Day 19 · Negative multiplication reverses the orderYear 8 Maths · T1 W3–4 · Day 19 lesson

Codes: AC9M8A02. Goal: solve an inequality with a negative coefficient and verify boundary/nearby values. Prepare: graph/number-line board.

1. Launch · 2 min. Consider a purely fictional counter tray that starts at 15 and loses 3 counters each turn: r=15−3t, t=0,1,2,3,4,5. Ask when more than 3 remain.
2. Model · 5 min. 15−3t>3; subtract 15: −3t>−12; divide by −3 and reverse sign: t<4. Allowed turns are 0,1,2,3. Test 3→6 (true), 4→3 (not greater).
3. Guided · 6 min. Show why the reversal is necessary by testing t=5: 15−15=0, so t>4 would be wrong. Draw an open dot at 4, arrow left, then restrict to the stated whole-number domain.
4. Practice · 6 min. D19-A/B/C solve other negative-coefficient inequalities, check boundary and a value on each side, and explain reversal in words.
5. Exit · 4 min. Solve 8−2u≥0: u≤4, with u=4 true at zero and u=5 false. If no physical context is specified, give the real-number set; if whole turns, list non-negative whole values through 4.
6. Note · 2 min. If sign stays unchanged after dividing negative, test a counterexample before re-teaching the symbolic rule.

Later: Day19 extra practises another reversal with a different sign.