Double Number Lines and Equivalent Ratios

Strip Diagrams and Double Number Lines

Tape Diagrams

• Tape diagrams are visual models that use rectangles to represent the parts of a ratio. 

• Since they are a visual model, drawing them requires attention to detail such as making sure the rectangles are the same size or that you have the correct ratio represented.

• These can also help with solving more complex problems that involve comparing ratios of 3 items or more.

That 60 is supposed to say 56.

Again, the 60 is supposed to say 56. It is a typo.

Double Number Lines

• Double number line diagrams are best used when the quantities have different units as comparing miles to hours.

• Double number line diagrams can also help us see that there are many different equivalent ratios.

• Is closely related to unit rate and will seem more common to you

Let's look at an example:

It took Megan 2 hours to complete 3 pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works?

Pogo the Dog can fetch 6 frisbees in 2 minutes. How many frisbees can he fetch in 7 minutes?

4 bottles of water cost $10 at the Spectrum Center home of the Charlotte Hornets. How many does 3 cost?

Ratio Table

• Works very similarly to a double number line

• Allows us to see our answers in a table format

• Later, a ratio table will allow us to easily see how to graph a proportional relationship (We won't do this until the end of this year into next year.)