# Day 45 — Equal, empty and most

**25 minutes · AC9MFST01 (compare object and image data for a given question); partial practice · educator review pending**

**Success:** The child recognises a tie and an empty category in a small data display, checks counts and answers only what the data show.

**Prepare per pair:** [D4](print-aids.md): five BALL and five CONE label cards, plus an empty labelled HOOP category mat; object/picture chart. The question is “Which sports-shed label is tied for most?” Do not put a fake “zero card” in the bag.

1. **Retrieve, 3 min.** Show two equal five-object groups on different-shaped mats. Ask whether one must be more because it looks wider; count to check.
2. **Model, 6 min.** Collect and sort two BALL and two CONE cards. Point to HOOP's empty category. Say, “No hoop card has appeared so far. We will finish collecting before we decide the final counts.”
3. **Guided investigation, 9 min.** Partners collect and sort the remaining six cards, transfer one picture mark per card and count each category. Ask for most, tie, zero and total, with a demonstration or count as evidence.
4. **Fresh try, 4 min.** Give a smaller new sample: one spiral, three star and zero square cards, with a labelled empty SQUARE mat. “Collect, sort and tell me which mark appears most, which fewest, and how many cards in this new set?” The full [D6](print-aids.md) is an optional later extension.
5. **Check, 3 min.** Return to the D4 question. **Key:** BALL 5 and CONE 5 are tied for most; HOOP 0; total 10. Fresh sample star 3 most, square 0 fewest, total 4. Optional full D6: star 6 most, square 1 fewest, total 10.

**If the child says the zero category does not belong:** Show its labelled mat and the given question; zero is a valid count after the whole deck is collected. If “most” is answered from picture size, count or pair the marks. Do not infer why a category is empty; only report that no matching card occurred in this deck.

**Access and record:** Raised category borders, large labels, plain text, AAC or directed movement are available. Record tie/zero reasoning, all three counts, total and prompts. Use [assessment.md](assessment.md) to plan any fresh check.