Division on a number line

Start at the number you are dividing and jump back to 0 in equal jumps. The number of jumps is the answer.

How division on a number line works

For 24 ÷ 6, start at 24. Jump back 6 to 18, then 12, then 6, then 0. That is 4 jumps, so 24 ÷ 6 = 4.

Each jump is one group of 6. The number line is a picture of repeated subtraction, and it shows the equal groups as equal-sized hops.

You can also jump forwards from 0 to 24 in 6s and count the jumps. Forwards is the same as counting in 6s, which links straight to the 6 times table.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

061218241234
24 ÷ 6: four jumps of 6 back to 0.
051015202530123456
30 ÷ 5: six jumps of 5. The same jumps forwards are the 5 times table.
04812162012345
20 ÷ 4: five jumps of 4 land exactly on 0, so there is no remainder.

Step by step

  1. Draw a line and mark 0 and the dividend. Add marks in steps of the divisor.
  2. Start at the dividend and draw jumps back, each the size of the divisor.
  3. Number the jumps as you go: 1, 2, 3 …
  4. When you land on 0, the last jump number is the quotient.
  5. If you can’t make another full jump, the gap to 0 is the remainder.

Remainders on a number line

Try 14 ÷ 4. Jump back from 14 in 4s: 10, 6, 2. One more jump of 4 would go below 0. So there are 3 full jumps and a gap of 2: 14 ÷ 4 = 3 r 2.

The picture makes the rule clear: the remainder is the gap left at the end, and it is always shorter than one jump. If the gap is as long as a jump, you missed a jump.

Jumping forwards: the times table link

Many children prefer to start at 0. For 35 ÷ 5, jump forwards in 5s: 5, 10, 15, 20, 25, 30, 35. Seven jumps reach 35, so 35 ÷ 5 = 7.

This is the same as saying the 5 times table until you reach 35. Each landing spot is a multiple of 5. Children who know the table can jump straight to the answer: 7 × 5 = 35.

Use whichever direction your child finds easier. Both show that division asks how many equal jumps fit.

When a number line helps most

A number line is best for small dividends and small divisors in grade 3, and for children who like to see division as movement. It is also a good way to explain remainders.

It gets crowded for big numbers. For 96 ÷ 4, use bigger jumps of 40 (10 fours), then 16 (4 fours), which leads to partial quotients. For facts, move on to fact families so answers become quick to recall.

Quiz: jumps on a number line

Count the jumps back to 0.

Where this fits: division step by step

  1. What is division
  2. Division as repeated subtraction
  3. Division on a number line (this page)
  4. Dividend, divisor and quotient
  5. Dividing by 2, 5 and 10
  6. Division facts
  7. Checking division with multiplication
  8. Division with remainders
  9. Interpreting remainders
  10. 2-digit by 1-digit division
  11. 3-digit by 1-digit division
  12. Partial quotients
  13. Short division
  14. Long division
  15. Zeros in the quotient
  16. Estimating quotients
  17. Long division with 2-digit divisors
  18. Division word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “Stand at 12 on our number line. We’ll take jumps of 3 back to 0.”
  2. “Jump! Where are you?” (9.) “Keep jumping and count.”
  3. “9, 6, 3, 0. How many jumps?” (4.) “So 12 ÷ 3 = 4.”
  4. “What if we start at 13?” (4 jumps and 1 step left over.)
  5. “That leftover step is the remainder.”

More worked examples

Example 1: 16 ÷ 4

From 16: 12, 8, 4, 0. Four jumps, so 16 ÷ 4 = 4.

Example 2: 27 ÷ 9

From 27: 18, 9, 0. Three jumps, so 27 ÷ 9 = 3.

Example 3: with a remainder: 11 ÷ 3

From 11: 8, 5, 2. Three jumps, then 2 is too short for another jump. 11 ÷ 3 = 3 r 2.

Example 4: forwards: 42 ÷ 7

From 0 in 7s: 7, 14, 21, 28, 35, 42. Six jumps, so 42 ÷ 7 = 6.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 10 ÷ 2
  2. 18 ÷ 3
  3. 20 ÷ 5
  4. 32 ÷ 8
  5. 21 ÷ 7
  6. 40 ÷ 10
  7. 13 ÷ 4
  8. 17 ÷ 3
  9. How many jumps of 6 from 36 to 0?
  10. Stretch: 100 ÷ 20 on a number line
Show the answers
  1. 5
  2. 6
  3. 4
  4. 4
  5. 3
  6. 4
  7. 3 r 1
  8. 5 r 2
  9. 6
  10. 5 jumps

Common mistakes

Counting marks, not jumpsCounts the numbers 24, 18, 12, 6, 0 and says 5.Fix: count the arcs between numbers. Number each jump as you draw it.
Uneven jumpsDraws one jump of 6, then one of 5.Fix: every jump must be the size of the divisor. Mark the line in steps first.
Ignoring the gapSays 14 ÷ 4 = 3 and forgets the 2 left.Fix: if you can’t land on 0, the gap is the remainder.

How to teach it at home

Hopscotch jumps

Chalk a number line outside and jump back in equal steps.

Ruler jumps

Use a ruler as a number line and hop a finger in 2s, 5s or 10s.

Stairs

Count stairs in 2s or 3s: how many big steps to the top?

By grade

More for each grade: Grade 3 math and the CBSE class 3 maths guide.

Worksheets and practice

Division facts worksheet, page 1

Division facts worksheet: printable PDF with an answer key. · Make a fresh test

Division practice · division speed test · division chart · division for kids

Last reviewed

Questions parents ask

How do you divide on a number line?

Start at the dividend and jump back to 0 in jumps the size of the divisor. The number of jumps is the quotient.

How do you show a remainder on a number line?

When the next jump would go past 0, stop. The gap between where you are and 0 is the remainder.

Can you divide on a number line going forwards?

Yes. Jump from 0 to the dividend in steps of the divisor and count the jumps. It is the same as counting in multiples.

Why use a number line for division?

It shows division as equal groups you can see, and it makes remainders easy to understand.

What grade uses number lines for division?

Grade 3 (class 3), when division is first taught.