Lesson 1: Understand Ratios6.AT.1

I can…

I can write and describe a ratio that compares two quantities.

Key words

• Understand Ratios — Use a ratio to compare two quantities by division.
• Ratio — A way to compare two amounts, like 3 to 2.
• Comparison — Looking at two or more amounts to see how they are related.
• Part-to-part — A ratio comparing one part of a group to another part.
• Part-to-whole — A ratio comparing one part to the whole group.
• Colon notation — Writing a ratio with two dots between the numbers, like 3:2.
• Tape diagram — A bar cut into equal parts that shows how two amounts in a ratio compare, and how they make up the whole.
• Double number line — Two number lines lined up so matching tick marks show the two quantities in a ratio at the same time.

Steps

1. Chef Reyes uses 3 cups of apple juice for every 2 cups of sparkling water.
2. I am comparing two amounts: apple juice and sparkling water.
3. I write apple juice to sparkling water, in that order, as 3 to 2, or 3:2.
4. I can also draw the ratio. On a tape diagram I give apple juice 3 equal parts and sparkling water 2 equal parts, so one batch is 5 parts in all.
5. Those same 5 parts show a second ratio: apple juice to the whole fruit drink is 3 to 5.
6. On a double number line I line the two amounts up: 5 cups of fruit drink pairs with 3 cups of apple juice, and 10 cups of fruit drink pairs with 6 cups of apple juice.

Try it

A bag of trail mix contains 8 peanuts and 5 raisins. What is the ratio of raisins to total pieces?

Check your answer

5:13

Total pieces = 8 + 5 = 13. The ratio of raisins to total is 5:13.

Sentence starter

I know ___ because ___.

Goal: I can explain a comparison using the words ratio, part-to-part, part-to-whole, and colon notation.