Foundation required
Familiarity with the numbers 1-10
Ability to count in 10s
Understanding that 1-10 forms a repeating block up to 100
Addition of 10 and Single Digits
10 + 5 = 15
10 + 7 = 17
Commutative Law of Addition.
3 + 5 = 8
5 + 3 = 8
Stage 1
The numbers 1-10 are represented by two blocks of 5 coins:
We begin with a single block of 5
Explanation:
Initially, fingers are essential for associating each number between 1 and 10 with a physical quantity.The numbers 5 and 10 are significant – they match our finger count (five per hand, ten total) and make counting in 5s and 10s intuitive. In the “fingerless” system, we use two blocks of five coins to explore relationships around 5 and 10. With practice, students visualise addition and subtraction mentally.
Practice 1
Working with the numbers 1 to 5 using a single block of 5 spaces.
Place a random number of coins and ask student to tell you the number of coins they see.
Important: Keep the coins together and align to the far left.
Ask them the number of additional coins required to reach 5 coins.
1 coin -> needs 4 -> 1 + 4 = 5
2 coins -> needs 3 -> 2 + 3 = 5
3 coins -> needs 2 -> 3 + 2 = 5
4 coins -> needs 1 -> 4 + 1 = 5
Stage 2
Now use two blocks of five spaces. The first is filled with 5 coins.
Practice 2
- Add a random number of coins (1-5) in the second block. Align the coins to the left.
- Ask how many are needed to reach 10.
5 coins -> needs 5 -> 5 + 5 = 10
6 coins -> needs 4 -> 6 + 4 = 10
7 coins -> needs 3 -> 7 + 3 = 10
8 coins -> needs 2 -> 8 + 2 = 10
9 coins -> needs 1 -> 9 + 1 = 10
Explain the pattern:
Numbers 1-10 identified visually without counting.
1-4 mirrors 6-9.
Numbers are identified relative to 5 and 10 – e.g. 7 is 2 more than 5, 7 is 3 less than 10.
Stage 3
Addition within 0-10.
Use two five space blocks. Distribute 0-5 coins in each
Practice 3
Example 4 + 3
- Move 1 coin from the “3” block to the “4” block to complete a block of 5, leaving 2
- Thus 4 + 3 = 7
Alternatively, moving 2 coins from the 4-block to the 3-block is valid – but shifting 1 is easier. Showing alternative methods of moving coins is encouraged.
Explanation:
Form full blocks of 5 to simplify mental addition. After practice, students quickly visualise:
4 + 3 -> 4 needs 1 to make 5, so take 1 from 3 -> 5 and 2 -> 7
Stage 4
Addition totalling more than 10.
Practice 4
Example 9 + 4
- Move 1 coin from the “4” block to the “9” block to complete a block of 10, leaving 3
- Thus 9 + 4 = 13
Explanation:
Form full blocks of 10 to simplify mental addition. After practice, students quickly visualise:
9 + 4 -> 9 needs 1 to make 10, so take 1 from 4 ->
10 and 3 -> 13
How long?
Progress varies, but with regular practice students often identify quantities usually within weeks. The transition to mental calculation typically follows this sequence:
- Physically manipulate coins in blocks.
- Observe blocks with coins and mentally visualise shifting coins (no physical moves).
- Observing blocks without coins and attempting to shift imaginary coins.
- Mentally solve similar problems without seeing blocks or coins.
Eventually the process becomes automatic.
SUBTRACTION
Subtraction needs to be seen as the reverse process of addition.
Stage 1
Subtraction with numbers below 10
Practice 1
Example 7 – 4
- 4 is made from 2 and 2. Removing 2 coins from 7 leaves 5 and taking away another 2 leaves 3
- Take 4 coins from the “5” block leaving 1. Thus 1 + 2 = 3
Either method is possible. Essentially we are using 5 as a point to work from.
Stage 2
Subtraction with numbers above 10
Practice 2
Example 13 – 8
- Take 8 coins from the “10” block leaving 2. Thus 2 + 3 = 5
Example 13 – 5
- Take 5 coins from the “5” block leaving 5 and 3
- 5 is made from 3 and 2.Removing 3 coins from 13 leaves 10 and taking away another 2 leaves 8
There are multiple ways of subtraction. However, working with 5 and 10 as the “stopping point” allows for easier calculation and should form the basis for all methods.
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