Ten does the work

Before you read anything

Two rows of ten, and fifteen stones. Draw two rows of ten boxes. Put 8 stones in the first row and 7 in the second.

Now fill the first row. Do not count anything — just move stones across until the top row is full.

Look at what is left in the bottom row, and read the answer off the picture.

The fifteen you laid out

Eight and seven. Not yet in frames — just fifteen things, in the two piles you were given.

What you actually did

The same two rows you just filled. Two counters cross, and the frame is full — the answer is read, not worked out.

You did not add $8 + 7$. You moved two stones — >watch the two cross over — and then read $10 + 5$, which nobody has to work out.

But how did you know it was two?

Because eight needs two — and that is a :number bond, which you already have. That is the pause module 1 ended on, gone — you read the parts off instead of working them out. That is the whole reason the bonds were worth learning: they are what makes the move possible without stopping to think.

:x nutshell-number-bond

A whole cut into two parts. Seven is four and three, and it is also five and two.

Every sum that crosses ten works the same way. Fill up to ten, and add what is left over.

Now do it yourself

Ten counters and a divider. Drag it and watch what each number needs to reach ten — that is the only fact this method runs on.

Every position is a true split. There is nothing here to get wrong.

The numbers get bigger and nothing changes

$48 + 7$. The eight still needs two, the two still comes out of the seven, and $50 + 5$ is still not a sum anybody has to do.

This is the test of a method. Counting on works for $8 + 7$ and falls apart at $48 + 7$. Filling up to ten does not care how big the tens are.

Check yourself

Six to try

Some of these want the answer and some want the steps. Both are asking the same thing — what does the first number need, and where does it come from.

1

What must be added to $2$ to make $10$?

2

Which of these is $8 + 5$, done by making ten?

3

Which of these is $9 + 6$, done by making ten?

4

$7 + 9$. You take $3$ out of the $9$ to make ten. How much of the $9$ is left?

5

Which of these is $7 + 7$, done by making ten?

6

$7 + 6$

Eighteen on paper · page 1 of 2 Print it

Eighteen on paper · page 2 of 2 Print it

Show that you have it

One fact, and the ones it hands you

You are given the small fact. The big one should take no working at all — if you find yourself adding, go back to the picture and move the stones again.

1

You know $7 + 9 = 16$. What is $67 + 9$?

2

You know $9 + 8 = 17$. What is $29 + 8$?

Next: The other route The whole thing on one page