Double Number Lines: Seeing Ratios in Two Directions
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Students will represent equivalent ratios using double number lines and use them to find unknown values in ratio situations, with multiple entry points and expression modalities to ensure access for all learners.
Lesson Overview
Students use double number lines to represent and reason about equivalent ratios, connecting the visual model to ratio tables and real-world contexts. This lesson follows an I-We-You (Open Up Resources 2.6) arc: teacher models, class practices together, then students work independently.
Materials
- Paper and pencils
- Whiteboard and markers
- Basic calculator (phone calculator is fine)
Scaffolded Task Progression
The teacher draws the following double number line on the board. Look at it for 30 seconds. Then share: *What do you notice? What do you wonder?*
[ Interactive graph / diagram, available in the full lesson ]
Teacher script: "Take a look at this diagram. I'm going to give you 30 seconds of quiet thinking time. Then turn to a partner and share one thing you notice and one thing you wonder. You don't need to know anything yet — just observe."
*Think about a time you've followed a recipe or mixed something. How did you know you had the right amounts?*
*Teacher think-aloud — students watch, listen, and annotate their own paper.*
Context: A recipe for green paint calls for parts blue paint for every part yellow paint.
The teacher says: "I'm going to build a double number line step by step. Watch what I do, and jot down anything that surprises you."
Step 1: Draw two parallel horizontal lines, both starting at . Label the top line 'Blue (parts)' and the bottom line 'Yellow (parts)'.
Step 2: Mark the first ratio: put on the top line and on the bottom line, directly below each other.
Step 3: Keep going — mark the next equivalent ratio by adding another on top and another on bottom.
The completed model looks like this:
[ Interactive graph / diagram, available in the full lesson ]
Teacher asks: "What do you notice about the spacing on the blue line? On the yellow line? What stays the same each time?"
Then: "How many parts yellow if I use parts blue? Point to the answer on the diagram."
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