X Tables
Problem Solving

Number line problem solving

Use jumps and distances to reason about calculations.

Quick answer

You can use a number line to solve maths problems by making jumps forward or backward to add or subtract numbers.

Learning outcome

By the end of this page, you will be able to use a number line to solve addition and subtraction problems by making jumps. Success signs:
  • You can show addition by jumping forward on a number line
  • You can show subtraction by jumping backward on a number line
  • You can solve word problems using number line jumps
  • You can check your answers by using the number line again

Why this matters

Number lines help you understand how numbers work and make solving maths problems easier. You use number lines in real life when you count steps, measure distances, or work out how much time is left. This skill helps you think about maths problems in a visual way, so you can solve them more easily.

How it works

Using a number line is like walking along a path. When you add, you walk forward. When you subtract, you walk backward. Here's how:
  1. Start at the first number
  2. Make jumps in the direction you need
  3. Count each jump carefully
  4. Land on the answer

Examples you can see

Let's look at how to solve problems using a number line. Example 1: Addition If you have 3 apples and get 4 more, how many apples do you have?
  • Start at 3
  • Jump forward 4 times
  • You land on 7
So 3 + 4 = 7 Example 2: Subtraction If you have 9 cookies and eat 3, how many are left?
  • Start at 9
  • Jump backward 3 times
  • You land on 6
So 9 - 3 = 6 Example 3: Word problem Tommy has 5 toy cars. His friend gives him 3 more. How many cars does he have now?
  • Start at 5
  • Jump forward 3 times
  • You land on 8
So 5 + 3 = 8

Try it as a mini adventure

Adventure: The Lost Treasure Hunt You are on a treasure hunt! You start at the big oak tree (number 0) and need to find treasure. 1st time: Walk 5 steps forward to find the first clue. 2nd time: From there, walk 3 more steps forward to find the second clue. 3rd time: From there, walk 2 steps backward to find the treasure. Where do you end up?
  • Start at 0
  • Jump forward 5 steps
  • Jump forward 3 more steps
  • Jump backward 2 steps
Let's count together:
  • 0 + 5 = 5
  • 5 + 3 = 8
  • 8 - 2 = 6
You find the treasure at step 6!

Common mistakes

  • Mistake: Jumping the wrong way (forward for subtraction or backward for addition)
    Why it happens: Not thinking about whether you're adding or subtracting
    Fix: Remember: Add = forward, Subtract = backward
  • Mistake: Counting the starting number as a jump
    Why it happens: Confusing where to start counting
    Fix: Count only the jumps you make, not the starting number
  • Mistake: Making too many or too few jumps
    Why it happens: Not reading the problem carefully
    Fix: Read the problem twice and count your jumps carefully

Parent and carer guide

You can help your child practice number line problem solving in just 5-10 minutes a day:
  • Draw a number line on paper or use a ruler to make one
  • Ask simple questions like "Start at 4, jump forward 3, where do you land?"
  • Use real objects like toys or food to show jumps
  • Encourage them to say the numbers as they jump
  • Don't worry if they make mistakes – it's part of learning
Watch for these signs that they're getting it:
  • They can explain how to make jumps
  • They use number lines to solve problems
  • They check their answers
  • They enjoy making up their own number line problems

Practice questions

  1. Start at 2, jump forward 5. What number do you land on?
    Answer: 7
  2. Start at 8, jump backward 3. What number do you land on?
    Answer: 5
  3. Start at 0, jump forward 4, then backward 2. What number do you land on?
    Answer: 2
  4. Start at 6, jump forward 3, then backward 1. What number do you land on?
    Answer: 8
  5. Start at 10, jump backward 5, then forward 2. What number do you land on?
    Answer: 7

FAQ

What is a number line?

A number line is a line with numbers in order. You can use it to show numbers and do maths problems.

How do I know which way to jump?

If you're adding, jump forward. If you're subtracting, jump backward.

Can I use number lines for big numbers?

Yes! Number lines work for any numbers, even big ones. You can even use them for negative numbers.

Why do we use number lines?

Number lines help us see how numbers work and make maths problems easier to understand.

Can I use number lines for multiplication?

Yes, but it's more for addition. For multiplication, you can add the same number many times using jumps.