# Day 26 · An estimate with a useful clue

**Try a quick estimate. What helped you guess?**

Useful purpose: Estimate a collection using a known group rather than treating a guess as an exact count.

## 1 · Find the starting point

Revisit tens/hundreds and reasonable group sizes. Ask what 'about' means and whether an estimate can be checked without shaming a first try.

## 2 · Prepare a suitable invitation

Offer a safe age-suitable collection of large paper pieces or a supplied description. Adult prevents choking/throwing issues; no public head count, identifiable class survey or collection purchase. Show one known group before revealing the exact total.

## 3 · Brief worked model

MODEL collection has four visible groups about the size of a known 20-piece group and a smaller loose group. I estimate 80–100 pieces. On checking there are 86. 'About 90' would help prepare enough space; it is not the exact 86-piece count. I keep both records.

## 4 · Guided new try

Use an unrelated known 10-piece group and a partially shown collection. Ask whether 10,50 or 500 could be sensible and why. Explain what hidden parts keep the result uncertain.

## 5 · Own attempt

Make a benchmark estimate and a reason before counting/reading the count. Then check and describe whether the estimate was useful for the purpose. No required closeness score.

## 6 · Observe and respond

Record benchmark, reasonable scale and purpose, not only distance from exact total. If the child sees the answer first, record exposure and choose another collection later.

## Specific next teaching

If the child makes an unanchored guess, compare one known group with two groups using new objects. If the estimate is purposeful, hide a small portion and ask what range is still justified.

## Pick a route

### 1 · Paper-piece estimate

**About how many could this be?**

Use a safe approved collection; choose a known group size and compare before counting. Count or direct grouping to check, then say which estimate would be useful for preparing storage.

Observe: Benchmark and order of estimate-before-count; true count separately.

Next teaching: Try a new collection with another benchmark.

Evidence boundary: Own estimation/counting/directing; exact outcome not predetermined.

### 2 · Hidden corner

**What could be in the part we cannot see?**

MODEL: three known groups of 15 pieces are visible; one similar-size group is partly hidden. Estimate around 60, but state the unseen count is unknown. Do not write 60 as an observed total.

Observe: Visible 45 and justified uncertain estimate.

Next teaching: Use an unrelated partly described collection with an explicitly empty unknown field.

Evidence boundary: Supplied partial-information reasoning.

### 3 · Storage proposal

**Which count sounds possible?**

MODEL: a known 25-piece pile fits one small square; another collection fills about four such squares. Compare estimates 10,100 and 1000 and choose 100 with a reason, not an exact count claim.

Observe: Scale/benchmark connection and uncertainty.

Next teaching: Ask what would be needed to establish the exact count.

Evidence boundary: Model estimate only.

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