.

Graph the relationship between time and distance on the coordinate plane below.

Assuming a consistent rate, how far had Elijah walked after 2 hours?




Check for Understanding

1. Sarah is making a batch of cookies. The recipe calls for 3 cups of flour for every 2 cups of sugar. If Sarah wants to make a larger batch and uses 12 cups of flour, how many cups of sugar will she need?





















Answers
1.  7 packages
2.  150 miles
3.  B
4.  Elijah had walked 8 miles.

      
Check for Understanding
1.  8 cups