1. Ratios, Unit Rates, and Proportions
Math 7 Plus

2. USING A TABLE TO FIND EQUIVALENT RATIOS
So far we have looked at the following ways to use ratios to find unit rates as well as to help us find other equivalent ratios.
USING A TABLE TO FIND EQUIVALENT RATIOS
Used to find equivalent ratios using the relationship represented in the table
Can be used to find the unit rate
USE MULTIPLYING/DIVIDING by one of the original numbers
Used to find equivalent ratios by mulitplying or dividing both numbers in the original ratio by the same number.
GRAPHING IN A COORDINATE PLANE
Best used to make predictions about equivalent ratios
Used to determine if a proportional relationship exists
DOUBLE NUMBER LINE DIAGRAMS
Best used when the two quantities have different units. But can also be used at other times to find equivalent ratios.
Help make visible that there are infinitely many pairs in the same ratio, including those with rational numbers
Same ratios are the same distance from zero

3. Today we will look at the “TAPE DIAGRAMS” method
to find unit rate:
TAPE DIAGRAMS
Best used when the two quantities have the same units.
Highlights the multiplicative relationship between
quantities.

4. TAPE DIAGRAMS
The ratio for three parts yellow paint to two parts blue paint can be shown with the following tape diagram: 5
What is the total number of parts represented? 1 5
How much of the total does each rectangle represent?
If the tape diagram represents 5 cups of paint then each of these rectangles would represent how much?
1 cup
If the diagram represents a total of one gallon, then each rectangle represents how much?
1 of a gallon 5
What part of the gallon is yellow paint?
3 of a gallon 5

5. USING TAPE DIAGRAMS TO SOLVE PROBLEMS
Slimy Gloopy mixture is made by mixing glue and liquid laundry starch in a ratio of 3 to 2. How much glue and how much starch is needed to make 85 cups of Slimy Gloopy mixture?
GLUE:
STARCH:
Start by making your base tape diagram:
The total amount represents how much?
5 parts =
85 cups
Each part represents how much?
1 part =
85 ÷ 5 = 17 cups
Amount of glue in 85 cups:
3 parts=
3 x 17 = 51 cups
Amount of starch in 85 cups
2 parts=
2 x 17 = 34 cups
You need 51 cups of glue and 34 cups of starch for 85 cups of Slimy Gloopy mixture.
Adapted from commoncoretools.wordpress.com

6. Mathscape, RATES, RATIOS, PERCENTS, and PROPORTIONS
Discuss page 18 in
Mathscape, RATES, RATIOS, PERCENTS, and PROPORTIONS
Blue “Buyer Beware”
and then apply TAPE DIAGRAMS
on worksheet D-60