Number bonds

The bit that sticks out

Before you read anything

Draw both, not one. Otim has 8 goats. Musa has 14. Two bars, one under the other, both starting at the same place on the left.

Nobody is being split

Two amounts, lined up at the left. The difference is the piece of Musa's bar with no Otim above it — a length, before it is a subtraction.

The last three lessons cut one bar into parts. Here there is no whole: Otim's goats are not part of Musa's. Two amounts sit side by side, and the only question is how far one goes past the other.

Why the left edge matters

Line them up at the left, or the picture is worthless. Started level, the difference is a length you can put a finger on. Started anywhere else, it is two rectangles and somebody's word that one is longer.

The subtraction arrives on its own

14 - 8 = 6
The picture first. The calculation is a caption for it.

You did not choose to subtract. You drew two bars and looked at the gap, and $14 - 8 = 6$ writes down a thing that had already happened.

The word that lies to you again

"More" means add. Usually. Not here.

Otim has 13 goats. That is 6 more than Musa. The 6 is the overhang, and Musa is the bar underneath it — so $13 - 6 = 7$.

Amina

drew both bars, saw the 6 sticking out, took it off

Musa

saw "more" and wrote $13 + 6$

Draw it and there is nothing left to decide. Musa's bar is the short one, and 19 is not shorter.

What this does not do yet

It compares two things. Three bars, or one bar three times another, is this same picture with more drawn on it. Module 12 comes back and names it.

Check yourself

Three to try

Two bars every time, both starting at the left, even for the first one where you can see the answer without drawing anything.

1

Akello has 5 mangoes. Bwire has 12. How many more does Bwire have?

2

Otim has 8 goats. Musa has 14. Which calculation says how many more Musa has?

3

Two bars are lined up at the left. The longer one sticks out past the shorter by 4. What does that 4 tell you?

Show that you have it

When the gap is the thing you are given

The first one hands you the difference and hides a bar. Draw the long one, mark the overhang, and what is left underneath is the answer.

1

Otim has 13 goats. That is 6 more than Musa. How many goats does Musa have?

2

Nakato has 9 beads and Musa has 9. Drawn as two bars lined up at the left, what does the picture show?

3

A bar for 20 and a bar for 14 are lined up at the left. Which calculation gives the bit that sticks out?

4

Why are the two bars always lined up at the left?

Check what stuck The whole thing on one page