The bridge, backwards

Before you read anything

$15 - 8$, and count it out loud. Actually do it — say the numbers.

Now count how many times you said a number before you got to the answer. That number is the point of this lesson.

Eight steps, eight chances

Counting back eight takes eight steps, and each one is a place to lose your thread. $15 - 5$ is not slow, because it lands on ten — and ten is a number you can stop at without thinking.

Stop at ten on the way

Eight small hops, then the same journey in two — and the first one stops somewhere you can stop.

Fifteen take five is ten. That used five of the eight, so three are left: $10 - 3 = 7$. Two easy steps instead of eight risky ones.

Nakato

counted back eight and got 8

Musa

stopped at ten, got 7

:x nutshell-bridging

Breaking a jump into two, so that one of them stops at ten. It works going up and going down.

That is :bridging, and it is the same move as the last two lessons walked backwards.

Or ask the addition instead

$15 - 8$ and $8 + \square = 15$ are one picture read two ways, which is module 1 and has not stopped being true.

15 - 8 = \square \quad\Longleftrightarrow\quad 8 + \square = 15

A missing part, whichever direction you read it from.

So use whichever you know. Eight needs two to reach ten and five more to reach fifteen: seven. That is the bridge again, going up.

The numbers get bigger and nothing changes

$85 - 8$. Drop five to eighty, then three more: seventy-seven. Counting back is hopeless here and stopping at a ten does not care.

Notice you did not think about the eighty once. So: why is eighty somewhere you can stop, when eighty-three is not?

Check yourself

Six to try

For each one, say where you would stop on the way. If you would not stop anywhere, that is worth noticing — go back to the animation.

1

$15 - 8$

2

$13 - 5$

3

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

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 $8 + 5$, done by making ten?

6

$7 + 6$

The same eighteen, read backwards · page 1 of 2 Print it

The same eighteen, read backwards · page 2 of 2 Print it

Show that you have it

One fact, and the ones it hands you

The small fact is given. The big one is the same fact with tens in front of it, and should need no working — that is what having a method means.

1

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

2

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

Check what stuck The whole thing on one page