In this lesson, students create double number line diagrams from scratch. They see that it is important to use parallel lines, equally-spaced tick marks, and descriptive labels. They are also introduced to using the word per to refer to how much of one quantity there is for every one unit of the other quantity.
Double number lines are included in the first few activity statements to help students find an equivalent ratio involving one item or one unit. In later activities and lessons, students make their own strategic choice of an appropriate representation to support their reasoning (MP5). Regardless of method, students indicate the units that go with the numbers in a ratio, in both verbal statements and diagrams.
Note that students are not expected to use or understand the term “unit rate” in this lesson.
- Comprehend and use the word “per” (orally and in writing) to mean “for each.”
- Draw and label a double number line diagram from scratch, with parallel lines and equally-spaced tick marks.
- Use double number line diagrams to find a wider range of equivalent ratios.
Let's draw double number line diagrams like a pro.
It may be helpful—but not required—to bring back the blue and yellow water mixtures.
- I can create a double number line diagram and correctly place and label tick marks to represent equivalent ratios.
- I can explain what the word per means.
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 \(4 \boldcdot 5 = 20\).
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