# Ten daily mathematics lessons: Days 1–10

**Timing for every day:** notice/retrieve 3 minutes; explicit model 5; guided construction 8; individual application 6; exit and record 3 = **25 minutes**. The five labelled moves below are written to those timings. Keep manipulatives visible during checks; these are learning observations, not speed tests. Codes AC9M1N01 and AC9M1N02 throughout; see [README](README.md) for exact national scope and rights. Use [aids](aids.md) and the [assessment](assessment.md).

## Day 1 — Find the entry point: zero to twenty

**Goal:** match a numeral, counted set and position from 0–20; notice who needs Foundation consolidation. **Materials:** counters, 0–20 portion of [track](aids.md#aid-2-number-track-and-card-bank), mat; cards 0, 8, 13, 17, 20.

1. **Notice, 3 min:** Put 0 counters on one tray, 8 on another. “Which tray shows zero? How do you know?” Accept “none” in any response mode. Do not treat silence as misunderstanding.
2. **Model, 5 min:** Count 13 counters into a ten and 3 ones, touching each once. “I can see ten and three: thirteen. The numeral is 13. On the track it comes after 12.” Model 20 as two known tens and zero ones.
3. **Together, 8 min:** Learners build 8, 17 and 20 from called numerals. Pause after each: “Show me each object was counted once. How many tens? How many ones?” Give 0 to a child wanting a contrast. Point on track and correct any skipped number by re-counting objects, not reciting faster.
4. **Try, 6 min:** Each learner chooses 13 or 17, builds it, then finds numeral and track position; partner may audit by a different route. Offer large counters/tactile strip or child-directed adult placement.
5. **Check, 3 min:** Show 1 ten and 7 ones; ask for numeral and a number immediately before it. **Key:** 17; 16. Record independent, prompted or not yet; if learner says 107, separate “one ten” from digit 1 and rebuild 10+7 tomorrow.

## Day 2 — Twenty plus ones: 21–24

**Goal:** see a two-digit number as known tens and ones. **Materials:** two ten-strips and four ones per learner, mat, library card.

1. **Notice, 3:** Build 20 from yesterday. Ask “What changes if I add one loose book picture?” **Key:** 21, not another ten.
2. **Model, 5:** Place 2 strips in TENS, 3 objects in ONES. “Two tens are twenty. Three ones are three. Twenty-three is 20+3. The 2 tells me tens, the 3 tells me ones.” Write 23 after building.
3. **Together, 8:** Build 21, 22, 23, 24 one at a time. For each, point to 20 then count on the loose ones, locate the numeral on the track, and swap models with a partner. Use the [library card](aids.md#aid-3-original-context-cards) for 23.
4. **Try, 6:** Give a mixed mat of 2 strips and 4 ones. Learner labels 24, then removes one and relabels 23. Offer digit cards 2 and 4 for selection rather than pencil control.
5. **Check, 3:** Display 2 tens and 1 one. “Show the numeral; tell me 20+__.” **Key:** 21 and 1. If 12 appears, point to column labels, rebuild 1 ten + 2 ones as 12 and contrast both.

## Day 3 — Twenty-five to twenty-nine

**Goal:** count on from 20 without recounting every item. **Materials:** 2 ten-strips, nine ones, toy workshop and music cards.

1. **Notice, 3:** Cover 25–29 on the track. Say 24, ask for the next numeral and show it with 2 tens + 5 ones. **Key:** 25.
2. **Model, 5:** “Two full strips are twenty. I touch six loose dots: twenty-one ... twenty-six.” Build 26; point out numeral 26 has six ones. Explicitly avoid saying each strip is “one” when naming the total.
3. **Together, 8:** Children build 25, 27, 29 from tens and ones. Compare 27/29 by pairing the two tens and then their ones: 29 has two more ones. Use toy-workshop card for 27.
4. **Try, 6:** Learner designs a music rhythm card with 2 lines of 10 marks and 6 more. Write/select 26 and say/show 20+6. If marks are taxing, use preprinted ten strips and six stickers or move six large counters.
5. **Check, 3:** 2 strips and 8 dots. **Key:** 28; 2 tens, 8 ones. If learner starts at 1 and says 10 for the strips, ask them to audit one strip's 10 cells and count 10, 20, 21…28.

## Day 4 — A new ten: 29 to 30

**Goal:** recognise ten ones as one new ten and 30 as 3 tens/0 ones. **Materials:** 2 strips, 10 loose counters, spare teacher-prepared strip, seed-design card.

1. **Notice, 3:** Show 29 as 2 tens + 9 ones. Ask “What if one more arrives?” Let learners predict and keep predictions visible.
2. **Model, 5:** Add one, count 10 ones, place them over a ten-strip and exchange. “The amount is unchanged; ten loose ones can be one ten. Now three tens and no loose ones: 30.” Write 29, 30; do not call the zero “nothing in the whole number.”
3. **Together, 8:** In pairs remake 28, 29, 30. Say the sequence, move one counter each time, exchange at 30; compare pictures for seed packet design (3 strips of 10 marks).
4. **Try, 6:** Learner receives 2 strips + 10 ones. Show 30 in two ways: before and after an exchange; draw/select 30. A child unable to handle ten small pieces directs an adult or uses ten large tactile spaces.
5. **Check, 3:** Ask “What numeral has 3 tens and 0 ones? What comes immediately before it?” **Key:** 30; 29. If 3 is given, point to the ten-cells on each strip and ask 10+10+10.

## Day 5 — Compare and order within 30

**Goal:** order numbers by tens first, then ones. **Materials:** strips/ones; numeral cards 23, 27, 30, 19; [check slip](aids.md#aid-4-quick-check-slip).

1. **Notice, 3:** Put 27 and 23 side by side. “Which has more? What is the same?” **Key:** both 2 tens; 27 has 4 more ones.
2. **Model, 5:** Build 19 and 23. “I compare full tens first: one versus two. 23 is greater even though 9 is greater than 3.” Show > in words “greater than” only after concrete comparison; symbol is optional here.
3. **Together, 8:** Pairs order 19, 23, 27, 30 with tens/ones mats; then reveal numerals. Ask a child to justify one adjacent pair with objects, not a memorised chant.
4. **Try, 6:** Give 26 and 29; children build or draw and say/select which is greater, then invent a number between. **Key:** 29; 27 or 28. A non-speaking learner may point to both models and intermediate track cell.
5. **Check, 3:** Order 30, 24, 29 least to greatest. **Key:** 24, 29, 30. If 29 comes after 30, revisit the Day 4 exchange with objects; use [assessment](assessment.md) only after instruction, not as a label.

## Day 6 — Three tens and some ones: 31–35

**Goal:** make/read numbers with 3 tens and 1–5 ones. **Materials:** 3 strips, five ones, transit/art cards.

1. **Notice, 3:** Rebuild 30. Add one paper seat; ask what the model now shows. **Key:** 31.
2. **Model, 5:** Build 34: “Three tens are thirty. Four loose ones make thirty-four. I write 34, not 304, because the 3 lives in the tens place.” Show 30+4.
3. **Together, 8:** Learners make 31, 33, 35, each time verify tens count and number of loose ones. Use transit model for 31 and art studio for 34; let children select which card matches a shown model.
4. **Try, 6:** Child creates a model for 32 or 35 then asks a partner to read it. Give a tactile mat and digit cards; require the child to control the adult placement if needed.
5. **Check, 3:** Show 3 ten-strips and 5 ones. **Key:** 35; 30+5. For 53, pair numeral digit positions with the tens and ones columns and contrast a model of 53 if materials permit.

## Day 7 — Finish the thirties: 36–40

**Goal:** make 36–39 and exchange ten ones for 40. **Materials:** 3 strips, 10 ones, fourth strip, stadium card.

1. **Notice, 3:** On track point to 35, 36, 37; learners continue to 39 then predict the next written number. **Key:** 40.
2. **Model, 5:** Build 39 with 3 strips + 9 dots. Add a dot; physically exchange 10 dots for strip 4. “Thirty-nine plus one is forty. I now have four tens, zero ones.”
3. **Together, 8:** Pairs build 36, 38, 39, 40. At each, name the tens and ones. Stadium ticket design card shows 39; contrast a 40-seat drawing without recounting all 40.
4. **Try, 6:** Learner places 37 and 40 on track and explains how many numbers lie strictly between. **Key:** 38 and 39, two numbers. Track or tactile number cards available.
5. **Check, 3:** Show 3 tens and 10 ones; ask two equivalent forms and numeral. **Key:** 3 tens +10 ones = 4 tens +0 ones = 40. If child calls it 310, preserve model and exchange ten ones visibly.

## Day 8 — Four tens and some ones: 41–45

**Goal:** connect 40+ones to 41–45 and order. **Materials:** 4 strips, five ones; bike-repair/wildlife cards.

1. **Notice, 3:** Say “forty-two”; children select 42 from 24, 40, 42. **Key:** 42. Do not score hearing/language access as number knowledge without an alternate display.
2. **Model, 5:** Build 42 and write 40+2. “Four tens stay the same; the ones change.” Compare 42 with 45 concretely by pairing four strips, then 2 versus 5 dots.
3. **Together, 8:** Use bike-repair picture card for 42 and wildlife drawing for 45. Children produce 41, 43, 45, and match printed numerals; check marks in ten groups are actually ten each.
4. **Try, 6:** Ask children to design 44 in a different everyday context: four boxes of ten stickers and four loose, four bus rows of ten icons and four more, or their own approved object. Record 40+4.
5. **Check, 3:** “Which is greater, 45 or 42? How do you know?” **Key:** 45; both four tens, five ones > two ones. A bare guess triggers paired models tomorrow.

## Day 9 — To fifty; keep the quantity when exchanging

**Goal:** make 46–50; preserve total across an exchange. **Materials:** 4 strips, 10 ones, fifth strip; space/market/craft cards.

1. **Notice, 3:** Show 4 strips +7 ones from craft card. Learners predict numeral. **Key:** 47.
2. **Model, 5:** Build 49; add one and exchange 10 ones for a fifth strip. “The amount did not jump to sixty; 49+1 is 50, five tens.” Contrast 50 with 5 ones.
3. **Together, 8:** Build 46, 48, 50 and locate each on track. Space mission card is 48; market sign card is 50. Children audit a deliberately wrong 48 model of 4 strips +6 ones; key correction: add 2 ones.
4. **Try, 6:** Give 4 strips +10 ones. Learner shows before/after exchange and says/selects 50. Let adult move objects under learner direction if access requires.
5. **Check, 3:** “What is one more than 49? Show tens/ones.” **Key:** 50 = five tens, zero ones. If 410 appears, revisit numeral place columns and write 40+10=50.

## Day 10 — Transfer and next teaching choice

**Goal:** independently represent, order and partition sampled numbers; decide next lesson. **Materials:** 0–50 track, mats, cards 28, 34, 43, 50, [assessment](assessment.md).

1. **Notice, 3:** Reveal 34 in three forms: 3 strips +4 ones, 30+4, numeral 34. Children select the two that show the same quantity; **key:** all three.
2. **Model, 5:** Model a different partition of 43: 4 tens +3 ones, then trade one ten into ten ones → 3 tens +13 ones. “The total is still 43.” This is a stretch; core expectation in this fortnight remains tens/ones with accurate total.
3. **Together, 8:** Mixed context audit. Give one correct card model (craft kit 47) and one incorrect 47 as 4 tens +5 ones. Children correct the latter by adding two ones. Order 28, 34, 43, 50 using track; pause at 34/43 digit reversal.
4. **Try, 6:** Each learner chooses **one reserved unseen card** from the final four in [aids](aids.md#aid-3-original-context-cards), builds/selects the total and explains the tens/ones. Teacher collects a photographed model only under school policy; a paper note is enough.
5. **Check, 3:** Ask for 43 as tens/ones and one number between 43 and 50. **Key:** 4 tens+3 ones (optional 3 tens+13 ones); any 44–49. Use this with the [two-week check](assessment.md), not alone, to choose a next lesson.

## Shared response rule

When a child reverses digits, writes a three-digit string for tens and ones, recounts every strip or skips an object, first ask them to show what each mark/object stands for. Model a contrasting number, then give one new equivalent problem. Record whether the new response was independent or scaffolded. Faster recitation is not the intervention for a place-value misconception. If 0–20 remains insecure, teach a shorter concrete sequence before advancing, while still allowing age-respectful contexts.

Original content © NeuroForgeIO Pty Ltd 2026, CC BY 4.0. National source and separate ACARA terms are in [README](README.md). Educator review pending.