L4 · Integer problem-solving clinic

Learning goal

“I can handle the problem types that hide integer operations: find a missing start, missing addend, or missing change using inverse operations; compare two integer expressions; and find the (always positive) distance between two positions.”

Unknown — the missing value in a problem, written as a box or a letter, that the calculation must find.

Inverse operation — the operation that undoes another: adding 14 undoes subtracting 14. Used to work backwards from a result.

Difference — the result of a subtraction; as a distance between two positions it is never negative.

Net change — the total combined change.

Worked example

After a drop of 14 degrees, the temperature is -9°C. What was the temperature before the drop? Step 1: Write what happened: (start) - 14 = -9. The start is the unknown. Step 2: Work backwards on the line: the drop moved LEFT 14. Undo it - move RIGHT 14 from the result: -9 + 14 = 5. Step 3: Check by running it forwards: 5 - 14 = -9. The start was 5°C. Counters confirm the check: 5 positives take away 14 - add 14 zero pairs, remove 14 positives - 9 negatives remain: -9. Say it plainly: to undo a move, make the opposite move from the result.

Check yourself — explain it

We add 14 to undo the drop of 14 because...

Paired problem — example still visible

A balance fell to -$21 after a $35 withdrawal. What was the balance before? -> -21 + 35 = $14 (check: 14 - 35 = -21)

Faded completion — last step is yours

"x + (-17) = -6, so x = -6 + ___ = ___" -> 17; 11

Ready to practise?

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

Start practice →Take the unit quiz