L4 · Opposites and additive inverses

Learning goal

“I can find the additive inverse of any integer - the opposite number that pairs with it to make zero - and I can show the pair with counters and on the number line.”

Opposite — two numbers the same distance from zero, on opposite sides: 6 and -6.

Additive inverse — the same idea named by what it DOES: the number you add to a number to get 0. The additive inverse of 6 is -6, because 6 + (-6) = 0.

Zero pair — one positive counter and one negative counter together. A zero pair is worth 0, so adding or removing zero pairs never changes a value.

Worked example

Show that 6 and -6 cancel. Step 1: On the line, 6 and -6 are mirror points: same distance from zero, opposite sides. Step 2: With counters: 6 positive counters and 6 negative counters form 6 zero pairs. Every pair is worth 0, so the total is 0. Step 3: As an addition sentence: 6 + (-6) = 0. That is why -6 is called the additive inverse of 6 - it is the number that "undoes" 6. Model both ways, side by side: the number line with the two mirror points and a path from 6 back to 0, AND the counter mat with pairs circled. Opposites don't just look mirrored - they cancel. Their sum is always 0.

Check yourself — explain it

The additive inverse of -3 is 3 because...

Paired problem — example still visible

Find the additive inverse of -11 and write the addition sentence that proves it: 11, because -11 + 11 = 0

Faded completion — last step is yours

"-7 + ___ = 0, so the additive inverse of -7 is ___." -> 7; 7

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