Day 17 · A variable can appear on both sidesYear 8 Maths · T1 W3–4 · Day 17 lesson

Codes: AC9M8A02, AC9M8A03. Goal: solve and graph the crossing of two fictional linear plans, then state what the equality means. Prepare: graph and number-line board.

1. Launch · 2 min. Fictional design plans: A 6+4n tokens, B 18+2n tokens for n whole batches. Ask what is fixed and what grows.
2. Model · 5 min. Set 6+4n=18+2n. Subtract 2n, then 6: 2n=12, so n=6. Check both equal 30. At n=5, A 26/B 28; at 7, A 34/B 32.
3. Guided · 6 min. Plot A's (0,6),(6,30) and B's (0,18),(6,30) with labelled axes. The intersection agrees with algebra; integer x-values are the actual batch cases. Draw a line for shape but do not interpret half a batch as offered.
4. Practice · 6 min. D17-A/B/C use new pairs; each route finds equality algebraically, verifies and sketches or describes the crossing.
5. Exit · 4 min. Which plan is lower at seven batches and by how much? B=32 versus A=34, so B by 2 tokens under this invented model.
6. Note · 2 min. If graph/intersection is approximate, use substitution to settle the exact equality. Record unit and omitted conditions.

Later: Day17 extra checks a nearby count.