Day 4 · Simplifying keeps the relationshipYear 11 Essential Maths · T1 W1–2 · Day 4 lesson

Goal: find Card B's simplest whole-number ratio and verify equivalence. 25 = 2 + 5 + 6 + 7 + 5.

1. 0–2: Show 4:6 beside 2:3; ask what operation could link both numbers.
2. 2–7: Model dividing both parts by common factor 2: 4÷2:6÷2 = 2:3. Reverse by multiplying each part by 2. Keep the ten actual cue cards visible.
3. 7–13: Learners simplify Card C's 8:12 by 4 to 2:3 and explain why dividing only the first term is invalid. Use a calculator only as a check.
4. 13–20: Routes: regroup counters into equal 2-or-4-part bundles on the simplify ladder; complete paired divide/multiply arrows; use offline ratio lab or type/speak two equivalent ratios and their common factor. All routes prove both terms changed by the same factor.
5. 20–25: Exit “Does simplifying 4:6 to 2:3 discard cards?” Key: no, it expresses the same relation in lowest whole-number terms. Move: reconstruct 4:6 from 2:3 to show equivalence.

Alternative domains: imaginary library badges or game tiles. Optional/home: simplify a made-up 10:15 symbol mix; no real counts. Two more cases.