Go one too far · Patans

Before you read anything

Nine sixes. Do not work it out. Count out ten sixes instead — ten small piles with six in each.

Now take one pile away. Say what you took, out loud, in two words.

Ten is always easier than nine

Ten sixes is sixty. One six comes off, and fifty-four is left — the number at the top goes to fifty-four, not to fifty-nine.

You went past on purpose and came back. Nobody counted in nines.

You have done this before

:x nutshell-compensation

Doing an easier sum than the one you were asked, then paying back the difference. The paying back is not optional, and it is not always one.

Module 2 did $47 + 29$ as $47 + 30 - 1$. That is :compensation, and this is the same move one operation up. Nothing here is new — it has only been pointed at something bigger.

What comes off is one lot

Otim

worked out 60, then wrote 59

Otim took away one. The thing he did not want was one six, and one six is six.

Say it to yourself every time: ten sixes, take one six. Never take one.

The other direction

$11 \times 7$. Ten sevens is seventy, and you are one seven short — so seventy-seven. Going past and coming back works going the other way round, and it is the same picture with a column added instead of removed.

When this is the wrong move

Cutting at the ten and going past it use the same easy row. Which you reach for depends on which side of it your number sits — and if it is nowhere near a ten, neither helps.

Check yourself

Six to try

Four of these ask how much comes off, or how much goes on — not what the answer is. Answer the question that was asked. Two of them are elevens, where you are one lot short rather than one lot over.

1

$9 \times 3$. Ten lots of $3$ is $30$. How much do you take off?

2

$9 \times 7$. Ten lots of $7$ is $70$. How much do you take off?

3

$11 \times 5$. Ten lots of $5$ is $50$. How much do you add on?

4

$11 \times 3$. Ten lots of $3$ is $30$. How much do you add on?

5

You know $7 \times 10 = 70$ and $7 \times 9 = 63$. What is $7 \times 19$?

6

You know $9 \times 10 = 90$ and $9 \times 3 = 27$. What is $9 \times 13$?

Past it, and back · page 1 of 3 Print it

Past it, and back · page 2 of 3 Print it

Past it, and back · page 3 of 3 Print it

Show that you have it

The one it does not help with

A method you use everywhere is a habit, not a method. One of these is a question where going to the ten costs more than it saves.

1

Otim cuts at the ten every time. Which one does that not help him with?

2

You know $3 \times 10 = 30$ and $3 \times 3 = 9$. What is $3 \times 13$?

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