# Ten mathematics lessons · 25 minutes each

Keep [teacher answers](TEACHER-KEY.md) out of learner view. All days use **2 min invite + 5 min model + 6 min guided attempt + 6 min independent choice + 4 min exit + 2 min evidence note = 25 min**. On Days 15 and 20, the independent and exit blocks combine into a ten-minute held-out check; the three choice cards are for a later, unscored practice slot. Read prompts aloud as needed. Circulate with a rotating list of 3–4 focus children: an entire class cannot each have a private interview in 25 minutes. A copied partner answer is practice, not independent evidence.

## Week 3 · fictional routes, fixed page orientation

The shared **Map A** is printed in [learner cards](STUDENT-CARDS.md) and reproduced without answers in the [route-grid aid](print/route-grid.pdf). Its columns A–D run left to right; rows 1–4 run top to bottom. “Up” means one row toward page top; “right” means one column toward D. One step enters an adjacent square. No diagonal moves, hidden walls, compass knowledge or actual school plan is assumed. Check the learner is using the page orientation, then invite a real-room comparison only if the school approves that local task.

### Day 11 · A place has a position

**Code:** `AC9M2SP02`. **Goal:** locate a feature and describe a position using both row and column. **Prepare:** Map A, 4 × 4 floor/paper grid, one counter.

1. **Invite · 2.** Point to the imaginary reading nook and say, “A friend cannot see where my finger points. What could I tell them?” Accept positional words, then name the need for a repeatable location.
2. **Model · 5.** Trace column A and row 1; meet at A1. Say, “A1 means column A, row 1. I can find it again when the paper is put down the same way.” Put a counter on the reading nook; move the counter off, then have a child relocate it from the label. Emphasise that A1 is a label here, not a number to calculate.
3. **Guided · 6.** Ask children to locate the water point at C1 and plant at D2. Say “show, say or type the square”; ask, “What happens if I give only row 2?” Compare all four squares in that row.
4. **Choice · 6.** Each learner chooses one of [D11-A/B/C](STUDENT-CARDS.md#day-11--find-it-again). A partner checks by moving a counter; the learner must say the column and row or identify them with AAC/pointing.
5. **Exit · 4.** Say “Show the label for book returns.” Observe independent A3, then ask one child how they checked. If a child reverses row/column, trace the header and side labels on a fresh grid.
6. **Note · 2.** Record whether the child located independently, after a label prompt, or not yet; save one verbatim explanation.

**Access/home/extension:** Adult reads place names; raised/string grid or large cells; partner moves counter as directed; home learner can label four objects in a 2 × 2 fictional picture. Extension: explain why “row 2” alone cannot name one square.

### Day 12 · Follow one step at a time

**Code:** `AC9M2SP02`. **Goal:** follow a sequence of adjacent moves and name the finish. **Prepare:** Map A and counter; leave arrows in one colour plus written words so colour is never the sole cue.

1. **Invite · 2.** Start at B2. Ask whether “go to the plant” tells a new reader *how* to travel on this map.
2. **Model · 5.** Say “Start B2. Right one to C2. Right one to D2.” Move the counter after each spoken word and draw arrows. Say, “I followed the moves in order; D2 is the plant.” Point to the fixed page top before saying “up.”
3. **Guided · 6.** Start A3. Children direct one square right to B3, then one square up to B2. Check that the path has two arrows and ends on open mat. Let a learner give the directions while you deliberately pause before each step.
4. **Choice · 6.** Use one [D12 card](STUDENT-CARDS.md#day-12--move-in-order). Partners exchange navigator/follower roles; the follower traces without guessing the finish from a familiar label.
5. **Exit · 4.** From C2, say “down, left”. Children show the final square and both intermediate squares. If they land at B2, reset the counter and enact “down” first.
6. **Note · 2.** Save the exact route and whether order was correct before a prompt.

**Access/home/extension:** Move a paper counter on a large map, tap adjacent squares, or speak the coordinates. Avoid required whole-body movement. At home, follow directions on the fictional map. Extension: reverse a two-step route and test it.

### Day 13 · Write a route someone else can test

**Code:** `AC9M2SP02`. **Goal:** compose and test a route with a marked start and finish. **Prepare:** Map A, two counters, paper arrows.

1. **Invite · 2.** Say, “We need a path to return a book from B2 to A3. How will someone know where to begin?”
2. **Model · 5.** Label `Start B2`, say “left to A2, down to A3”; make two arrows. Give the route to a second counter and actually follow it. Name `Finish A3` and check against “book returns.” Show that “go left and down” without a start is incomplete.
3. **Guided · 6.** As a class, route from C3 to A3 with two left moves. Ask for another valid path, such as C3 up to C2, left to B2, left to A2, down to A3. Test rather than assume “shortest” is the only good path.
4. **Choice · 6.** Choose a [D13 card](STUDENT-CARDS.md#day-13--test-my-route). One child writes/speaks/places arrows; another follows exactly. If it fails, keep the first version and repair one instruction.
5. **Exit · 4.** Prompt: “Route from D4 to C4.” Expect one move left with start and finish marked. Ask whether a different route could also arrive, and why this one is simple.
6. **Note · 2.** Photograph only the route sheet if school policy allows; otherwise transcribe. Record initial/revised route separately.

**Access/home/extension:** Sentence strips “Start __; move __; finish __”, textured arrows, AAC directions; adult scribe follows the child's choices. Extension: compare two valid routes by counting steps, not by declaring one correct merely because it differs.

### Day 14 · Repair unclear directions

**Code:** `AC9M2SP02`. **Goal:** identify missing information and revise a direction after a follower test. **Prepare:** Map A and the fictional note “Go to the table.” There are two differently named tables on Map A.

1. **Invite · 2.** Read “Go to the table.” Ask which table; show that two answers fit the note.
2. **Model · 5.** Choose the quiet table at D1. Write “Start C1. Move right one square. Finish D1 at quiet table.” Trace it. Contrast a note “Start C1. Move left” and show where that actually lands; do not call a child careless for following it literally.
3. **Guided · 6.** Show “Start B3. Go to the plant.” Ask for a testable route. Build B3 → C3 → D3 → D2 together; compare with an alternate valid path if a learner proposes one. Discuss which information every version needs.
4. **Choice · 6.** Use one [D14 card](STUDENT-CARDS.md#day-14--make-it-clear). Follower must trace only the written/spoken steps. Navigator saves the first wording and one revision.
5. **Exit · 4.** Read “From C3, go up, then right.” Learners show C2 then D2 and name the feature. If a child jumps diagonally, trace both single-square moves.
6. **Note · 2.** Record whether the revision fixed start, order, direction or finish, and whether a prompt was required.

**Access/home/extension:** Offer large print, text-only grid, tactile layout, direct partner dictation or AAC. At home a learner can fix the fictional note without showing their own home. Extension: explain how a direction can be grammatically tidy yet mathematically ambiguous.

### Day 15 · Follow and check a new map

**Code:** `AC9M2SP02`. **Goal:** use an unseen 2D representation to locate, trace and repair directions. **Prepare:** closed [Day 15 learner check](STUDENT-CHECKS.md#day-15--new-map-b), Map A for rehearsal, staff [key](TEACHER-KEY.md#day-15-held-out-check).

1. **Invite · 2.** Say: “Today I want to see how you read a map you have not used yet. If you are unsure, show the part you do know.”
2. **Model · 5.** On Map A only, rehearse `B2 → B1 → C1` and how to record start, arrows, finish. Do not display Map B or its answers.
3. **Guided · 6.** Still on Map A, have children independently point to D4 and then compare with a partner. Rehearse the fixed page orientation and one-square rule. Collect or turn over Map A.
4. **Held-out independent · 6.** Give Map B. Learners answer items 1–2 without partner hints; read words neutrally if needed. Offer scribe/pointing/AAC and record assistance.
5. **Held-out exit · 4.** Learners answer items 3–4. No answer is discussed until work is retained. If a learner needs more time, finish privately later rather than rushing or scoring a blank as misconception.
6. **Note · 2.** Mark rubric evidence and the exact next move from the teacher key. D15-A/B/C choices are **unscored later practice**, not preview items for this check.

**Access/home/extension:** A 4 × 4 text grid, enlarged/tactile copy and adult reader are equivalent access routes; the adult does not steer the counter. Optional home practice uses D15 choice cards after the check.

## Week 4 · the quantity stays while its groups change

Use `H = hundreds`, `T = tens`, `O = ones`; read these labels aloud and show full words on the [exchange mat](print/exchange-mat.pdf). A paper hundred-square is one group of 100, not a count of a pictured object's physical size. **One H ↔ ten T; one T ↔ ten O**. If a child cannot yet trust an exchange, count the ten strips/singles before moving on.

### Day 16 · Open a hundred bundle

**Codes:** `AC9M2N01`, `AC9M2N02`. **Goal:** represent a three-digit quantity and exchange one hundred for ten tens without changing the total. **Prepare:** 2 hundred squares, 14 ten-strips, 6 singles, mat.

1. **Invite · 2.** Build 246 and ask, “If I open one hundred bundle, is it still 246?” Invite prediction.
2. **Model · 5.** Name `2H 4T 6O`, then replace one H with ten T. Count `1H 14T 6O = 100 + 140 + 6 = 246`; leave both drawings visible. Say “the grouping changed; the number did not.”
3. **Guided · 6.** Build 324. Learners tell you to exchange one H. Together record `2H 12T 4O`. Ask them to verify with `200 + 120 + 4`.
4. **Choice · 6.** Choose a [D16 card](STUDENT-CARDS.md#day-16--one-hundred-becomes-ten-tens). Child makes/sketches both groupings and says why they are equal. Partner tests by counting tens, not copying digits.
5. **Exit · 4.** Ask for another grouping of 231 after opening one hundred; check `1H 13T 1O`. If a child writes `1H 3T 1O`, put the missing ten strips back one by one.
6. **Note · 2.** Record independent exchange, prompted exchange or not yet observed.

**Access/home/extension:** Use folded paper bundles or sketches; partner manipulates on request. Home: 10 dots per strip on scrap paper. Extension: open both hundreds and explain `24T 6O` for 246.

### Day 17 · A zero names an empty place

**Codes:** `AC9M2N01`, `AC9M2N02`. **Goal:** explain zero in a three-digit numeral and show an equivalent non-standard grouping. **Prepare:** mat, 4 hundreds, 10 tens, 5 ones.

1. **Invite · 2.** Show 405 and 45. Ask, “How do these tell different quantities when one digit is zero?”
2. **Model · 5.** Build `4H 0T 5O` and point to the empty tens place. Compare 45 as `0H 4T 5O`. Then exchange one H in 405 to show `3H 10T 5O` and total `300 + 100 + 5 = 405`. Do not erase the standard form.
3. **Guided · 6.** Children direct the build for 506, naming `5H 0T 6O`, then one valid exchange `4H 10T 6O`. Compare with 560 by moving six tens into the tens column and leaving ones empty.
4. **Choice · 6.** Choose [D17-A/B/C](STUDENT-CARDS.md#day-17--zero-keeps-a-place). Ask learners to point to the zero place before renaming.
5. **Exit · 4.** Display 304 and 340. Child selects which has no tens and shows the empty column. If they compare the digit 4 first, lay both builds side by side.
6. **Note · 2.** Record whether they read zero as empty *in its specific place* and preserve value after exchange.

**Access/home/extension:** Blank place card with tactile border, enlarged numbers, oral/AAC selection; no colour code required. Extension: contrast `405 = 40T 5O` with `45 = 4T 5O`.

### Day 18 · Open a ten bundle

**Codes:** `AC9M2N01`, `AC9M2N02`. **Goal:** exchange one ten for ten ones and show two equivalent forms. **Prepare:** 3 hundreds, 7 tens, 12 ones, mat.

1. **Invite · 2.** Build 372 and ask, “Can I make more loose ones without adding anything?”
2. **Model · 5.** Replace one of seven tens with ten ones. Count `3H 6T 12O`, then check `300 + 60 + 12 = 372`. Say “12 ones is allowed in a regrouped form; the usual numeral still has 2 in its ones place.”
3. **Guided · 6.** Build 324 and ask learners to direct the ten-to-ones exchange. Check `3H 1T 14O = 324`. Return to standard grouping to show reversible exchange.
4. **Choice · 6.** Choose [D18-A/B/C](STUDENT-CARDS.md#day-18--one-ten-becomes-ten-ones); ask for a drawn or physical exchange and a total check.
5. **Exit · 4.** Ask if `4H 6T 12O` and `4H 7T 2O` are equal. Expected yes, both 472; ask which ten was opened. If not, count ten loose ones into one strip.
6. **Note · 2.** Record model and language separately; a correct total with no exchange reasoning needs a next step.

**Access/home/extension:** Pre-draw ten dots on strips to reduce cutting; adult moves pieces at learner direction. Extension: show 372 a third way after opening one H as well.

### Day 19 · Choose the grouping that helps

**Codes:** `AC9M2N01`, `AC9M2N02`. **Goal:** make at least two true groupings for one quantity and explain which form helps a task. **Prepare:** fictional materials-store cards, bundles, 0–1000 open number line as optional comparison support.

1. **Invite · 2.** Say, “A pretend art store counts 284 tags. It has large packs, tens and loose tags. Must there be only one way to pack them?”
2. **Model · 5.** Show `2H 8T 4O`; open one H to make `1H 18T 4O`. Explain how both total 284. If the store needs many ten-packs, the second description is useful; neither is a different amount.
3. **Guided · 6.** For 407 tags, children choose a non-standard form: `3H 10T 7O` or `40T 7O`. Check totals. If someone offers `4H 7T`, ask them to show where the extra seventy came from.
4. **Choice · 6.** Choose [D19-A/B/C](STUDENT-CARDS.md#day-19--choose-a-useful-grouping). Require two representations and a sentence, drawing or AAC explanation of why they match. Optionally put the quantity on a 0–1000 line and identify its interval without pretending this completes `AC9M2N01`.
5. **Exit · 4.** Write `530 = 5H 3T 0O = __H __T __O` after opening one ten. Check `5H 2T 10O`. If a learner writes 5H 2T 1O, count the ten loose tags.
6. **Note · 2.** Record which exchange the child chose and whether their explanation referred to unchanged quantity.

**Access/home/extension:** Fictional stock avoids money and home-resource disclosure. Use counters, number sentences, oral explanation or tactile groups. Extension: find two *different* non-standard forms for 284 and prove each.

### Day 20 · Show what stays the same

**Codes:** `AC9M2N01`, `AC9M2N02`. **Goal:** independently represent an unseen three-digit number, rename it and explain the role of zero. **Prepare:** closed [Day 20 learner check](STUDENT-CHECKS.md#day-20--new-number-cards), bundles, staff [key](TEACHER-KEY.md#day-20-held-out-check).

1. **Invite · 2.** Say, “Your models will show me what to teach next. You may use bundles, a sketch, words or numerals.”
2. **Model · 5.** Rehearse 251 only: `2H 5T 1O = 1H 15T 1O`. Count one exchanged hundred as ten tens. Hide this example before checks.
3. **Guided · 6.** Still with 251, invite the class to reverse the exchange and explain why the amount remains 251. Revisit zero place using 320, **not** either check number. Do not reveal check prompts.
4. **Held-out independent · 6.** Give the [student check](STUDENT-CHECKS.md#day-20--new-number-cards). Children answer items 1–2 without partner assistance; adult reads wording neutrally and records any mathematical prompt.
5. **Held-out exit · 4.** Children answer items 3–4. Retain work before feedback. Finish privately later if access time is needed rather than treating an unfinished item as an error.
6. **Note · 2.** Use the [rubric and next moves](TEACHER-KEY.md#formative-rubric-and-next-moves) by item. D20 practice choices follow the check later.

**Access/home/extension:** Child can direct an adult to move pieces, point to place labels, use AAC or dictate a check sentence. Home choices are practice and do not replace a teacher-observed independent sample. Extension after the check: demonstrate a third equivalent grouping and use a number line to estimate position.