and ones on a sheet of paper, large enough to arrange popsicle sticks or bread tabs under each. Note in the example below that (IIIIIIIIII) means a bundle of ten popsicle sticks.

Tens Ones

(IIIIIIIIII) IIIII 15

(IIIIIIIIII) 27

(IIIIIIIIII) IIIIIII

5 and 7 gives 12 which is regrouped as 10 in a bundle (1 ten) and 2 individual sticks (2 ones). Move the 5 and 7 individual sticks together and band the sticks together to show 1 bundle and 2 individual sticks.

Now, the 2 ones can still stay in the Ones Room and it is written as 2 in the Ones Room below the line drawn under 27.

But the 1 ten must move to the bigger Tens Room to the left together with 1 ten in 15 and 2 tens in 27. Write 1' between the Tens and 1 to remind you 1 ten has just moved from Ones Room. Together the numbers 1, 1 and 2 in the Tens Room make 4 tens which is written as 4 in the Tens Room below the line drawn under 27. Move the 1 bundle from 15 and 2 bundle from 27 as well as the 1 ten together to show 4 bundles.

So, 15 + 27 = 42 Repeat the story with other sets of 2 numbers.

TEACHING SUBTRACTION

Example: 42 + 15

Say that 15 quarreled with some members of 42 and wanted to leave the House of 42.

Tens Ones

4 2 - 1 5

Show the 4 bundles of tens and 2 individual sticks. Since 5 cannot go away from 2, we regroup 1 ten into 10 ones. That makes 3 tens and 12 ones.

We have no more 4 tens but we now have 3 tens, so cancel the number 4 and write the number 3 above. We have 12 individual sticks now instead of 2, so cancel the number 2 and write the number 12 above the canceled 2.

Do not teach children to just write the digit 1 next to the number 2, right in between 4 and 2. The reason is that this digit 1 does not have the same meaning as the digit 1 written between Tens and 1 in the addition story above. It also does not represent a value 1 one but a value 1 ten.

Next, move 5 ones from 12 ones and 1 ten from 3 tens. The remaining bundles and individual sticks will show 2 tens and 7 ones.

So, 42 - 15 = 27

The concepts of tens and ones, renaming and regrouping are very important to the four operations of numbers, namely addition, subtraction, multiplication and division.

By teaching children to represent the regrouping of numbers, as in the subtraction story above, children become clearer that the digit 1' represents a different quantity below Tens and below Ones. They will be less confused when they learn the Division Algorithm which involves renaming and regrouping as well.

Why do children get more confused and grades fall as they grow older? It is not because they grow more stupid or that the Mathematics is beyond their understanding. It is because they do not understand the basic concepts taught to them at a younger age. They could 'do' Mathematics by memorizing the steps of an addition or subtraction algorithm. As they grow older, they need understanding and thinking skills to be able to solve problems which cannot be memorized.

It is thus important for teachers to think through teaching processes carefully, rather than use short cuts which help children do Mathematics without a clear grasp of the concepts to be learnt.

Learn more about this author, Lokemun Magar.
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