# Ten extra projects and questions

Each is optional; choose a useful part. Practical mathematical making includes actual own decisions/direction, not necessarily physical handling or public presentation. Keep completed work, proposals and adult-made examples distinct.

## X01 · Repair a question

Rewrite “Which game and colour is best?” as one useful categorical question. Use fictional replies, check categories and a way to pass; a preference count is not a claim of best quality.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X02 · A traceable record

Give six fictional reply cards temporary IDs1–6; sort one at a time, then trace every ID to one place. These are model-record IDs, not real children's names. Explain why identical replies still count separately.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X03 · Make zero visible

Use C04 rescue3/explore2/return0 plus two no replies. Create a zero row and a separate unknown note. Ask what would change if one new willing reply were return; do not rewrite the previous record.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X04 · Two displays, same data

Represent C08 stripe3/spot3/plain0 as a table and equal-symbol display, one symbol per reply. Compare count precision and immediate tie visibility. Do not make one large symbol mean a larger group without a key.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X05 · Local fact swap

An adult chooses a current public list using FACTS-AND-LOCAL.md; child sorts one reviewed categorical feature. Keep date, source and unknowns. Reading supplied headings is not a visit or survey. If a source is unavailable, keep a fictional model.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X06 · A number-line help strip

Create/direct a useful line for three adult-checked numbers in a chosen two/three-digit range. Label reference values and equal-interval scale. Test a new number; explain why the numeral's physical width cannot decide position.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X07 · A bundle-trade museum

Make/direct two valid displays for308:3 hundreds0 tens8 ones and2 hundreds10 tens8 ones. Add a third if wanted and check value. Use broad drawings/read-aloud units; no purchased manipulatives or touch requirement.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X08 · One problem, two methods

Choose C17 or C18. Keep two own or explicitly modelled strategies and an inverse check. Explain which is useful to you for this problem. A method copied from an adult is named; speed is not the comparison criterion.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X09 · An additive project plan

Create a larger optional paper-gallery plan: needed72 labels,39 ready,33 more by39→40(+1)→70(+30)→72(+2). Child may change the fictional totals and check. Ask about permission/real dimensions separately; this is not completed installation.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

## X10 · A new question board

After actual work, name one further mathematical question: actual money values, equal-group multiplication, fair-length graph scale, measuring a real display, or a larger data sample. This pack gives partial starts, not those complete targets. Choose a next source/lesson rather than inventing its answer.

**A helpful next step:** ask what your chosen representation helps a reader know and what still needs checking. Keep an actual self/reader trial if it happens; otherwise leave a test plan.

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