Open Number Line: Free Interactive Tool for Mental Math
Updated · By Edulist · 3 sources
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How to use it
- Set a start
Type a whole number in Start at and press Set. The line shows only that number to begin.
- Make jumps
Tap a jump (+1, +2, +5, +10, +100, −1, −10, −100) or type any jump, such as +25 or −8. Each jump starts where the last one landed, and the line rescales to fit.
- Read the strategy
The readout writes your jumps as a number sentence, like 38 + 2 + 20 + 3 = 63, and shows the total jump. Remove the last jump to try another path.
- Work the task cards
Eight cards cover adding tens and ones, jumping to the next ten, counting up to subtract, friendly numbers and compensating.
Printables to go with it
What an open number line is
An open number line is a straight line with nothing printed on it. To solve 38 + 25, a child writes 38 near the left, draws a jump of +2 to 40, a jump of +20 to 60, and a jump of +3 to 63. The line holds only the numbers the child chose, so it shows how they thought.
An open number line records the start, jumps and landing points without drawing every intervening tick. Use it to explain how a calculation was split into manageable steps, and compare more than one route to the same answer.
Unlike a ruler-style line, the open line doesn't make children count marks. It asks them to choose friendly jumps, the ones place value makes easy, and to keep track of them. That is the heart of mental math in the Common Core standards for 2nd and 3rd grade, which ask children to add and subtract within 1,000 using strategies based on place value and the relationship between addition and subtraction (2.NBT.B.7, 3.NBT.A.2).
How to use the open number line
- Start. Type the first number and press Set.
- Choose a jump that's easy. Often that's the jump to the next ten (+2 from 38) or a jump of a whole ten (+20).
- Keep going. Each jump starts where the last landed. The line rescales so everything fits.
- Add up the jumps. The readout shows the total jump (+25) and the sentence 38 + 2 + 20 + 3 = 63.
- Try another path. Remove the last jump or undo, and solve it a different way: +20, +5 lands in the same place.
Open number line strategies
| Strategy | Example | Jumps |
|---|---|---|
| Tens, then ones | 38 + 25 | +20 to 58, +5 to 63 |
| Jump to a ten | 47 + 6 | +3 to 50, +3 to 53 |
| Friendly numbers | 199 + 46 | +1 to 200, +45 to 245 |
| Count up to subtract | 72 − 28 | +2 to 30, +40 to 70, +2 to 72 (total 44) |
| Back by tens | 85 − 30 | −10, −10, −10 to 55 |
| Compensate | 64 − 19 | −20 to 44, +1 to 45 |
| Hundreds | 350 + 270 | +200 to 550, +50 to 600, +20 to 620 |
Activities to try
- Many paths. Solve 46 + 37 three ways and compare. Which used the fewest jumps? Which felt easiest?
- Count up. For any subtraction where the numbers are close, like 81 − 76, start at the smaller number and count up. It's often faster than counting back.
- Make it friendly. Solve 298 + 135 with a +2 jump first. Then talk about why 300 + 133 is the same problem.
- Elapsed time. How long from 9:45 to 11:00? Start at 0 for 9:45, jump +15 to reach 10:00, then +60 for the next hour: 75 minutes. Number lines are how many teachers teach elapsed time.
- Money. Start at 37 cents and count up to a dollar: +3, +10, +50.
- Explain it. Have a child solve a problem on the line, press Share, and send the link to someone who has to explain the strategy from the picture.
Tips for teachers and parents
- Value the thinking, not one method. There is no single right set of jumps. A child who jumps +20, +5 and one who jumps +2, +20, +3 both understand.
- Model it first. Think out loud: "38 is close to 40. I'll jump 2 to get there, so I have 23 left."
- Connect to blocks. The +20 jump is two ten rods; the +3 is three units. Building the problem with base ten blocks first helps children who aren't sure what a jump of 20 means.
- Expect rough scale on paper. When children draw their own lines, jumps only need to look about right. This tool keeps them in proportion so children see what "about right" looks like.
- Use the marked line first. Children who still count by ones benefit from the interactive number line with marks before moving to the open line.
Why the open number line works
The open line sits between counting and the written algorithm. Children still see the problem as movement along numbers, so they don't lose track of what the numbers mean, but they choose jumps that use place value instead of counting by ones. It also makes thinking visible: a teacher can see at a glance whether a child added the tens first, jumped to a friendly number, or counted up.
Because the line has no fixed scale, the same picture works for 47 + 6 and for 350 + 270. And because children choose their own jumps, two correct solutions can look different, which leads to good classroom conversation about which path was easiest and why.
Using it with a class
Put a problem on the board, ask students to solve it two ways, and have them press Share to send you a link to each. Show a few links on the projector and compare. Task cards work well as a warm-up: they check themselves, so students get feedback right away.
Open number line by grade
| Grade | Typical work |
|---|---|
| 1st | Add within 100 by counting on in tens and ones; make ten. |
| 2nd | Add and subtract within 100 fluently and within 1,000 with strategies (2.NBT.B.5, 2.NBT.B.7). |
| 3rd | Add and subtract within 1,000 fluently; round and estimate; elapsed time. |
| 4th | Multi-digit addition and subtraction checks; mental math with compensation. |
Common mistakes and fixes
| What you see | Try |
|---|---|
| Many +1 jumps instead of +10 | Ask how many tens are in the number being added. |
| Loses track of how much is left to add | Write the jumps in a list as you go, or read the total jump in the readout. |
| Lands on the wrong number after a jump to a ten | Check the jump size: from 47, the next ten is 3 away, not 4. |
For paper practice, print a blank number line sheet and draw the jumps, or use a number line to 100 for jumps by ten.
Choosing an activity
Grade bands describe possible curriculum connections, not an assessment of an individual learner. Start with an example the learner can explain, then change one feature at a time. The activity suggestions here are editorial teaching ideas, not results from a classroom trial of this software. Use the model alongside written work and physical materials when useful. The linked standards describe learning objectives; they do not endorse Edulist or require this particular tool.
Sources
Questions
What is an open number line?
A blank line with no tick marks or printed numbers. Children write the starting number, draw jumps for each part of the problem, and label where they land. Because nothing is pre-marked, the jumps can be any size, which makes it a tool for mental math rather than counting.
Is an open number line the same as an empty number line?
Yes. Both names refer to a line where the learner chooses useful labels and jumps instead of starting with every number marked.
Does an open number line have to be to scale?
No. Jumps only need to look roughly right: a +20 jump should look bigger than a +3. This tool scales the jumps for you, so they stay in proportion.
What grade uses open number lines?
Mostly 1st through 3rd grade, for adding and subtracting within 100 and 1,000. Older students use them for elapsed time, money and checking estimates.
How do you subtract on an open number line?
Either jump back from the bigger number (85 − 30: three jumps of −10) or count up from the smaller number (72 − 28: +2 to 30, +40 to 70, +2 to 72, so the difference is 44).
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