Same Math › Grade 6 › Double number line
What is a double number line?
A double number line is two number lines lined up, one for each quantity in a ratio. Each tick mark pairs a value on top with its match below, like 2 cups of flour and 12 cookies.
- The top line counts one quantity: cups.
- The bottom line counts the other: cookies.
- Every tick is a matching pair: 3 cups make 18 cookies
Why schools teach it
It shows both quantities growing together
Sixth graders solve ratio and rate problems using tables, tape diagrams and double number lines; the standard names all three (6.RP.A.3). The double number line is especially good for unit rates, because the tick for 1 sits right there.
It also builds toward graphing. Each pair of ticks is a point you could plot, which is where proportional relationships go in 7th grade.
At the kitchen table
What to say, and what to skip
Say this
What's on the top line? What's on the bottom?
What goes under the tick for 1?
That's the unit rate.If you double the top, what happens to the bottom?
Are the ticks evenly spaced on both lines?
They should be, since both lines grow at the same rate.
Skip this
- Lining up ticks that don't match.Each tick on top must pair with the right value underneath.
- Adding the same amount to both lines.Ratios multiply. 1 and 6, then 2 and 12, not 2 and 7.
Just set up a proportion.
Proportions come in 7th grade. The line shows why they work.
See it in action
Finding a unit rate
4 notebooks cost $10. How much is 1 notebook?
Put 0 and 4 on the notebooks line, 0 and $10 on the dollars line
Split the space into 4 equal parts
ticks at 1, 2, 3, 4 notebooksSplit the dollars line the same way
$10 ÷ 4 = $2.50 per notebook
Once the tick for 1 is filled in, every other value is easy to find.
Free practice sheet
Make a double number line sheet
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Parents also ask
How is this different from a ratio table?
Same pairs of numbers, drawn as lines instead of a table. The line makes the spacing visible.
What is a unit rate?
The value for 1, like $2.50 per notebook or 6 cookies per cup.
Do the lines have to start at 0?
Usually, yes. Starting at 0 shows the ratio grows evenly from nothing.
Is this the same as a tape diagram?
Cousins. Both show ratios; the tape diagram uses bars, the double number line uses ticks.