Mathematics · Days 11–20 · ten… | Year 6 Maths · T1 W3–4 · Lessons

Daily rhythm: launch 2 + model 5 + guided 6 + one learner route 6 + exit 4 + evidence note 2 = 25 minutes. On Days 15 and 20, the six-minute route and four-minute exit become a ten-minute fresh check; the three routes on those days are later practice. Use clean learner prompts, three daily routes, original A4 aids and their full alternatives, and the staff key. Record whether the learner reasoned independently, used a reader/scribe or received a mathematical hint. Do not mistake an access route for weaker reasoning or a single check for an achievement-standard verdict.

Week 3 · Properties of prime, composite and square numbers

Teacher convention: a prime is a whole number greater than 1 with exactly two positive factors; a composite is a whole number greater than 1 with more than two positive factors; a square number is n × n for a whole number n (this fortnight uses positive n). A square number greater than 1 is composite. 1 is square (1 × 1) but neither prime nor composite. The words “prime/composite” classify differently from “square”: 4 is both composite and square. Material and safety choices are in MATERIALS.

Day 11 · Classify by factors, not appearance

Code: AC9M6N02. Goal: use a factor-array explanation to classify 1, 2, 12 and 16. Prepare: blank factor-array lab or text/tactile route, 16 counters/cards.

Launch · 2 min. Ask whether a number can be both square and composite; collect a tentative answer without rating speed.
Model · 5 min. Arrange 12 as 1 × 12, 2 × 6, 3 × 4; show factor pairs. Twelve has more than two positive factors, so composite. Arrange 16 as 4 × 4; it is square and composite (2 × 8 also works). Say why 1 has just one positive factor and 2 has exactly two.
Guided · 6 min. Learners use tiles, drawn cells or spoken factor pairs for 1 and 2, then check 16. Name the rule greater than 1 for both prime and composite. Do not call “odd” a prime test.
Choice · 6 min. One D11-A/B/C route: each requires a correct classification and factor evidence.
Exit · 4 min. “Is 16 prime because its square array looks special?” No, since 16 has factors 1, 2, 4, 8, 16. “Is 1 prime?” No, it has one positive factor.
Note · 2 min. Save factor language and a diagram/spoken explanation. If labels are memorised without proof, reteach with a new array.

Home/extension: Make 12 with bottle-cap substitutes or sketch boxes; no purchase. Extension: explain why every positive square above 1 has at least factors 1, n, n² (for n>1, these are distinct).

Day 12 · A complete factor check

Code: AC9M6N02. Goal: find factor pairs without skipping one and justify why 23 is prime. Prepare: scratch grid, D12 routes.

Launch · 2 min. Show 18 and ask for two different rectangular row plans.
Model · 5 min. List 18 as 1 × 18, 2 × 9, 3 × 6; stop when the next trial would repeat a pair. For 23, test possible small divisors 2, 3 and 4; none divide evenly, and 5 × 5 > 23, so an unseen factor pair cannot begin at 5 or more. Therefore only 1 × 23 and 23 is prime. “Not obvious” alone is no proof.
Guided · 6 min. Check 20's factor pairs 1 × 20, 2 × 10, 4 × 5; compare 21's 1 × 21, 3 × 7. Learners explain how pairs link to arrays, not only a yes/no label.
Choice · 6 min. D12-A/B/C, using seats, archive trays or a number detective game; check the full pair list or a justified prime decision.
Exit · 4 min. “Why can 23 have no pair 5 × something whole?” Because 5 × 5 already exceeds 23 and the smaller member of any factor pair must be at most the square-root boundary. Accept a concrete pair-table explanation without requiring square-root notation.
Note · 2 min. Record whether the learner tried all needed small divisors and knew when to stop; recheck with a fresh two-digit number.

Home/extension: Draw rectangles for 18/20. Extension: compare how 2 × 11 = 22 and 3 × 8 = 24 flank prime 23 without treating neighbours as proof.

Day 13 · Squares belong in two conversations

Code: AC9M6N02. Goal: locate square numbers in a factor grid and state when they are composite. Prepare: square-and-factor strip or tactile cards.

Launch · 2 min. Show 1 × 1, 3 × 3, 7 × 7; learners predict their totals.
Model · 5 min. Fill 1, 4, 9, 16, 25, 36, 49 as squares of 1–7. Explain 49 as 7 × 7 and composite since factors include 1, 7, 49. State the exception: 1 is square but neither prime nor composite.
Guided · 6 min. Investigate 36 with 6 × 6 and another array 4 × 9; use two routes to justify both labels. Sort 9 and 17; 9 is square/composite, 17 prime/not square. A learner may speak equations instead of moving small counters.
Choice · 6 min. D13-A/B/C: square mosaic, factor-card sort or a careful reply to “all squares are prime”.
Exit · 4 min. “Can a positive square greater than 1 be prime?” No: n × n gives a factor n between 1 and n². Ask for 25 or 49 as an example.
Note · 2 min. Keep evidence for square property and prime/composite property separately; reteach the exception with 1 if necessary.

Home/extension: Draw 4×4 and 5×5 on grid paper. Extension: compare consecutive squares 25 and 36 using visible border growth; no general algebra rule is required here.

Day 14 · Use properties to choose a plan

Code: AC9M6N02. Goal: use factor/square properties in a practical decision and simplify a product. Prepare: fictional event layout cards, D14 choices.

Launch · 2 min. A fictional gallery has 28 display cards. Can it have more than one equal row and column? Yes, e.g. 4 × 7.
Model · 5 min. Compare 29 cards: no pair of whole rows/columns with both sides >1 (2,3,4,5 do not divide; next square 6²>29), so a complete 29-card rectangle is only 1 × 29. For 36 cards, 6 × 6 makes a square and 4 × 9 another rectangle. Show mental 12 × 15 = (3 × 4) × (3 × 5) = 9 × 20 = 180; re-grouping uses factor properties without changing the product.
Guided · 6 min. Give 24 rehearsal seats: list 2 × 12, 3 × 8, 4 × 6; decide which fits a six-seat-wide area. It is 4 × 6, with no assumptions about actual room access or capacity.
Choice · 6 min. D14-A/B/C: gallery, game-board or calculation route. Require a factor statement and a reason tied to the context.
Exit · 4 min. “For 36 items, is 6 × 6 the only rectangle?” No; name 4 × 9 or 3 × 12. “What is 12 × 15?” 180, by a checked regrouping.
Note · 2 min. Check if the learner confused “a square exists” with “only one array exists”; use 16 as a new counterexample.

Home/extension: Design a fictional 24-cell board on paper. Extension: explain which factors make 36 quick to multiply without changing a product.

Day 15 · Fresh number-properties check

Code: AC9M6N02. Goal: transfer classification and factor reasoning to unseen 27, 37, 64, 31 and 33. Prepare: fresh learner check, separate staff key. Do not show its numbers in practice first.

Launch · 2 min. Tell learners a new set helps decide the next teaching move; access tools and a quiet response are available.
Model · 5 min. Revisit different numbers: 9 is 3 × 3 and composite; 17 has no 2, 3 or 4 factor and is prime. Put examples away.
Guided · 6 min. Use 20: 1 × 20, 2 × 10, 4 × 5. Ask why it is composite but not square. Keep fresh-check values unseen.
Independent check · 6 min. Give unseen Day 15 Items 1–2. Read wording neutrally if needed; do not offer a factor or label.
Check exit · 4 min. Items 3–4 ask for a square/composite overlap and a layout decision. Save first answers before feedback; later D15 routes are separate practice.
Note · 2 min. Score definitions, factor evidence, square overlap and contextual choice separately. If access/time interrupted, mark not yet observed rather than incorrect.

Home/extension: After the first check response, optional routes can go home. Do not turn the held-out sheet into a coached homework task.

Week 4 · Equivalent common fractions on the same whole and line

Use a fixed unit whole and equal-length sections. On a 0–1 line divided into 12 equal gaps, 1/4=3/12, 1/3=4/12, 1/2=6/12, 2/3=8/12, 3/4=9/12. The same mark can have two fraction names. The 12-gap and 24-gap lines and equal-whole bars are blank learner aids; the full text/tactile route gives scales without pre-filling answers. A 0–2 printed line has a different physical scale than a same-length 0–1 printed line; compare fraction values, not centimetres across those two diagrams.

Day 16 · Fix the whole before comparing

Code: AC9M6N03. Goal: locate 1/4, 1/3, 1/2 in order on one 0–1 line. Prepare: fraction line and equal-whole bars or 12 equal tactile strips.

Launch · 2 min. Ask why “one half is bigger than one third” needs the same-size whole.
Model · 5 min. Mark 0 and 1, then 12 equal spaces. Place 1/4 at gap 3, 1/3 at gap 4, 1/2 at gap 6. Explain 3/12 < 4/12 < 6/12; point to the same endpoint 1 for all.
Guided · 6 min. Learners use bars split into 2, 3, 4 or 12 equal parts and map 1/2=6/12, 1/3=4/12. Ask whether gap 6 on a different 6-gap 0–1 line has the same value as gap 6 on this 12-gap line. No: 6/6=1, while 6/12=1/2; the scale matters.
Choice · 6 min. D16-A/B/C: line, recipe-share cards or a musical-cycle fraction route; each uses one whole and justifies order.
Exit · 4 min. On the same whole, order 1/2, 1/4, 1/3: 1/4 < 1/3 < 1/2. Explain by twelfths or equal bars, not denominator size alone.
Note · 2 min. Record whether endpoints and equal spacing were checked. If not, restore a shared whole before rechecking.

Home/extension: Fold a paper strip into 2 then 4 equal parts, or draw 12 gaps; no food or instrument needed. Extension: explain why differently sized physical wholes make direct piece comparisons unsafe.

Day 17 · Equivalent names, one position

Code: AC9M6N03. Goal: show equivalent fractions and compare 2/3 and 3/4 using one 12-gap line. Prepare: bars/line or spoken gap sequence.

Launch · 2 min. Ask whether 2/4 and 1/2 need two marks on the same 0–1 line.
Model · 5 min. Place 2/4=1/2=6/12 at one mark. Place 2/3=8/12 and 3/4=9/12; 3/4 > 2/3 by 1/12 of the same whole. Say numerator and denominator both scale by the same factor when making equivalent names.
Guided · 6 min. Match 1/3=4/12, 2/4=6/12, 3/4=9/12; have learners correct a claim that 2/3 > 3/4 merely because 3 is greater than 4 in a numerator/denominator comparison.
Choice · 6 min. D17-A/B/C: line explanation, archive-space diagram or original game-state explanation. Require equivalent names and same whole.
Exit · 4 min. “Which is larger, 2/3 or 3/4, and by how much?” 3/4 by 1/12. Ask where both sit between 0 and 1.
Note · 2 min. Check whether learner can justify order, not only convert by rote. Recheck with 1/3 versus 1/2 if needed.

Home/extension: Use one folded strip as the whole. Extension: find 3/6 and 6/12 on the same half mark, with equal partitions shown.

Day 18 · Fractions beyond one on the same scale

Code: AC9M6N03. Goal: represent and compare 5/4 and 3/2 on a 0–2 line. Prepare: 24-gap line or tactile equivalents, two equal unit strips.

Launch · 2 min. Ask whether a fraction greater than 1 can still be marked on a number line. Yes, if the line extends beyond 1.
Model · 5 min. On 0–2 with 12 equal gaps in each unit, mark 5/4 = 1 + 1/4 = 15/12 at gap 15, and 3/2 = 1 + 1/2 = 18/12 at gap 18. Thus 5/4 < 3/2 by 3/12=1/4.
Guided · 6 min. Locate 1 1/2 at the same gap as 3/2 and 6/4. Locate 1 1/4 with 5/4. Ask why a second whole must match the first whole's length.
Choice · 6 min. D18-A/B/C: extended line, 12-beat loop over two cycles or art-tile strip. Show an equivalence and a reason for order.
Exit · 4 min. “Is 5/4 to the left or right of 3/2?” Left. “How far?” 1/4 of the unit whole.
Note · 2 min. Record if learner labelled 1 at gap 12 and 2 at gap 24; recheck scale before fraction work.

Home/extension: Draw two matching strips and split each into four; extension: explain why 6/4=3/2 is one mark, not two.

Day 19 · Justify an order and repair a false rule

Code: AC9M6N03. Goal: use equivalent names to order common fractions and diagnose denominator-only reasoning. Prepare: 12-gap line/bars, D19 routes.

Launch · 2 min. Display false claim: “1/3 > 1/2 because 3 > 2.” Ask which whole/mark would disprove it.
Model · 5 min. On the same 0–1 whole, 1/3=4/12 and 1/2=6/12, so 1/3 < 1/2. A larger denominator of a unit fraction means smaller equal parts when the whole stays fixed. Do not turn this into an unsafe rule for every pair of fractions.
Guided · 6 min. Order 1/4, 1/2, 2/3 as 3/12,6/12,8/12. Learners compare another same-whole pair 3/4 and 1/2 using marks 9 and 6, then say why a different whole would change physical sizes.
Choice · 6 min. D19-A/B/C: evidence to a fictional exhibit maker, an error-repair dialogue or a tactile same-whole sequence. State an exact comparison and explain it.
Exit · 4 min. A peer places 2/4 to the right of 1/2 on one line. Repair: both equal 6/12 and occupy the same mark.
Note · 2 min. Distinguish a correct order with reasoning from a memorised slogan. Recheck a new pair without the model in view.

Home/extension: Draw a new line and give an adult a deliberate error to repair. Extension: show 3/6, 2/4 and 1/2 as one point with same-size whole.

Day 20 · Fresh fraction-line check

Code: AC9M6N03. Goal: transfer equivalent-name, order and same-whole reasoning to unseen 5/3 and 7/4 plus a new 24-tile context. Prepare: closed learner check, blank line/strips, separate staff key.

Launch · 2 min. Remind learners to mark 0, 1 and 2 before deciding an order; response mode is open.
Model · 5 min. Revisit different numbers: 5/4=15/12, 3/2=18/12; put away. Do not show the check's 5/3 or 7/4.
Guided · 6 min. Use 1/4=3/12 and 1/2=6/12 on one fixed 0–1 line. Ask why six gaps on a 12-gap line represent half. Put it away.
Independent check · 6 min. Give unseen Day 20 Items 1–2. Adult can read wording neutrally or provide a tactile line without placing answers.
Check exit · 4 min. Item 3 asks for a same-whole comparison and a false-rule repair. Preserve first response and route; D20 choices are later practice.
Note · 2 min. Mark endpoints/equal scale, equivalent names, order and justification separately. If learner had no usable access route, mark not yet observed and arrange a valid later check.

Home/extension: Fresh check stays in class. Afterward, optional D20 routes use different numbers and a learner-selected everyday context.

Later in the day: The ten optional extra cards give short practice or transfer, not a full mathematics timetable. No learner needs a home device, purchase or personal finance disclosure. The exact curriculum descriptions and taught limits are in the crosswalk. Original SubjectNest lessons © NeuroForgeIO Pty Ltd 2026, CC BY 4.0.