Key takeaway: A double number line is a diagram with two parallel number lines, one for each quantity, whose aligned tick marks show pairs of equivalent ratios and make a unit rate easy to read.
Grade 66.RP.A.3Ratios, Rates and Percents
Definition of Double Number Line
A double number line stacks two number lines on top of each other. One line measures the first quantity and the other measures the second. Marks that line up vertically form a pair that has the same ratio.
If a hiker walks 3 miles in 50 minutes, 3 sits above 50. Halving both gives 1.5 above 25, and doubling both gives 6 above 100. Both lines start at 0, and equal steps on one line match equal steps on the other.
Formula and notation
Draw the lines parallel, label each with its unit, and start both at 0. Every pair of aligned marks \((x, y)\) satisfies
\[\frac{y}{x} = \text{the same constant}\]
for all marks, where \(x\) is read on the top line and \(y\) on the bottom line.
Key facts
- Spacing must be even: if the top line steps by 3, the bottom line steps by a fixed amount too.
- The mark above or below 1 gives the unit rate directly.
- Jumping the same number of steps on both lines keeps the ratio equivalent.
- A double number line is a sideways version of two rows of a ratio table.
Double Number Line example
A hiker walks 3 miles in 50 minutes on a steady trail. Use a double number line to find how far she walks in 200 minutes.
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Mark 0 and 3 on the miles line above 0 and 50 on the minutes line.
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Step again: 6 miles with 100 minutes, 9 miles with 150 minutes.
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One more step: 12 miles with 200 minutes.
In 200 minutes she walks 12 miles.
Common mistake
Watch out
Ravi marks 3 miles above 50 minutes, then 4 miles above 100 minutes because he added 1 mile for the second step.
Why it is wrong
Equal steps on the minutes line must match equal steps on the miles line. A jump of 50 minutes is always 3 miles, so 100 minutes pairs with 6 miles. Keep the same jump size on each line.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Ratios, Rates and Percents