Double Number Line
In short: A double number line is a pair of parallel number lines that shows two related quantities at once, so matching marks give equivalent ratios such as 12 miles in 1 hour.
6th GradeRatios and Percents6.RP.A.3
What is Double Number Line?
A double number line stacks two scales, one for each quantity in a situation. A mark on the top line lines up with the matching mark on the bottom line, so distance and time, or cost and weight, can be read together.
Precisely, the pairs \((0, 0)\), \((a, b)\), \((2a, 2b)\) and so on are equivalent when the marks are spaced evenly. Each pair gives the same ratio \(a : b\), and the mark paired with 1 unit shows the unit rate.
How to spot it
- A problem moves at a steady pace, like miles per hour or dollars per pound, and asks for values between known marks.
- You are given one matching pair and must find the partner of a different amount.
- Two units must be lined up, such as minutes with laps or cups with servings.
- Both quantities start at zero and grow together by equal jumps.
The method
- Draw two parallel lines and label each with its quantity and unit, then mark 0 on both.
- Place the known pair on the lines at matching positions, spacing the equal jumps evenly.
- Divide or multiply the jumps to reach the amount you need, doing the same operation on both lines.
- Read the partner value, and write it with its unit.
Double Number Line: solved example
Problem
Marcus bikes along a lake trail at a steady pace and covers 14 miles every hour. How far does he ride in 2.5 hours?
Solution
Mark 0, 1 and 2 hours on the top line with 0, 14 and 28 miles below. Half an hour is half of one jump, so the 0.5 mark pairs with \(14 \div 2 = 7\) miles.
Add the jumps: \(28 + 7 = 35\). Marcus rides 35 miles in 2.5 hours.
Try it
Question 1
A hose fills 6 gallons in 4 minutes. Use a double number line idea to find the gallons after 10 minutes.
Show the answer
Two minutes pair with 3 gallons, so 10 minutes is 5 jumps of 2 minutes: \(5 \times 3 = 15\) gallons.
Question 2
On a double number line, 5 pounds of apples pair with $9. What does 1 pound cost?
Show the answer
Divide both marks by 5: \(9 \div 5 = 1.8\), so one pound costs \$1.80.
Double Number Line vs. Ratio Table
A double number line spaces the pairs evenly along two scales, which makes steady growth easy to see and fractions of a unit easy to place. A ratio table lists the same pairs in cells and works well when you want to add or scale columns.
Keep going
Lessons
Worksheets and quizzes
- Ratio Tables and Graphs of Ratios – Worksheet
- Ratio Tables and Graphs of Ratios – Quiz
- Unit Rates and Rate Language – Worksheet
- Unit Rates and Rate Language – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Ratios and Percents