# Foundation / Prep mathematics · Days 91–100

Ten **25-minute** blocks. Use [exact setup cards](MATERIALS.md), large safe counters, labelled trays and [number mat](number-and-change-mat.svg) or equivalents. Give the child time to move, point, draw, sign, AAC-compose or direct a scribe. Sample first independent reasoning before a hint; record the exact access route. AC9MFN01/03/04/05 are proposed **partial** Foundation links, not a judgement that the full descriptions are met. A mathematical count from a fictional card is separate from the science test's observed movement.

## Week 19 · Day 91 — Start, add, now

**Goal:** represent a practical increase from 5 to 7 and explain what changed. **Codes:** AC9MFN05, AC9MFN03. **Prepare:** card A and three labelled trays.

1. **Retrieve · 3 min.** Flash 4 large counters briefly; child names the amount or counts, then checks. Record whether it was subitised or counted.
2. **Model · 5 min.** Place 5 paper ramp marks in **Start**. Move them to a row, add 2 distinct marks and count each once: 1–7. Say “Five, then two more; seven now.” The number is a **card count**, not the toy's movement.
3. **Guide · 5 min.** Repeat with 3 then 2 on a new tray; child says, signs or selects “add” and shows 5. Check by pairing each count word to one object.
4. **Independent · 7 min.** Child uses **new** 5 then 2 with card A, chooses objects/digital marks and records **7** or shows a seven collection. Ask “How do you know?” before demonstrating. Exact expected total: **7**.
5. **Compare · 3 min.** Ask whether adding paper marks proves the toy will travel farther. Expected **no**; numbers model the setup only.
6. **Exit · 2 min.** Give 4 then 1; expect **5**. Next day reteach one-to-one counting if any mark was skipped or counted twice.

## Week 19 · Day 92 — Remove from a paper plan

**Goal:** model taking away while preserving the starting count. **Codes:** AC9MFN05, AC9MFN03. **Prepare:** card B, eight large plant-picture cards.

1. **Retrieve · 3 min.** Show yesterday's 5 + 2 as objects and ask for the result before giving any numeral.
2. **Model · 5 min.** Count **8** paper plants into a row. Move **3** into a labelled **removed** tray, leaving 5 visible. Say “Eight in the paper plan; three removed; five remain.” Do not call them living plants.
3. **Guide · 5 min.** Use 6 then remove 2. Child moves exactly two and checks **4** remain; point out that removed cards still exist but are outside this plan.
4. **Independent · 7 min.** Present a new 8-card set. Child removes 3 and shows/records **5**. Ask for a reason using their objects, not a memorised fact.
5. **Transfer · 3 min.** With 5 art paper squares remove 1; expect **4**. Note whether the child recounts all or counts back accurately.
6. **Exit · 2 min.** Ask “Did we add or remove?” and point to the **start** count. Reteach the starting state if the child reports only the final five.

## Week 19 · Day 93 — Another setting, same structure

**Goal:** recognise addition in a made-up library card scenario and represent 6 + 4 with objects. **Codes:** AC9MFN05, AC9MFN03. **Prepare:** card C and ten book-picture cards.

1. **Retrieve · 3 min.** Give 7 then remove 2 with counters; expect **5**, check with visible objects.
2. **Model · 4 min.** Place six book cards in a drawn tray, then four more. Group six as five and one if helpful, then count all: **10**. Say this is a **fictional** return tray.
3. **Guide · 6 min.** Child builds 5 then adds 3, counts **8**, and explains how they avoided recounting a card twice.
4. **Independent · 7 min.** Child models the new 6-and-4 card, writes/selects **10**, then checks by one-to-one recount. If the child uses a valid count-on strategy, record it exactly.
5. **Compare · 3 min.** Show ten as two groups of five; ask if moving cards into a different shape changes the total. Expect **no** if none added/removed.
6. **Exit · 2 min.** Give 3 then 4 large counters; expect **7**. Tomorrow ask for a direct removal setup if addition is secure.

## Week 19 · Day 94 — Take away, then check by replacing

**Goal:** show 9 − 2 as a change and verify by returning the removed objects. **Codes:** AC9MFN05, AC9MFN03. **Prepare:** card D, nine frame cards and a separate removed tray.

1. **Retrieve · 3 min.** Ask child to show 6 then 4 with counters and say the resulting ten.
2. **Model · 5 min.** Count **9** paper art frames, take away **2**, count **7** left, then put 2 back and recount **9**. Say the return checks the starting collection; it is not a new art event.
3. **Guide · 5 min.** Child starts with 7, removes 1, shows **6**, replaces it and checks 7. Use exact matching rather than guessing.
4. **Independent · 7 min.** Child performs card D with new cards; expected **7** left and **9** after replacing two. Record first result before verbal help.
5. **Explain · 3 min.** “If I kept the two removed cards in the same count row, what mistake could happen?” Expected: count them as still on the wall/model, giving nine instead of seven.
6. **Exit · 2 min.** 8 take away 3 leaves **5**. Group missed one-to-one/removal children for a fresh concrete recheck.

## Week 19 · Day 95 — Two parts can make one total

**Goal:** combine and partition 7 in a new context; distinguish a part from the whole. **Codes:** AC9MFN04, AC9MFN05. **Prepare:** card E, two textured or labelled trays.

1. **Retrieve · 3 min.** Show a 9-card paper model, remove two, ask the child to demonstrate seven left.
2. **Model · 5 min.** Put **4** game markers in tray A and **3** in tray B. Slide together without losing any: **7** whole. Separate again: 4 and 3 are **parts** of 7.
3. **Guide · 5 min.** Build 7 as 5 and 2 using seven counters; child names both parts and checks by recombining.
4. **Independent · 7 min.** Child receives seven blank counters and two trays. Find **another** split, such as 6 and 1, and show that all seven are present. Record the split actually made; more than one answer is correct.
5. **Transfer · 3 min.** Ask whether 4 + 3 markers tells how far a ramp toy went. Expected **no**; it is a marker count.
6. **Exit · 2 min.** Show 3 in one tray and 4 in the other, ask for whole **7** and one alternative part split. If whole and part were confused, start Week 20 with a five-object version.

## Week 20 · Day 96 — A full ten and some more

**Goal:** represent and name 14 as ten and four. **Codes:** AC9MFN01, AC9MFN03. **Prepare:** card F, a ten-frame and four separate large counters.

1. **Retrieve · 3 min.** Make 7 as 5 and 2; ask which is the whole and check all seven are present.
2. **Model · 5 min.** Fill **ten** spots, then place **four** beside the frame. Count “ten, eleven, twelve, thirteen, fourteen”; show numeral **14**. Say the 1 names one ten, not one loose counter.
3. **Guide · 5 min.** Give one full ten-frame plus 2 separate counters; child names **12**, then shows the numeral card.
4. **Independent · 7 min.** New one full ten-frame plus **4**; child builds/chooses **14**, points to the ten and four, and recounts if needed. Record whether the child shows a matching collection.
5. **Compare · 3 min.** Place numeral **41** beside **14**; ask which matches ten and four. Expected **14**. Avoid a place-value lecture beyond this concrete distinction.
6. **Exit · 2 min.** Full ten plus one; expect **11**. If teen naming is uncertain, retain the full frame tomorrow.

## Week 20 · Day 97 — Order is a claim we can check

**Goal:** order selected numerals from 0 to 20 and verify with matching collections. **Codes:** AC9MFN01, AC9MFN03. **Prepare:** card G and numeral path.

1. **Retrieve · 3 min.** Build ten and four and match **14**.
2. **Model · 5 min.** Place **0, 7, 12, 16, 20** on the number path in order. Make seven with counters, then ten and two for twelve; explain why twelve comes after seven.
3. **Guide · 5 min.** Give mixed **0, 5, 10, 15** cards; child places them increasing and checks with path positions or collections. Zero represents none in an empty tray, not missing data.
4. **Independent · 7 min.** Shuffle card G; child orders **0, 7, 12, 16, 20**, points to one matched collection, and says which is just before/after **16** in **this selected list** (12/20). Do not confuse list neighbours with consecutive integers.
5. **Reason · 3 min.** Compare 12 and 16 as one ten plus two versus one ten plus six; expect **16 greater**.
6. **Exit · 2 min.** Ask child to show **0** with an empty tray and name a card greater than 12. Reteach numeral–collection matching if necessary.

## Week 20 · Day 98 — Same total, different useful pictures

**Goal:** represent 10 as two parts and explain that arrangements do not change the whole. **Codes:** AC9MFN04, AC9MFN01. **Prepare:** ten counters and two labelled trays.

1. **Retrieve · 3 min.** Ask which is greater, 14 or 12, using a ten-frame if needed.
2. **Model · 5 min.** Split ten into **6 and 4**, then **5 and 5**. Count all ten each time. “The parts changed; no counter was added or removed from the whole.”
3. **Guide · 5 min.** Child makes **8 and 2**, slides together and checks ten. If a counter falls, pause and restore the exact collection.
4. **Independent · 7 min.** Child chooses a new split of ten, records both parts with marks/digital tiles and proves total ten by one-to-one count or an accurate known composition.
5. **Explain · 3 min.** Show two layouts of the same ten. Ask whether a long row has more than a compact group; expected **same** if one-to-one matches.
6. **Exit · 2 min.** Show seven and three; expect whole **10**. Tomorrow use fresh parts if the child relied on copying.

## Week 20 · Day 99 — Choose and explain a number sample

**Goal:** explain one dated number model and identify what it does and does not show. **Codes:** AC9MFN01, AC9MFN03, AC9MFN04. **Prepare:** two invented adult examples and optional consented child sample.

1. **Retrieve · 3 min.** Use ten and four counters; child names **14** and shows ten/four.
2. **Model · 5 min.** Show an invented card with 8 dots and numeral **8**. Say “This shows one collection of eight; it does not prove I can order every number to twenty.”
3. **Guide · 5 min.** Show a second invented card with a full ten-frame plus seven; ask what it shows (**17**) and what to check (all ten filled, seven extras).
4. **Independent · 7 min.** Child chooses a previously made sample or builds a new **13** as ten and three; explains how the collection matches the numeral. Preserve the child's first representation.
5. **Feedback · 3 min.** Ask “What could you add to help a new viewer?” Child may add a numeral, ten-frame boundary or spoken label. Record revision separately.
6. **Exit · 2 min.** One child-selected next target is written as a teaching action, not a trait label.

## Week 20 · Day 100 — Fresh number and change check

**Goal:** independently show number, order, compare and add/remove reasoning with new objects. **Codes:** AC9MFN01, AC9MFN03, AC9MFN04, AC9MFN05. **Prepare:** unseen [assessment](ASSESSMENT.md), ten-frame, large counters, blank trays.

1. **Welcome · 3 min.** Explain this helps choose tomorrow's practice; no race or public rank.
2. **Number · 6 min.** Give new ten-frame and counters; child shows **15** as ten and five and names numeral. Then compare **13 and 15** with representations.
3. **Change · 6 min.** Give the fresh 6-plus-3 and 9-remove-2 setups from the assessment, one at a time. Keep the first response before a hint.
4. **Parts/order · 5 min.** Ask for a fresh split of 8 and the selected 0/9/14/20 order. Let the child show the reasoning physically or digitally.
5. **Explain · 3 min.** Child states or selects one way they checked. Record exact strategy and any prompt.
6. **Close · 2 min.** Choose a concrete next lesson from the rubric. A task inaccessible under the provided route is **not observed** and needs another route.

Continue daily counting in meaningful contexts after this sample. The integrated portfolio conversation records other learning separately; do not derive a whole-child label from these four mathematical items.