# Year 3 mathematics · Days 11–20 · 25 minutes each

Keep [staff answers](TEACHER-KEY.md) away from learner displays. Every ordinary session has **2 min invite + 5 min explicit model + 6 min guided attempt + 6 min one independent choice + 4 min exit + 2 min evidence note = 25 min**. The three [practice routes](STUDENT-CARDS.md) per day are alternatives, not 18 minutes of mandatory work. On Days 15 and 20, the six-minute independent phase and four-minute exit combine as a ten-minute held-out check; three later-practice routes remain available after evidence is retained. Read task language aloud without giving a mathematical cue. Rotate 3–4 focus learners per lesson; a teacher cannot privately interview every child in 25 minutes.

## Week 3 · two-dimensional views and relative landmarks

Use fictional **Map A** from [learner cards](STUDENT-CARDS.md#map-a--imaginary-community-courtyard) and the [A4 aid](print/courtyard-map.pdf). Page top means *up*; the map does not assert real compass north. Columns A–E run left to right, rows 1–5 top to bottom. A named landmark is a top-view symbol occupying one cell. Empty cells are open spaces. “Directly left” means one adjacent cell; “left of” may be farther away in the same row. Make the difference explicit. No real school layout or route-safety promise is involved.

### Day 11 · What does the view show?

**Code:** `AC9M3SP02`. **Goal:** interpret a top-view representation, key and location. **Prepare:** Map A, grid aid, a token, a simple key card saying “named cell = landmark; blank = open space.”

1. **Invite · 2.** Ask: “If I look down on this made-up courtyard, which details can a flat map show? What might it leave out?” Listen for position, not assumed distances/heights.
2. **Model · 5.** Point to meeting mat C3. Trace column C and row 3; say, “They cross at C3. This symbol stands for a place, seen from above.” Compare blank B3: it is open space, not an unnamed landmark. Read the key.
3. **Guided · 6.** Learners locate entrance A1 and water point E1, then tell where garden bed A3 is relative to meeting mat C3. Accept “left in the same row” but not “directly left” because B3 lies between. Test by placing counters.
4. **Choice · 6.** Learner selects [D11-A/B/C](STUDENT-CARDS.md#day-11--read-a-view). Ask for location **and** evidence from row/column or another landmark; partner may move a counter at learner direction.
5. **Exit · 4.** Ask: “What occupies D4? Is it directly below shade tree D2?” Correct response: seats; no, D3 lies between. A learner may point, say or type. If they confuse the cell name with a count, trace labels again.
6. **Note · 2.** Record whether the child interprets top view and relative placement independently, after cue, or not yet observed.

**Access/home/extension:** Large grid, raised/string borders, complete text table and adult read-aloud. Home task uses the fictional map. Extension: identify one fact the map cannot justify, such as exact walking distance or height.

### Day 12 · Relative to what?

**Code:** `AC9M3SP02`. **Goal:** name locations relative to a chosen landmark with precise “between/above/below/left/right” language. **Prepare:** Map A and two labelled tokens.

1. **Invite · 2.** Say: “The shade tree is ‘over there’ to me. Would ‘over there’ help someone with only this map?”
2. **Model · 5.** Place a token on meeting mat C3 and another on shade tree D2. Say, “The shade tree is one column right and one row above the mat. That is upper-right **on this page**.” Move the mat token to show the description must name its reference point.
3. **Guided · 6.** Ask: “Which named places are on the same row as meeting mat?” Garden bed A3 and art wall E3. The mat is between them; there is one blank cell on each side. Have a learner verify with tokens.
4. **Choice · 6.** Use one [D12 card](STUDENT-CARDS.md#day-12--say-the-reference). Require a reference landmark and accurate relation; a drawing or AAC pair of labels is fine.
5. **Exit · 4.** “Where is compost B4 relative to storage C5?” Expected one column left and one row above; ask the child to identify **storage** as reference. If they reverse direction, swap the two tokens and ask which is being described.
6. **Note · 2.** Record exact words/pointing sequence and whether “directly” was used accurately.

**Access/home/extension:** Let a learner direct another's token moves. Avoid required bodily orientation or eyesight. Extension: give two true descriptions of the same relative location, one using cell labels and one using landmark names.

### Day 13 · Make a map from clues

**Code:** `AC9M3SP02`. **Goal:** create a top-view 3 × 3 plan from a small set of relational clues and check another person's interpretation. **Prepare:** blank [lower grid on aid](print/courtyard-map.pdf) or 9 paper squares, three removable landmark labels.

1. **Invite · 2.** Say: “A map-maker must choose positions so someone else can recover the same layout. Today the words are the design brief.”
2. **Model · 5.** On a fresh 3 × 3 grid, put *meeting place* in centre B2, *water* directly above at B1, and *books* directly right at C2. Keep labels visible. Read the clues back against the drawing; a map with water at A1 would not meet “directly above.”
3. **Guided · 6.** Reset the grid. Together place *entrance* at A3, *quiet seat* directly above it at A2, and *art* directly right of quiet seat at B2. Ask learners to verbalise each placement before moving its label.
4. **Choice · 6.** Use one [D13 design brief](STUDENT-CARDS.md#day-13--make-the-view). Learner draws, places cards or directs a partner; another person tests each clue without being coached.
5. **Exit · 4.** New tiny brief: *mat at B2; shade directly left; notice directly below*. Expected shade A2, notice B3. Retain a quick sketch. If relative placement fails, move one label at a time while rereading the reference phrase.
6. **Note · 2.** Record first design and any correction separately; correct after feedback is learning evidence, not an independent first attempt.

**Access/home/extension:** Large tactile cells, dictation, movable symbols and adult scribe. Home uses invented places. Extension: add a fourth clue that has only one possible cell and explain why.

### Day 14 · Test and repair a representation

**Code:** `AC9M3SP02`. **Goal:** compare a written description with a top-view plan; identify a conflict or missing key and repair it. **Prepare:** Map A and a deliberately faulty note: “The water point is left of the notice board.”

1. **Invite · 2.** Ask: “Could a beautifully drawn map still mislead someone?” Name that we will test claims against symbols.
2. **Model · 5.** Locate notice board C1 and water point E1. Trace the same row: E is right of C, so the note conflicts with Map A. Write a repair, “Water point is right of notice board on row 1.” Keep original and repair visible; do not move symbols silently.
3. **Guided · 6.** Show a sketch with meeting mat C3 but no explanation of whether a blank means open space. Have learners add a key. Then test “seats D4 are below shade tree D2”: true, but **not directly** below because D3 is between. Name the precision difference.
4. **Choice · 6.** Select one [D14 card](STUDENT-CARDS.md#day-14--test-and-repair). Partner reads only the recorded map/key and tries to locate the intended feature. Learner keeps one revision.
5. **Exit · 4.** Say: “Tool shed B2 is directly above compost B4.” Expected false: B3 is between. Repair to “above in the same column, two rows away.” If a child says true because “above,” ask which word makes the claim fail.
6. **Note · 2.** Record whether the issue was orientation, “directly,” missing key or an actual positional conflict.

**Access/home/extension:** Text table and tactile symbols are full participation. An adult can read the faulty note but not pre-identify the conflict. Extension: describe information the map cannot show, without inventing a real path.

### Day 15 · Create and interpret an unseen map

**Code:** `AC9M3SP02`. **Goal:** transfer interpretation and creation to a new fictional layout. **Prepare:** closed [Day 15 learner check](STUDENT-CHECKS.md#day-15--unseen-makers-fair), Map A only for rehearsal, staff [key](TEACHER-KEY.md#day-15-held-out-check).

1. **Invite · 2.** Say: “Today your own map reading and map making will tell us what to practise next.”
2. **Model · 5.** Rehearse only Map A: find entrance A1, describe garden bed A3 as lower on the same column, then check a classmate's three-cell plan from Day 13. Hide these examples.
3. **Guided · 6.** Give a fresh 3 × 3 practice grid with *post* centre, *seat* above, *bin* right. Learners place independently then compare. Do not show the held-out map or its layout.
4. **Independent check · 6.** Give unseen Map B and items 1–2. Read neutrally or let the child use text/tactile copy; record access support and any mathematical cue. No partner hints.
5. **Check exit · 4.** Items 3–4 ask the learner to create and repair. Retain the first answer before feedback. If time/access is insufficient, complete privately later and mark it unfinished until then.
6. **Note · 2.** Mark the staff rubric by interpretation, relation, creation and repair. D15 cards are unscored **later** practice, not check previews.

**Access/home/extension:** Use a raised 5 × 5 Map B or its text table; adult may move symbols exactly as directed. At home, use later-practice cards after the check, not a copied check answer.

## Week 4 · a quantity can have different groupings

`TT` = ten-thousands, `Th` = thousands, `H` = hundreds, `T` = tens, `O` = ones. Use full words aloud. **One TT ↔ ten Th; one Th ↔ ten H; one H ↔ ten T; one T ↔ ten O**. Keep a standard numeral visible while regrouping, since a non-standard set of groups is not a new numeral. Use actual pieces for H/T/O, and labelled cards/envelopes for larger groups. [Place-exchange aid](print/place-exchange.pdf) provides a labelled layout and text alternative.

### Day 16 · Rename a five-digit stock count

**Code:** `AC9M3N01` (partial). **Goal:** represent, read and rename 24 306 without changing its quantity. **Prepare:** place cards `TT, Th, H, T, O`, paper group symbols and a fictional stock card.

1. **Invite · 2.** Show `24 306`. Ask what the zero communicates; accept an initial idea without giving the answer.
2. **Model · 5.** Build `2TT 4Th 3H 0T 6O`, read “twenty-four thousand, three hundred and six”, then open one TT into ten Th. Record `1TT 14Th 3H 0T 6O`; check `10 000 + 14 000 + 300 + 6 = 24 306`.
3. **Guided · 6.** Build `32 105`: `3TT 2Th 1H 0T 5O`. Learners direct opening one TT to `2TT 12Th 1H 0T 5O`; count its value. If “12 thousands” is mistaken for 12, draw 12 separate thousand cards.
4. **Choice · 6.** Choose one [D16 stock card](STUDENT-CARDS.md#day-16--same-count-new-groups). Require numeral, standard place names, a new grouping and a sum/check, in any accessible mode.
5. **Exit · 4.** Display 43 020; ask which place is empty and how to read it. Expect zero hundreds **and** zero ones; “forty-three thousand and twenty.” If only one zero is noticed, align every place card.
6. **Note · 2.** Record place naming and exchange as separate evidence.

**Access/home/extension:** Use labelled envelopes rather than thousands of loose objects. Adult writes exactly the child-directed grouping. Extension: exchange one thousand into hundreds too and prove all forms equal.

### Day 17 · A zero still holds a place

**Code:** `AC9M3N01` (partial). **Goal:** distinguish similar five-digit numerals and preserve zero-place meaning after regrouping. **Prepare:** `30 507`, `30 570`, place mat.

1. **Invite · 2.** Show both numerals. Ask, “Which counts are different? Which first place decides?”
2. **Model · 5.** Read `30 507` as `3TT 0Th 5H 0T 7O`. Point to empty thousands and tens. Compare `30 570 = 3TT 0Th 5H 7T 0O`: equal through hundreds; tens decide that 30 570 is larger. Exchange one TT in 30 507 to `2TT 10Th 5H 0T 7O` and check total.
3. **Guided · 6.** Sort `40 205`, `40 250`, `42 005` least to greatest using the first differing place; learners point to each zero's place. Ask whether changing the zero's position changes the count.
4. **Choice · 6.** Choose [D17-A/B/C](STUDENT-CARDS.md#day-17--zero-and-order). Child builds or sketches place cards and explains which place decides an order.
5. **Exit · 4.** Compare `50 080` with `50 008`; expect 50 080 larger because 8 tens exceed 0 tens after the earlier places tie. If a child sees only the final 8, realign cards by place.
6. **Note · 2.** Record whether reading, ordering, or exchange needs reteaching.

**Access/home/extension:** Large spaced numerals and tactile empty-place tokens; home may use paper place names. Extension: write a different numeral between 30 507 and 30 570 and justify.

### Day 18 · Regroup while adding

**Code:** `AC9M3N03` (partial). **Goal:** explain a three-digit addition by two physical exchanges, then check reasonableness. **Prepare:** H/T/O cards and large paper counters.

1. **Invite · 2.** Ask whether `347 + 286` is closer to 300, 600 or 900; `350 + 280 ≈ 630` gives a benchmark, not exact evidence.
2. **Model · 5.** Combine 7 and 6 ones → 13, exchange ten for one T. Combine 4 and 8 tens plus new one → 13 T, exchange ten for one H. Combine 3 and 2 H plus new one → 6 H. State `347 + 286 = 633`, close to estimate.
3. **Guided · 6.** Learners direct `268 + 175`: 8+5=13 ones, 6+7+1=14 tens, 2+1+1=4 hundreds; total 443. Reverse-check 443−175 if ready.
4. **Choice · 6.** Choose [D18-A/B/C](STUDENT-CARDS.md#day-18--add-by-place). Require a model or labelled exchange and a reasonable estimate, not just a final numeral.
5. **Exit · 4.** Solve `156 + 278`; expected 434. Ask where each exchange happened and why 334 is not enough. If a learner writes 334, recount hundreds after ten exchange.
6. **Note · 2.** Record model, accurate total and reasonableness separately; schedule a two-digit revisit if needed.

**Access/home/extension:** Pre-cut bundles, adult moves at direction, speech/AAC or number-line addition as an alternative. Do not time calculation speed as the only achievement. Extension: show a second correct partition of 347+286.

### Day 19 · Regroup across a zero to subtract

**Code:** `AC9M3N03` (partial). **Goal:** solve a three-digit subtraction with transparent exchanges and verify by addition. **Prepare:** H/T/O cards, open number line.

1. **Invite · 2.** Show `705 − 368`; ask whether an answer over 705 could be sensible, and why the empty tens place matters.
2. **Model · 5.** Start `7H 0T 5O`. Exchange one H for ten T, then one of those T for ten O: `6H 9T 15O`. Remove `3H 6T 8O` → `3H 3T 7O = 337`. Check `337 + 368 = 705`.
3. **Guided · 6.** Work `602 − 157` together. Exchange to `5H 9T 12O`; subtract → `4H 4T 5O = 445`. Draw the exchange arrows rather than saying “borrow”.
4. **Choice · 6.** Choose one [D19 card](STUDENT-CARDS.md#day-19--subtract-and-check). Learner may use exchange cards or count up from the smaller quantity. Check by addition and name the unit.
5. **Exit · 4.** Solve `503 − 268`; expected 235. If a learner says 345, rebuild the hundred-to-ten and ten-to-one exchanges one at a time.
6. **Note · 2.** Record whether the child conserved the total during exchanges and checked independently.

**Access/home/extension:** Use labelled, touchable groups; a scribe may move pieces only as directed. At home, use invented quantities of blank cards. Extension: count up 368→400 (+32)→700 (+300)→705 (+5), total 337, and compare with regrouping.

### Day 20 · Show a model someone can verify

**Codes:** `AC9M3N01`, `AC9M3N03` (partial). **Goal:** transfer five-digit place/zero and three-digit regrouping to unseen numbers. **Prepare:** closed [Day 20 learner check](STUDENT-CHECKS.md#day-20--unseen-stock-and-calculation), place cards and staff [key](TEACHER-KEY.md#day-20-held-out-check).

1. **Invite · 2.** Say: “Use a model and a check so someone else can see how you know. This helps me choose the next lesson.”
2. **Model · 5.** Rehearse `52 304 = 5TT 2Th 3H 0T 4O` and open one TT. Do not use the check number. Remind the class that regrouping changes parts, not total.
3. **Guided · 6.** Work `421 − 176 = 245` with cards, then verify `245 + 176 = 421`. Hide the example. Let learners rehearse what counts as a check, not the held-out answer.
4. **Independent check · 6.** Give items 1–2 on the new check; child uses objects, sketch, words, typing or AAC. Adult may read but does not suggest the exchange.
5. **Check exit · 4.** Give items 3–4. Retain work before class discussion. Give additional accessible time later rather than scoring a blank as incorrect.
6. **Note · 2.** Use [rubric/next moves](TEACHER-KEY.md#formative-rubric-and-next-moves) by skill. D20 practice routes follow the check later.

**Access/home/extension:** A partner can act as hands; the learner directs and explains. Home cards are practice, not teacher-observed evidence. Extension after check: show a different verified exchange or a count-up subtraction path.