This lesson introduces students to the idea of unit price. Students use the word “per” to refer to the cost of one apple, one pound, one bottle, one ounce, etc., as in “\$6 per pound” or “\$1.50 per avocado.” The phrase “at this rate” is used to indicate that the ratios of price to quantity are equivalent. (For example, “Pizza costs \$1.25 per slice. At this rate, how much for 6 slices?”) They find unit prices in different situations, and notice that unit prices are useful in computing prices for other amounts (MP7).
Students choose whether to draw double number lines or other representations to support their reasoning. They continue to use precision in stating the units that go with the numbers in a ratio in both verbal statements and diagrams (MP6).
Note that students are not expected to use or understand the term “unit rate” in this lesson.
- Calculate equivalent ratios between prices and quantities and present the solution method (using words and other representations).
- Calculate unit price and express it using the word “per” (orally and in writing).
- Understand the phrase “at this rate” indicates that equivalent ratios are involved.
Let’s use ratios to describe how much things cost.
- I can choose and create diagrams to help me reason about prices.
- I can explain what the phrase “at this rate” means, using prices as an example.
- If I know the price of multiple things, I can find the price per thing.
double number line diagram
A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. The locations of the tick marks match on both number lines. The tick marks labeled 0 line up, but the other numbers are usually different.
The word per means “for each.” For example, if the price is \$5 per ticket, that means you will pay \$5 for each ticket. Buying 4 tickets would cost \$20, because \(4 \boldcdot 5 = 20\).
The unit price is the cost for one item or for one unit of measure. For example, if 10 feet of chain link fencing cost \$150, then the unit price is \(150 \div 10\), or \$15 per foot.