Ratios, Unit Rates, and Proportions Math 7 Plus

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

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.

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

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

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