# Year 4 mathematics · Days 11–20 · 25 minutes each

**Daily rhythm:** invite 2 + explicit model 5 + guided attempt 6 + one learner choice 6 + exit 4 + evidence note 2 = **25 minutes**. On Days 15 and 20 the independent-choice and exit windows form a ten-minute held-out check; the three practice routes remain available *after* evidence is retained. Read a check neutrally and record the first response, mode and mathematical cues. Rotate a few focus learners each day; a whole-class check does not require ten private interviews at once. The [learner routes](STUDENT-CARDS.md) contain no answers and the [staff key](TEACHER-KEY.md) must stay away from learner displays.

## Week 3 · Where does a decimal sit?

The first number line has equal distances between 0 and 1. A tenth is a gap of `0.1`; a hundredth is a gap of `0.01`. A line between 0.2 and 0.3 can be **zoomed** into ten equal hundredth steps. Mark endpoints before counting ticks. The page-top or paper length carries no special value: labels and **equal spacing** make the scale. Use the original [decimal-line sheet](print/decimal-line.pdf), a drawn line or the [text/tactile route](print/TEXT-ALTERNATIVES.md).

### Day 11 · Ten equal jumps

**Code:** `AC9M4N01` (partial). **Goal:** locate a tenth on an equal 0–1 line and connect the fraction of one whole to decimal place. **Prepare:** ten-space line, ten equal paper tiles, labelled 0 and 1.

1. **Invite · 2 min.** Show an unlabelled line with ten equal spaces. Ask what its endpoints and equal gaps need to mean before a mark can be named. Keep the unit whole visible.
2. **Model · 5 min.** Label 0 and 1, count ten **spaces**, not ten marks, and locate the third internal tick: `3/10 = 0.3`. Explain that each move adds one tenth of the same whole. Contrast the third tick with the number 3.
3. **Guided · 6 min.** Learners place `0.7` and `0.9`, then mark `0.4` by counting from zero and from one. Discuss why the same distance cannot represent two different tenths if the scale is fixed.
4. **Choice · 6 min.** Choose D11-A, B or C in [learner cards](STUDENT-CARDS.md). Each requires a marked location and a reason, via strip, line, tactile token or explanation.
5. **Exit · 4 min.** Ask for the tick one tenth after `0.5` and one tenth before `0.7`. Both are `0.6`; require reference to adjacent equal spaces.
6. **Note · 2 min.** Record whether the child counted spaces accurately and kept a fixed whole; if they counted marks, reteach with ten connected paper tiles.

**Access/home/extension:** Adult can draw/mark under child direction. A tactile line needs 11 tick positions for ten gaps. At home use pencil dots. Extension: describe `0.3` from the 1 endpoint as seven tenth-steps left.

### Day 12 · Zoom a tenth into hundredths

**Code:** `AC9M4N01` (partial). **Goal:** locate a hundredth between adjacent tenths using a clear zoomed scale. **Prepare:** 0.2–0.3 interval and a second line divided into ten equal subspaces; hundred-grid.

1. **Invite · 2 min.** Retrieve that `0.2 = 0.20` and `0.3 = 0.30`. Ask whether anything lies between them; listen for a number, not just a mark.
2. **Model · 5 min.** Enlarge only the interval `0.20–0.30`, divide it into ten **equal** gaps and count `0.21, 0.22, …, 0.26` at the sixth tick. Each step is one hundredth; `0.26` is 26 of the same hundred equal parts of one whole.
3. **Guided · 6 min.** Place `0.24` and `0.29` on the zoom, then show `0.25` midway in this interval. Ask how many hundredths after `0.20` and before `0.30` each is.
4. **Choice · 6 min.** Choose D12-A, B or C; use a ten-step zoom or move ten small tokens between the tenths labels.
5. **Exit · 4 min.** “What number is seven hundredths after `0.20`?” Answer `0.27`, at seventh of ten equal steps toward `0.30`.
6. **Note · 2 min.** Record whether the child names the endpoints, counts spaces and preserves the hundredths place. If `0.27` is put beyond `0.30`, rebuild the interval with 20–30 hundred-grid cells.

**Access/home/extension:** Say the full ten-number sequence aloud or use raised ticks. No measurement of a real object is assumed. Extension: explain why `0.2` and `0.20` occupy one point.

### Day 13 · Beyond one whole, zoom when needed

**Code:** `AC9M4N01` (partial). **Goal:** place `1.2` and `1.05` with a sensible whole/tenth/hundredth scale. **Prepare:** labelled 0–2 line with equal tenth gaps, then a 1.0–1.1 hundredth zoom.

1. **Invite · 2 min.** Show `1.2` and `1.05`. Ask which is farther from one whole. Predictions must be checked against places, not digit-string length.
2. **Model · 5 min.** Place `1.2` two tenth-steps after 1.0 on the 0–2 line. Rename `1.2 = 1.20`. On a separate enlarged `1.00–1.10` interval, place `1.05` five hundredth-steps after 1.00. Therefore `1.05 < 1.20`. Do not draw `1.05` as if a 0–2 tenth line had hundredth precision.
3. **Guided · 6 min.** Compare `1.3 = 1.30` and `1.03`, placing the first on the whole/tenth line and the second on a 1.00–1.10 zoom. Ask which digit names tenths in each.
4. **Choice · 6 min.** Select D13-A, B or C for a fiction-based quantity. A learner can build one full strip plus tenths/hundredths instead of drawing a fine line.
5. **Exit · 4 min.** Compare `1.06` with `1.6`: `1.06 < 1.60` because 0 tenths after one is less than 6 tenths. Point to what scale is needed to show `1.06` exactly.
6. **Note · 2 min.** Record whether the child uses fixed whole, tenths and hundredths; if they decide by number of printed digits, use matched hundred-grids.

**Access/home/extension:** Two linked lines avoid tiny inaccessible ticks. Adult reads “one and five hundredths” accurately; child selects the point. Extension: compare distances from 1 of `1.05` and `1.2` in hundredths (5 and 20).

### Day 14 · A line can mislead

**Code:** `AC9M4N01` (partial). **Goal:** test scale, equal spacing and decimal labels before trusting a number-line claim. **Prepare:** one deliberately uneven teacher line and a correct equal-spaced line; two marker tokens.

1. **Invite · 2 min.** Display five spaces drawn with noticeably different lengths between 0 and 1 but labelled `0, 0.2, 0.4, 0.6, 0.8, 1` as if equal. Ask what would have to be fixed before calling this an equal scale. Focus on equal spacing.
2. **Model · 5 min.** On a **correct** `0.00–0.10` ten-gap zoom, show that `0.07` is seventh hundredth tick. On a separate 0–1 ten-gap line, `0.7` is seventh tenth tick. They are not the same point; `0.70 > 0.07`. Mark the first line's endpoints and gap size.
3. **Guided · 6 min.** Audit a claim that `0.43 > 0.5` because 43 is greater than 5. Rename `0.5 = 0.50`; on matched same-whole hundred-grid/line `0.43 < 0.50` by 7 hundredths. Repair the uneven line by marking equal gaps.
4. **Choice · 6 min.** Select D14-A/B/C and keep the incorrect first claim visible beside the correction. The learner explains which feature—place or scale—caused the error.
5. **Exit · 4 min.** Compare `0.49` with `0.5 = 0.50`; `0.49 < 0.50` by one hundredth. If a learner thinks `49 > 5`, match decimal places first.
6. **Note · 2 min.** Record whether the error is scale, endpoint, gap-count or tenths/hundredths value; use the matched repair in [staff key](TEACHER-KEY.md).

**Access/home/extension:** Use tactile equal tiles instead of relying on visually judged line lengths. No real measurement or personal score is required. Extension: write a false scale claim for a partner to diagnose without changing the number values.

### Day 15 · Unseen decimal-line check

**Code:** `AC9M4N01` (partial). **Goal:** transfer number-line naming, scale and decimal order to new points. **Prepare:** reserve the [unseen Day 15 learner check](STUDENT-CHECKS.md) and [staff key](TEACHER-KEY.md); do not display their values in preparation.

1. **Invite · 2 min.** Say that today's fresh lines help decide the next small group, not a permanent maths label.
2. **Model · 5 min.** Rehearse a **different** `0.10–0.20` ten-gap zoom; place `0.14` four hundredth-steps after `0.10`. Fold away the example.
3. **Guided · 6 min.** On a fresh `1.20–1.30` ten-gap interval, ask for `1.25` and verify the fifth space. Do not reveal check values or layout.
4. **Independent check · 6 min.** Give the first two [student check](STUDENT-CHECKS.md) items. Read text neutrally; allow the same tactile/large-print relationships without saying which tick is correct.
5. **Check exit · 4 min.** Items 3–4 compare and repair. Keep the child's first representation before feedback. If time or access is inadequate, finish in a quiet session and mark incomplete for now.
6. **Note · 2 min.** Use separate rubric rows for line/zoom, comparison and scale explanation. D15 practice cards are for **after** the retained check.

**Access/home/extension:** A helper may place tokens precisely as the learner directs and must not signal the answer. The unseen values do not appear on the reusable aid. Home routes use fresh later-practice cards, not the held-out sheet.

## Week 4 · Fractions of the same whole can share a point

Keep the unit whole the **same size** in every paired strip/grid. Splitting one whole into more equal parts changes the part name, not the amount shaded. Use the [equal-whole sheet](print/equal-whole.pdf), paper strips, 10×10 squares and the [text/tactile version](print/TEXT-ALTERNATIVES.md). The decimal links here are exact, not rounded. Use fraction language aloud before notation.

### Day 16 · A half has many exact names

**Codes:** `AC9M4N03`, `AC9M4N01` (partial). **Goal:** show `1/2 = 5/10 = 50/100 = 0.5 = 0.50` on one equal whole.

1. **Invite · 2 min.** Show the same-length blank strip divided once into two and once into ten. Ask how many tenths cover a half.
2. **Model · 5 min.** Shade one of two equal parts, five of ten equal parts and 50 of 100 same-whole cells. Align endpoints: all shaded lengths/areas are half. Write `1/2 = 5/10 = 50/100 = 0.5 = 0.50` and place each at the midpoint on 0–1 line.
3. **Guided · 6 min.** Split each of two equal half-parts in two: `2/4 = 1/2`. Pair this with `5/10`; ask why counting different pieces is not a different total share. Test with equal-sized wholes only.
4. **Choice · 6 min.** Select D16-A/B/C. Each route requires at least two representations and a reason the whole did not change.
5. **Exit · 4 min.** Is `0.5` less than `0.50`? No: five tenths is 50 hundredths. Ask learner to align same-sized strips or use place value.
6. **Note · 2 min.** Record equal-part and fixed-whole reasoning separately from correct symbols; if a strip's parts are unequal, rebuild it before claiming an equivalent fraction.

**Access/home/extension:** Paper-fold, tactile lengths, a described equal grid and AAC are valid. An adult may shade under direction. Extension: explain why two of four equal parts gives the same amount as one of two.

### Day 17 · One and three quarters

**Code:** `AC9M4N03` (partial). **Goal:** connect a quarter and three quarters of one equal whole to hundredths and decimals. **Prepare:** four-part same-sized strips, 10×10 grid, 0–1 line.

1. **Invite · 2 min.** Fold one strip into four equal sections. Ask how many of the hundred small cells in a same-sized whole would match one quarter.
2. **Model · 5 min.** Partition 100 equal cells into four groups of 25. Shade one: `1/4 = 25/100 = 0.25`. Shade three groups on a new matching whole: `3/4 = 75/100 = 0.75`; place both at quarter and three-quarter points on a 0–1 line.
3. **Guided · 6 min.** Build `2/4 = 50/100 = 1/2 = 0.50`; contrast one quarter and half using aligned equal wholes. Explain why 25 cells are one quarter of this grid.
4. **Choice · 6 min.** Choose D17-A/B/C. Use 25-cell groups, quarter folds or a learner-directed tactile grid.
5. **Exit · 4 min.** Compare `1/4 = 0.25` with `0.2 = 0.20`: the quarter is greater by five hundredths, with the same whole.
6. **Note · 2 min.** If a child maps one quarter to `0.4`, count four groups of **25** or fold the same whole again; do not rely on a memorised decimal alone.

**Access/home/extension:** A 100-cell grid can be described as four equal 25-cell blocks, not visually scanned. Extension: explain `3/4` as one whole minus one quarter.

### Day 18 · Fifths into tenths and hundredths

**Code:** `AC9M4N03` (partial). **Goal:** use related denominators `5→10→100` to rename fifths exactly. **Prepare:** equal five-part and ten-part strips, 10×10 whole grid.

1. **Invite · 2 min.** Ask: “If I split each of five equal parts in two, how many equal parts will the same whole have?” Answer ten.
2. **Model · 5 min.** One of five equal parts becomes two of ten; each tenth becomes ten hundredths. Record `1/5 = 2/10 = 20/100 = 0.2 = 0.20`, with strips aligned to the same whole.
3. **Guided · 6 min.** Build three fifths: `3/5 = 6/10 = 60/100 = 0.6`. Ask what stayed the same while each fifth split into two tenths.
4. **Choice · 6 min.** Choose D18-A/B/C; label all representations and explain at least one splitting step.
5. **Exit · 4 min.** `5/5 = 10/10 = 1`: one complete whole. Explain why `5/5` is not five wholes.
6. **Note · 2 min.** Record if the learner multiplies both numerator and denominator when partitioning; if only the denominator changes, rebuild the strip with pieces paired.

**Access/home/extension:** Five paper boxes can be split in two with pencil marks. Extension: use a point on the 0–1 line to explain why three fifths and six tenths coincide.

### Day 19 · Decide if two names share a point

**Codes:** `AC9M4N03`, `AC9M4N01` (partial). **Goal:** test equivalent representations and compare across related fractions/decimals with fixed wholes. **Prepare:** candidate cards `3/4, 0.75, 1/5, 0.20, 1/2, 0.50`, same-sized strips.

1. **Invite · 2 min.** Ask whether a larger denominator automatically makes a larger amount. Keep the unit whole fixed while gathering claims.
2. **Model · 5 min.** Match `3/4 = 75/100 = 0.75` and `1/5 = 20/100 = 0.20`. On the same 0–1 line, their positions differ; the denominator alone does not order them. Link each to its same-whole model.
3. **Guided · 6 min.** Match `1/2, 5/10, 0.50` at one point and order `0.25, 0.50, 0.75`. Ask why one full-size strip cannot be compared by raw cell count with a differently sized strip.
4. **Choice · 6 min.** Select D19-A/B/C. Learner creates or rejects a match with an exact model/reason and names the whole.
5. **Exit · 4 min.** Are `0.50` and `0.5` different points? No; 50 hundredths = 5 tenths. Ask for a second representation of the same point.
6. **Note · 2 min.** Record whether the learner matched by quantity or by digit appearance. If wholes drift, overlay same-size outlines and recheck with a new pair.

**Access/home/extension:** Tactile strips, line locations and verbal ratio explanations work without colour. Extension: give a counterexample to “more pieces means more shaded amount.”

### Day 20 · Unseen equivalent-fraction check

**Codes:** `AC9M4N03`, `AC9M4N01` (partial). **Goal:** independently connect an unpractised fifths fraction with tenths/hundredths and decimal location. **Prepare:** [Day 20 unseen learner check](STUDENT-CHECKS.md), blank equal-whole aids and separate [staff key](TEACHER-KEY.md).

1. **Invite · 2 min.** Say the fresh situation shows what to practise next; a pupil may explain in a chosen mode.
2. **Model · 5 min.** Revisit `1/5 = 2/10 = 0.2` only on a practice strip. Fold it away before the check.
3. **Guided · 6 min.** Rehearse `3/5 = 6/10 = 0.6` with a different fictional context and confirm the same whole. Keep the held-out fraction unshown.
4. **Independent check · 6 min.** Give Items 1–2 from the new [learner check](STUDENT-CHECKS.md); adult may read but not select or point to the answer.
5. **Check exit · 4 min.** Items 3–4 compare and repair. Retain first answers and exact prompts. If no accessible opportunity or time, complete later without scoring a blank as wrong.
6. **Note · 2 min.** Record equivalent grouping, number-line location, comparison and claim repair separately. Only after evidence, offer D20-A/B/C for later practice.

**Access/home/extension:** Folded paper and ten raised positions give the same whole without printing or colour. Do not send the held-out check home as a coached worksheet.

**Responsive teaching across all ten days:** If a learner counts tick *marks* rather than equal *spaces*, re-establish endpoints. If `0.7` and `0.07` are conflated, show seven of ten versus seven of a hundred using same-sized wholes. If a child treats `1/4` as `0.4`, pair four equal 25-cell groups with the written 100. If an equivalence changes only denominator, split each original part visibly and recount numerator. Recheck on a **different** number or fraction and record the support; avoid fixed “visual/auditory/kinaesthetic learner” labels.

Original SubjectNest lessons © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Curriculum wording is separately attributed in the [crosswalk](CURRICULUM-CROSSWALK.md).