Mathematics · Days 11–20 · 25… | Year 4 Maths · T1 W3–4 · Lessons

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 contain no answers and the staff key 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, a drawn line or the text/tactile route.

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.

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.
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.
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.
Choice · 6 min. Choose D11-A, B or C in learner cards. Each requires a marked location and a reason, via strip, line, tactile token or explanation.
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.
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.

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.
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.
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.
Choice · 6 min. Choose D12-A, B or C; use a ten-step zoom or move ten small tokens between the tenths labels.
Exit · 4 min. “What number is seven hundredths after 0.20?” Answer 0.27, at seventh of ten equal steps toward 0.30.
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.

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.
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.
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.
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.
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.
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.

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.
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.
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.
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.
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.
Note · 2 min. Record whether the error is scale, endpoint, gap-count or tenths/hundredths value; use the matched repair in staff key.

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 and staff key; do not display their values in preparation.

Invite · 2 min. Say that today's fresh lines help decide the next small group, not a permanent maths label.
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.
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.
Independent check · 6 min. Give the first two student check items. Read text neutrally; allow the same tactile/large-print relationships without saying which tick is correct.
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.
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.

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, paper strips, 10×10 squares and the text/tactile version. 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.

Invite · 2 min. Show the same-length blank strip divided once into two and once into ten. Ask how many tenths cover a half.
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.
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.
Choice · 6 min. Select D16-A/B/C. Each route requires at least two representations and a reason the whole did not change.
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.
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.

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.
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.
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.
Choice · 6 min. Choose D17-A/B/C. Use 25-cell groups, quarter folds or a learner-directed tactile grid.
Exit · 4 min. Compare 1/4 = 0.25 with 0.2 = 0.20: the quarter is greater by five hundredths, with the same whole.
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.

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.
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.
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.
Choice · 6 min. Choose D18-A/B/C; label all representations and explain at least one splitting step.
Exit · 4 min. 5/5 = 10/10 = 1: one complete whole. Explain why 5/5 is not five wholes.
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.

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.

Invite · 2 min. Ask whether a larger denominator automatically makes a larger amount. Keep the unit whole fixed while gathering claims.
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.
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.
Choice · 6 min. Select D19-A/B/C. Learner creates or rejects a match with an exact model/reason and names the whole.
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.
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, blank equal-whole aids and separate staff key.

Invite · 2 min. Say the fresh situation shows what to practise next; a pupil may explain in a chosen mode.
Model · 5 min. Revisit 1/5 = 2/10 = 0.2 only on a practice strip. Fold it away before the check.
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.
Independent check · 6 min. Give Items 1–2 from the new learner check; adult may read but not select or point to the answer.
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.
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. Curriculum wording is separately attributed in the crosswalk.