1.2 to 1.4 Comparing and Scaling Ratios

Lesson Objectives:

• Students will be able to create and use a table to scale ratios up and down.
• Students will be able to use a variety of strategies to compare ratios.

Part 1: The Language of Ratios

Remember that ratios are about comparing two quantities using the language of "There are ____ _____ for every ____ _____".

Look at the image below and see how many ratio descriptions you can come up with:

Part 2: Scaling Ratios

Take a look at your ratio statements.  Do you have any statements that are really describing the same relationship, but using different numbers?  For example:

• There are 2 pigs for every 1 sheep.
• There are 4 pigs for every 2 sheep.

These two statements are really the same but the second set of numbers has been "scaled" up by a factor of 2.  So what is "scaling"?

Scaling is the process of multiplying or dividing one ratio by a particular "scale factor" to create an equivalent ratio.

Work through the task below.  Be sure to clearly show your "scale factor".

Part 3: Comparing Ratios

While scaling produces equivalent ratios, other situations require that we compare ratios.  Complete the task below.  If you get stuck, try some of the following strategies:

• Rewrite each ratio so that the "cups of concentrate" is the same.
• Rewrite each ratio so that the "cups of water" is the same.
• Convert each ratio into a part:whole fraction.
• Convert each ratio into a percentage.

Here is what you MUST do before next class:

• ACE (10, 17, 18, 22, 23)
• Remember to set these up as a table when possible to make your work more organized.