Day 12 · Exponents make the hypothesis… | Year 9 Inquiry · T1 W3–4

Question: What exactly would repeated halving predict? Kit: Source B, model table, calculator optional. 35 = 3 + 7 + 12 + 8 + 5.

0–3: Call the baseline 160 arbitrary units and the number of layers n; no real lux is implied.
3–10: Model P(n)=160×2^-n=160/2^n for integer n≥0. At n=0, 2^0=1, so 160; at n=4, 2^-4=1/16, so 10. State the identical independent half-transmission assumption explicitly.
10–22: Learners fill predictions for n=0,1,2,3,4 and compare to B's recorded column without changing either. Explain why 2^-2 = 1/4 rather than −4 and why 2^a×2^b=2^(a+b) describes repeated factors.
22–30: Label a graph/table key conditional prediction versus invented recorded value. Routes: 160 paper-unit strips halved successively with proportional drawing; tactile powers-of-two/place-value cards; symbolic table and written/AAC explanation. No route demands memorising the formula without meaning.
30–35: “If an untested fifth layer obeyed the same model, what would P(5) be, and is it a measured result?” Key: 5 model units, prediction only. Response move: if 5 is called observed, draw a boundary beneath n=4 in the record.

Another domain: Model a fictional rehearsal cue that halves a count each stage; retain the if. Home: explain 2^-3 using eight equal paper marks.