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 with a single digit.
10 + 5 = 15
10 + 7 = 17
Commutative law of addition.
3 + 5 = 8
5 + 3 = 8
Stage 1
The numbers 1 to 10 can be represented by 2 blocks of 5 coins:
Working with a single block of 5 coins
Explanation:
When first learning the numbers 1 to 10, fingers are an invaluable tool for associating numbers to an actual physical quantity.
The numbers 5 and 10 are important for several reasons. We have 5 fingers on each hand, both hands total 10 fingers. We use a base-10 number system where the number 5 is exactly the midpoint, making counting in 5’s and 10’s simple.
Using the fingerless system, the numbers 5 and 10 are represented as 2 blocks of 5 coins. By playing with coins within the 2 blocks of 5 coins, we learn how other numbers are related to the number 5 and 10. Over time addition and subtraction becomes a rapid mental operation, where numbers are visualised as a quantity relative to 5 and 10.
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, 4 more coins needed to get 5 coins
1 + 4 = 5
2 coins, 3 more coins needed to get 5 coins
2 + 3 = 5
3 coins, 2 more coins needed to get 5 coins
3 + 2 = 5
4 coins, 1 more coin needed to get 5 coins
4 + 1 = 5
Stage 2
Numbers 6 to 10.
Working with two blocks of 5 spaces. The first block is filled with 5 coins.
Practice 2
Place a random number of coins in the second empty block and ask student to tell you the number of coins they see. Again keep the coins aligned to the far left and keep them together.
Ask them the number of additional coins required to reach 10 coins.
5 coins, 5 more coins needed to get 10 coins
5 + 5 = 10
6 coins, 4 more coins needed to get to 10 coins
6 + 4 = 10
7 coins, 3 more coins needed to get to 10 coins
7 + 3 = 10
8 coins, 2 more coins needed to get to 10 coins
8 + 2 = 10
9 coins, 1 more coin needed to get to 10 coins
9 + 1 = 10
Explanation:
After working with both practice 1 and 2 for some time, point out the similarity between the first and second practice exercises and the number pairs 1 and 6, 2 and 7, 3 and 8, and 4 and 9.
We can point out that the numbers 1 to 10 are distinct numbers but also mirrored by 2 similar blocks of 5 coins, where the second block is a repeat of the first block.
With practice students will be able to identify visually without counting:
- Quantities between 0 to 10 coins
- The quantity relative to 5 and 10 coins
What do I mean by quantity relative to 5 and 10 coins?
3 coins is 2 coins short of 5 coins.
7 coins is 2 coins more than 5 coins and also 3 coins less than 10 coins etc.
By being able identify the number of coins required to make 5 or 10 coins, students will be able to reposition coins into patterns that they can identify without counting.
Stage 3
Adding numbers that total a maximum of 10.
Working with 2 blocks of 5 spaces. A random number of coins from 0 to 5 is placed in each block of 5 spaces. Keep the coins together and align to the left.
For this example, I shall be adding 4 coins and 3 coins together.
Practice 3
4 coins + 3 coins
Moving 1 coin from the block with 3 coins to the block with 4 coins. A complete block of 5 coins is formed and 2 coins remain in the other block.
Another possible way is to move 2 coins from the block with 4 coins to the block of 3 coins. Both are possible but most would find moving 1 coin easier than moving 2 coins.
Explanation:
Coins are moved to form complete blocks of 5 or 10 coins. In the above example, a block of 5 coins was formed and 2 coins remained in the second block – hence the answer 7 was obtained without counting coins.
This practice can be done with any number of coins and students will eventually realise that forming complete blocks of 5 and 10 coins can be done rapidly.
How long does it take to get to Stage 3?
Every student is different, with regular practice most students will be able to identify quantities visually within a few weeks.
The process of moving from seeing and moving around coins within 2 blocks of 5 coins to being able to do the sums mentally is done through a few stages:
- Moving coins around within 2 blocks of 5 spaces
- Seeing the coins and the blocks but not allowing the student to move them – they move the coins in their mind
- Removing coins from one block. 4 coins plus 3 coins. Leave 4 coins in the first block ask students to add 3 coins without them seeing 3 coins.
Eventually a student will automatically see the following:
4 + 3
4 needs 1 coin to make 5, remove 1 coin from 3 to make 2
5 coins and 2 coins equals 7 coins.
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