This video lesson introduces the double number line diagram, a useful, efficient, and sophisticated tool for reasoning about equivalent ratios. The lines in a double number line diagram are similar to the number lines students have seen in earlier grades in that numbers correspond to distances on the line; scale can be chosen; lines can be extended as needed. In a double number line diagram, two parallel number lines are used—one line for each quantity in the ratio. Scales are chosen on each line so equivalent ratios line up vertically.

Because they represent quantities with length on a number line rather than with counts of objects, double number lines are both more abstract and more general than discrete diagrams. Connecting the concrete to the abstract helps students connect quantitative reasoning to abstract reasoning (MP2). Students continue to have autonomy in choosing representations to solve problems (MP5) and explain their meaning (MP3).

Grade 6, Episode 2: Unit 2, Lesson 6 | Illustrative Math