## The enemy of your enemy is your friend: mnemonics and negative integers

From April 26, Tuesday: J-‘s studying for Thursday’s “in-class performance assessment” on integers. (In-class performance assessment? What happened to the good old word “quiz?” Too much anxiety?) We’re spreading the review out over the next two evenings.

The test will cover adding and subtracting positive and negative numbers. J- and her study group are already off multiplying and dividing (which apparently don’t turn up until grade 8 – really?). W- made up a quick worksheet for J- to practise adding, subtracting, multiplying, and dividing integers.

“The enemy of your enemy is your friend,” I heard her say as she solved the exercises, writing down the correct signs for all the products and quotients. I grinned. I’d taught them that mnemonic two weeks ago. It’s a way to remember the results of multiplying or dividing numbers.

As I explained to the kids: you don’t have to stick to this in real life. Pou can certainly be friends with the friends of your enemy. But this might help you remember the signs for multiplication and division:

- The friend of your friend is your friend. Positive times positive is positive.
- The friend of your enemy is your enemy. Positive times negative is negative.
- The enemy of your friend is your enemy. Negative times positive is negative.
- The enemy of your enemy is your friend. Negative times negative is positive.

A | B | Result |

Friend + | Friend + | Friend + |

Friend + | Enemy – | Enemy – |

Enemy – | Friend + | Enemy – |

Enemy – | Enemy – | Friend + |

Glad to see it stuck in her head! She answered all the exercises correctly (and quickly, too).