Hopping on a number line
A number line is a straight line with numbers marked at equal distances. Starting at 0 and hopping forward shows us how addition and multiplication work.
What is this?
A frog stands at 0 on the number line. Each jump takes it forward by a fixed number of steps. If it jumps 2 at a time, it lands at 2, 4, 6, 8, 10 … , the multiples of 2.
If a rabbit jumps 3 at a time, it lands at 3, 6, 9, 12, 15 … , the multiples of 3.
Skip counting is exactly this , counting in jumps. Skip-counting by 2s gives even numbers. By 3s gives the 3-times table. By 5s gives 5, 10, 15, 20, … (always end in 0 or 5).
Multiplication is repeated jumping. 4 jumps of 3 steps each = 4 × 3 = 12. The frog lands at 12.
Addition is also jumping. 5 + 3 means: start at 5 and jump 3 forward. You land at 8.
Subtraction is jumping backwards. 10 − 4: start at 10, jump 4 back, land at 6.
Number lines also handle bigger ideas:
- Multiples of a number are the landing spots if you keep jumping with the same step.
- Common multiples of two numbers are spots where two different animals land at the same place (a 2-jumper and a 3-jumper both land at 6).
Worked examples
Example 1. A frog jumps in 4s, starting at 0. Where after 5 jumps?
- 4, 8, 12, 16, 20.
- After 5 jumps: 20.
Example 2. A rabbit jumps in 3s. Where after 8 jumps?
- 3 × 8 = 24.
Example 3. A grasshopper at 12 jumps back in steps of 4. Where after 2 backward jumps?
- 12 − 4 = 8. 8 − 4 = 4.
- After 2 jumps: 4.
Try it
- A frog jumps in 5s from 0. Where after 7 jumps?
- A rabbit jumps in 6s. Where after 5 jumps?
- A 2-jumper and a 3-jumper start at 0. List 3 spots where they both land.
- Where does a 4-jumper land after 9 jumps?
- A bug at 30 jumps back in 6s. Where after 4 jumps back?
Hands-on
Floor number line. With chalk, draw a number line on the floor from 0 to 30, with each step about 30 cm apart. Stand at 0 and play frog , hop 2 steps at a time. Stand at 0 and play rabbit , hop 3 at a time. Where do you meet?
Two animals. Pick two different jump sizes (say 3 and 4). Mark each animal's landing spots on a paper number line with different colours. Spot the common landing spots , they are common multiples.