L3 · Combined integer problems in context

Learning goal

“I can solve multi-step integer problems in context: I rewrite every subtraction as an addition, keep track of each change in order (or group positives and negatives), and report the final value with its sign and unit.”

Net change — the single total change after all the gains and losses are combined (rises 11 then falls 6 -> net change +5).

Balance — the amount in an account at a moment in time; it can be negative when more has been taken out than is there.

Deposit — money put INTO an account: a positive change to the balance.

Withdrawal — money taken OUT of an account: a negative change to the balance. (A fee is also money taken out.)

Worked example

At 6 a.m. the temperature was -8°C. By noon it had risen 11 degrees. By 10 p.m. it had fallen 6 degrees. What was the temperature at 10 p.m.? Step 1: Write the chain: -8 + 11 - 6. Each change is one move on the line. Step 2: First two steps: -8 + 11 = 3 (the noon temperature). Step 3: Then the fall: 3 - 6 = 3 + (-6) = -3. Temperature at 10 p.m.: -3°C. A counter check on the final step agrees: 3 positives, 6 negatives - 3 zero pairs cancel, 3 negatives remain. Say it plainly: work the chain in the order the events happened, and say each landing point out loud before the next move.

Check yourself — explain it

The fall of 6 degrees is written as -6 (subtract 6) because...

Paired problem — example still visible

A diver is at -24 m. She rises 9 m, then descends 5 m. Where is she? -> -24 + 9 = -15; -15 - 5 = -20 m

Faded completion — last step is yours

"A game score: start 0, gain 15, lose 20, gain 8: 0 + 15 - 20 + 8 = ___" -> 3

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