What it shows
Adding is jumping forwards along the number line and subtracting is jumping backwards. The frog shows that 7 + 5 and 5 + 7 land on the same number, and that 12 take away 5 brings you back to 7.
The science
A number line puts numbers in order at equal spaces. Moving one space to the right adds one, so a jump of 5 spaces adds 5. Because jumps can be taken in any order and still end at the same place, children see that addition is commutative. A jump backwards undoes a jump forwards, which is what subtraction means.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A string or rope 2 metres long tied between two chairs
- 21 clothes pegs numbered 0 to 20 with stickers
- A paper frog on a bent paper clip that slides along the string
- Number cards 0 to 10
- A dice
Safety
For this project: Keep the string at waist height so no child walks into it at neck level.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Tie the string tight between two chairs and clip on the pegs in order from 0 to 20, with equal gaps of about 9 cm.
Hook the paper frog on the string at 0.
Roll the dice twice, for example 4 and 3. Jump the frog 4 pegs, then 3 more, and read where it lands: 7.
Start again at 0, jump 3 first and then 4. It lands on 7 again, so the order does not matter.
Put the frog at 12 and jump back 5 pegs to find 12 take away 5. Count the pegs you pass, not the one you start on; that is the usual mistake.
Play a race: two players roll in turn and jump; the first to reach 20 exactly wins.
Write five sums you made and check each one with the frog.
What you should see
The frog lands on 7 for both 4 + 3 and 3 + 4, and on 7 for 12 take away 5, so the model makes adding and subtracting visible and checkable.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1If the frog is on 8 and jumps 6 forwards, where does it land?
On 14.
2What does jumping backwards show?
Subtraction, or taking away.
3Why is 4 + 3 the same as 3 + 4?
Jumping 4 then 3 is 7 pegs in total, and so is 3 then 4. The order of adding does not change the total.
4What is 20 take away 20?
Zero. The frog goes back to the start.
Take it further
Add pegs for negative numbers to the left of 0 and jump backwards past zero to show minus 3.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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