L5 · Adding integers: sums and zero pairs

Learning goal

“I can add any two integers using number-line movement and zero pairs: same signs - add the distances and keep the sign; different signs - cancel zero pairs and see what is left.”

Integer — a whole number that can be positive, negative, or zero (review from L1).

Sum — the result of an addition. -3 + (-2) has sum -5.

Zero pair — one positive and one negative counter, worth 0 together (review from L4 - today it becomes the main adding tool).

Worked example

-3 + (-2). Step 1: On the number line, start at -3. Adding a negative moves LEFT. Step 2: Move 2 more units left: -3, then -4, then -5. So -3 + (-2) = -5. Step 3: Counters agree: 3 negative counters plus 2 more negative counters is 5 negative counters. Same sign, so the distances add (3 + 2 = 5) and the sign stays negative. Model both ways, side by side: line movement with two leftward arrows, AND the counter mat. When both numbers pull the same way, you end up further from zero in that direction. The sign of the sum is the sign they share.

Check yourself — explain it

-4 + (-4) is negative because...

Paired problem — example still visible

4 + 3, shown as movement: start at 4, move 3 right: 7

Faded completion — last step is yours

"-4 + (-1): start at -4, move ___ unit left, land on ___." -> 1; -5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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