Read the clue aloud slowly, then give five seconds of quiet think-time before any hands go up.

Take three hands-up answers, not open call-outs. Listen for pupils who correctly hear "no hundredths" as a zero placeholder in the hundredths column. Do not confirm the answer yet — the point is that one clue can name some columns and still leave others open, and that is what the lesson builds on.

Clue 1: tenths and hundredths named, thousandths left open. Ask how many numbers still fit, draw out ten candidates 0.340 to 0.349 (0.341, 0.342, 0.343 among them).

Clue 2: name the two fences 0.3 and 0.35. Ask which numbers this crosses off, not just which it keeps, e.g. 0.36 and 0.4 sit past 0.35. Point: a clue can keep every candidate and still do work by ruling out numbers never on the list.

Clue 3: the finish. A leftover thousandths digit means x100 never lands whole, e.g. 0.343 x 100 gives 34.3. Only 0.340 x 100 gives 34, a whole number, so the answer is 0.340.

The reasoning move the lesson rests on: each clue rules candidates out until one is left.

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Build the candidate list on the mat as you go. After clue 1: the number is 0.4?, so 0.40 to 0.49. After clue 2 (hundredths above 5): 0.46, 0.47, 0.48, 0.49. After clue 3 (rounds up to 0.5): all four still round up, so no change — let pupils notice that a clue can rule nothing out and still be useful for confirming. After clue 4 (hundredths odd): only 0.47 and 0.49 survive. Pause here on your prediction check, then ask what single extra clue would settle it to one (e.g. "my hundredths digit is smaller than 8").

Revoice a strong answer: "so the clue didn't name the number, it just crossed some off."

These are the practice questions — pupils work each clue in turn on paper, then the class confirms the surviving numbers aloud before moving on. Keep the pace brisk rather than over-explaining.

The answer is 0.604. Track the narrowing together: clue 1 gives 0.6??, clue 2 fixes the hundredths to zero (0.60?), clue 3 confirms it stays between 0.6 and 0.61, clue 4 leaves thousandths of 4 or 8 (0.604 or 0.608), clue 5 (below 6) crosses off 8, leaving 0.604 alone.

The puzzle is worked on paper; the place-value mat from the earlier steps is the model to think with. Ask a stretch question to fast finishers: "which clue did the most work — which one crossed off the biggest chunk?"