# Day 64 — Spacing can trick us

**25 minutes · AC9MFN03 · educator review pending**

**Success:** Child compares sets that look misleading because of spacing, then verifies by counting and/or one-to-one pairing. Child says which evidence changed or confirmed the first impression.

**Prepare:** [C04](print-aids.md), A=10 close together, B=17 wide apart; [C09](print-aids.md), A=18 close together, B=16 wide apart. Use the same-sized counters; later use differently sized paper outlines to show that picture size is also irrelevant. New check: A=12 spread, B=18 close.

1. **Retrieve, 3 min.** Show two empty labelled trays and ask for two reliable comparison tools: move/count and pair.
2. **Model, 5 min.** Show C09 with B's row longer because of gaps. Say, “My eyes notice space, but space may not tell the number.” Pair or count: A18/B16. State A more with two unmatched after pairing.
3. **Detective game, 10 min.** Pairs take C04 and C09. For each, they privately predict, then use **both** count and pair to test. They do not erase an earlier guess; they say what the evidence showed. Teacher focuses on three learners and asks for the exact unpaired object or count, not “it just looks bigger.”
4. **Fresh check, 4 min.** Set A=12 widely spaced and B=18 tightly grouped. Ask which has more and require a count or pairing demonstration. Child may direct another person to move objects.
5. **Close, 3 min.** Ask, “What stayed the same when we moved the counters farther apart?” **Key:** C04 B more 17/10, B seven unmatched; C09 A more 18/16, A two unmatched; fresh B more 18/12, B six unmatched.

**If the child changes a count when pieces spread:** Recount by moving each piece once across a boundary, then return to the same set without adding or removing. **Access and record:** Tactile spacing can be misleading too; use physical pairing cups and clear spoken evidence. Record prediction separately from checked result and note the strategy used.