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.

As students progress through the activities, they learn to draw double number line diagrams with decreasing levels of scaffolding. In a preceding lesson, students put the numbers on pre-drawn lines with tick marks and extrapolated the values up the number line. Here, students start by placing their own tick marks and interpolating the given values down to smaller numbers. Next, they draw a double number line diagram from scratch but by following instructions. Finally, in an optional activity, they create a double number line diagram with no guidance.

In the optional activity, students revisit a situation previously represented with a discrete diagram. They examine how the new representation can help to answer questions about the ratios in the situation.

In later lessons, students make their own strategic choice of an appropriate representation to support their reasoning. Regardless of method, students practice attending to precision (MP6) as they 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.