# Ten Year 5 mathematics lessons: 25 minutes each

Use the original [task cards](MATERIALS.md), [print line](../print/decimal-line.svg), [factor array](../print/factor-array.svg) and [assessment keys](ASSESSMENT.md). Each lesson has **2 + 4 + 5 + 7 + 4 + 3 = 25 minutes**. Model with concrete, spoken and written forms; invite a route that lets the learner show number reasoning. Codes are partial lesson links: `AC9M5N01`, `AC9M5N02`, `AC9M5N09`.

## Day 1 — Make a thousandth visible

**Success:** read and build a number to three decimal places, including a zero placeholder. Prepare place-value cards or four-column table. (`AC9M5N01`)

1. **Notice · 2 min.** Display `1.235`. Ask what the last digit is worth; do not accept “five” without a place.
2. **Model · 4 min.** Build `1 + 0.2 + 0.03 + 0.005` in columns. Say “one and two hundred thirty-five thousandths” and “one point two three five”; connect the forms.
3. **Build together · 5 min.** Learners show `1.205`; ask why the hundredths position is zero. Contrast `1.25` by writing `1.250`.
4. **Independent turn · 7 min.** Build `2.074` and `0.905`, say or label the value of the 7 and 5, and expand one number. Counters, typing or AAC selection allowed.
5. **Explain · 4 min.** Pairs compare `1.205` and `1.25`: which place first differs? Teacher listens for hundredths `0<5`.
6. **Exit · 3 min.** “What is the value of 5 in `1.205`?” Key: `0.005`, five thousandths. Record if learner says five hundredths.

## Day 2 — Compare from the first different place

**Success:** compare decimals without treating a longer numeral as automatically greater. Prepare comparison set. (`AC9M5N01`)

1. **Hook · 2 min.** Vote: `1.25` or `1.205` greater? Ask for a reason, not speed.
2. **Model · 4 min.** Rename `1.25` as `1.250`. Compare ones, tenths, then hundredths: `5>0`, so `1.250>1.205`.
3. **Guided pairs · 5 min.** Order `0.905, 0.950, 0.959`, using columns. Ask whether `0.905` could mean 905 whole units.
4. **Independent turn · 7 min.** Learners order `2.074, 2.470, 2.407` and write one `<` or `>` explanation. They may move cards or dictate the comparison.
5. **Error clinic · 4 min.** Show “2.074 is largest because 074 has three digits.” Learners explain the first differing place and repair the statement.
6. **Exit · 3 min.** “Are `1.25` and `1.250` equal?” Key: yes, a trailing zero does not change value.

## Day 3 — Place numbers on a useful line

**Success:** locate thousandths relative to labelled hundredths and half-hundredths. Prepare [line 1.230–1.260](../print/decimal-line.svg). (`AC9M5N01`)

1. **See · 2 min.** Ask what changes from `1.230` to `1.235`: five thousandths.
2. **Model · 4 min.** Label line ticks at `1.230, 1.235, 1.240 … 1.260`. Point out `1.250` equals `1.25`.
3. **Guided locate · 5 min.** Learners place `1.245` and `1.255`; ask where `1.253` sits between ticks and why.
4. **Independent turn · 7 min.** Mark `1.232` and `1.258` approximately; then give exact intervals: between `1.230`–`1.235` and `1.255`–`1.260` respectively. A tactile strip or verbal interval statement is valid.
5. **Compare · 4 min.** Pairs explain whether `1.253` is nearer `1.250` or `1.255`: distances `0.003` and `0.002`, so nearer `1.255`.
6. **Exit · 3 min.** “Which tick is immediately after `1.245`?” Key: `1.250`.

## Day 4 — The shorter model route

**Success:** compare and order a set with units and check a claim against the actual numbers. Prepare fictional route cards A–D. (`AC9M5N01`)

1. **Context · 2 min.** Say clearly that the route values are invented; no real travel advice is being given.
2. **Model · 4 min.** Compare A `1.235 km` and B `1.253 km` by aligned place values. A is shorter; do not compare 235 with 253 alone without the shared whole.
3. **Guided sort · 5 min.** Class orders D `1.205`, A `1.235`, C `1.250`, B `1.253` km. Ask why C may be written `1.25`.
4. **Independent turn · 7 min.** Learners challenge “B is shortest because 253 has a bigger final digit.” Write a corrected sentence, naming the first decimal place where A and B differ.
5. **Transfer · 4 min.** Substitute paper strip lengths with the same numerals but a chosen common unit. Ask why every card must use the same unit before comparison.
6. **Exit · 3 min.** “Which is longer, C or B?” Key: B, since `1.253>1.250` by `0.003 km`.

## Day 5 — Decimal check without a shared answer

**Success:** independently order, locate and justify three-place decimals. Prepare [new card](ASSESSMENT.md#day-5-check-a), not the worked route set. (`AC9M5N01`)

1. **Ready · 2 min.** Explain independent check and access options; read numbers neutrally if needed.
2. **Example of format · 4 min.** Show unrelated `0.5=0.500`; do not solve the check values.
3. **Plan · 5 min.** Learners draw columns or line and select a comparison strategy.
4. **Independent response · 7 min.** Complete all three fresh items on paper, keyboard or accessible number cards. No peer answer during this stage.
5. **Self-check · 4 min.** Ask whether trailing zeros changed values and whether their order makes sense; collect both initial and revised work.
6. **Exit · 3 min.** Explain in one sentence the first different place for two chosen values. Use [key and next teaching](ASSESSMENT.md#day-5-check-a).

## Day 6 — See all the rectangles

**Success:** build factor pairs and name all factors of 24. Prepare 24 counters or [array mat](../print/factor-array.svg). (`AC9M5N02`)

1. **Hook · 2 min.** Ask whether 24 can make 5 equal rows of whole counters. Accept “let's test”.
2. **Model · 4 min.** Arrange `1×24` and `2×12`; turn each rectangle to show a rotated pair is not a new factor pair.
3. **Guided arrays · 5 min.** Make `3×8` and `4×6`. Test `5×?` and explain why no whole row length works.
4. **Independent turn · 7 min.** Learners list all four unordered pairs and the factor set `{1,2,3,4,6,8,12,24}`. They may direct a partner to place tiles or use a multiplication table.
5. **Completeness check · 4 min.** Ask why stopping at `4×6` is enough: swapped pairs then repeat. Do not demand formal square-root terminology.
6. **Exit · 3 min.** “Is 8 a factor of 24? Show the matching number.” Key: yes, `8×3=24`.

## Day 7 — Multiples meet

**Success:** recognise common multiples by generating and checking lists. Prepare multiples cards from [materials](MATERIALS.md). (`AC9M5N02`)

1. **Warm · 2 min.** Count by fours to 20; ask what a multiple means.
2. **Model · 4 min.** List positive multiples of 4 and 6 to 36. Circle `12, 24, 36` as common values.
3. **Guided why · 5 min.** Show that `12=3×4=2×6`. Ask if `18` appears on both lists; it does not appear on the 4 list.
4. **Independent turn · 7 min.** Find common multiples of 3 and 5 up to 30; key `15, 30`. Then invent a packing or calendar situation where a common multiple matters, without claiming an actual timetable.
5. **Check method · 4 min.** Partners swap lists, circle an error, and verify it with multiplication rather than agreement.
6. **Exit · 3 min.** “Is 24 a multiple of 6? Give the fact.” Key: yes, `6×4=24`.

## Day 8 — Divisible, with a reason

**Success:** determine divisibility by factor evidence and show a remainder when appropriate. Prepare 36 counters or number cards. (`AC9M5N02`)

1. **Recall · 2 min.** Ask whether a factor pair gives a division fact. Example `4×6=24` gives `24÷6=4`.
2. **Model · 4 min.** Arrange 36 into six equal rows: `36÷6=6`. Test five rows: five groups of seven use 35, one remains.
3. **Guided compare · 5 min.** Check divisibility of 36 by 4, 9 and 5 with facts: `4×9`, `9×4`, and no whole factor 5.
4. **Independent turn · 7 min.** For 30, test divisors 3, 4, 5 and 6. Key: yes `3×10`, no `4×7=28` with 2 left, yes `5×6`, yes `6×5`.
5. **Explain · 4 min.** Learners compare a quick rule with an array or inverse multiplication check. Teacher looks for reasoning, not a memorised slogan.
6. **Exit · 3 min.** “Is 36 divisible by 5 into whole equal groups?” Key: no; one is left after seven in each of five groups.

## Day 9 — Model a real choice without hidden assumptions

**Success:** test equal-box plans against both arithmetic and constraints. Prepare fictional 36-book scenario. (`AC9M5N02`, `AC9M5N09`)

1. **Frame · 2 min.** Read the constraint: six boxes available, capacity eight each. This is an invented problem.
2. **Model · 4 min.** Put six books in each available box: `6×6=36`, `6≤8`, so equal sharing and capacity both work.
3. **Guided options · 5 min.** Test four boxes of nine: arithmetic works, but nine exceeds each box's capacity of eight. Test five boxes: 7 each and one left; not equal shares of all 36.
4. **Independent choice · 7 min.** Learners recommend a plan in a table `number of boxes / books each / spare capacity / constraint`. They may recommend four boxes of nine **only if** boxes with capacity at least nine become available, and say why.
5. **Partner audit · 4 min.** Partners ask whether the plan fits every stated condition. No prices have been supplied, so no one can calculate cheapest.
6. **Exit · 3 min.** “Why isn't four boxes of nine the immediate plan?” Key: each available box holds at most eight books.

## Day 10 — Fresh factor and grouping check

**Success:** independently find factor pairs and interpret a remainder for a new grouping problem. Prepare [42-card assessment](ASSESSMENT.md#day-10-check-b). (`AC9M5N02`, `AC9M5N09`)

1. **Set task · 2 min.** Explain that values are new and the goal is reasoning; allow arrays, number facts or text.
2. **Read card · 4 min.** Present 42 cards and 7 trays; do not point out the solution. Clarify that cards stay whole.
3. **Plan · 5 min.** Learners select an array, multiplication fact family or systematic factor list.
4. **Independent response · 7 min.** Answer all items, including a sentence about a five-tray plan. Record supports.
5. **Reasonableness check · 4 min.** Learners multiply back and check whether their plan uses all 42 cards.
6. **Exit · 3 min.** “What new information would you need to choose the cheapest plan?” Key: actual tray costs and availability, possibly reuse/waste conditions. See [key](ASSESSMENT.md#day-10-check-b).

**Rights:** Original lesson prose © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/); credit, link and indicate changes.