Resource 2 · Reviewed by an experienced teacher. Not yet classroom-trialled.
Goal: compare the same nonzero digit in adjacent whole-number places. One place further left gives that same digit ten times the value. This is not a rule for any two different digits.
Entry: in 110 ask for 100 and 10 and how many tens make 100; in 3300 ask for 3000 and 300. Unclear units → Resource 1. Explain comparison language as needed; record help. Keep 440/470 for the later contrast check.
Prepare: solve the examples; an aide rehearses with the teacher. One short bar matches one long-bar part and one interval. Count circled parts/jumps 1–10, naming each value. Ten intervals have eleven ticks. Ask what 10 and 20 mean in 200 = 10 × 20. Each page’s labelled scale is separate.
Use: teacher chooses pace; every pupil shows a response. Guided labels: 50, 150, 300, 450; five 50s = 250; ten 50s = 500. Jump 5 ends at 250; jump 10 at 500. In 500 = 10 × 50, 10 counts parts/jumps and 50 is each part’s value/jump size. Fade support when pupils can explain; restore it when needed.
Contrast: 530: the ten-part 30 bar and ten +30 jumps end at 300, short of the 500 bar. All share one scale. Place units remain tenfold; different digit values need checking. 440: 400 = 10 × 40, yes. 470: 10 × 70 = 700, not 400, so no. On the guides, pupils draw/number ten copies and label their endpoint. Each small space matches the short bar. Require equations and explanations, not “same digits”. Record the guided explanation separately. Immediate Form A does not test this overgeneralisation; delayed Form B samples it in Question 5, but still ask for a fresh explanation. No fractional ratio is required.
Practice key: after correcting 500 = 10 × 50, fresh 770: 700 = 10 × 70. 990: tens-place 9; 900 and 90. 554: 500 = 10 × 50. 7770: 7000 = 10 × 700. 9960: 9000 = 10 × 900.
“In 880, name the two 8s’ values and explain their relationship.” Expect 800 and 80; ten equal 80s make 800. A bare “10” is insufficient. Record help; prompted work is not independent.
Questions 1–5: immediate A: A, C, D, B, C; delayed B: C, D, B, D, C.
Later: after a few days try 5520 (5000 = 10 × 500) without models; record date/help. Independent success → reduce support and revisit. Persistent/mixed errors → inspect explanations and prerequisites. No response is missing evidence. No fixed mastery score.
Next step: identify both digit values and explain why the same nonzero digit has ten times the value one place further left.