Ten mathematics lessons: 25… | Year 5 Maths · T1 W1–2 · Lessons

Use the original task cards, print line, factor array and assessment keys. 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)

Notice · 2 min. Display 1.235. Ask what the last digit is worth; do not accept “five” without a place.
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.
Build together · 5 min. Learners show 1.205; ask why the hundredths position is zero. Contrast 1.25 by writing 1.250.
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.
Explain · 4 min. Pairs compare 1.205 and 1.25: which place first differs? Teacher listens for hundredths 0<5.
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)

Hook · 2 min. Vote: 1.25 or 1.205 greater? Ask for a reason, not speed.
Model · 4 min. Rename 1.25 as 1.250. Compare ones, tenths, then hundredths: 5>0, so 1.250>1.205.
Guided pairs · 5 min. Order 0.905, 0.950, 0.959, using columns. Ask whether 0.905 could mean 905 whole units.
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.
Error clinic · 4 min. Show “2.074 is largest because 074 has three digits.” Learners explain the first differing place and repair the statement.
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. (AC9M5N01)

See · 2 min. Ask what changes from 1.230 to 1.235: five thousandths.
Model · 4 min. Label line ticks at 1.230, 1.235, 1.240 … 1.260. Point out 1.250 equals 1.25.
Guided locate · 5 min. Learners place 1.245 and 1.255; ask where 1.253 sits between ticks and why.
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.
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.
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)

Context · 2 min. Say clearly that the route values are invented; no real travel advice is being given.
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.
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.
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.
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.
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, not the worked route set. (AC9M5N01)

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

Day 6 — See all the rectangles

Success: build factor pairs and name all factors of 24. Prepare 24 counters or array mat. (AC9M5N02)

Hook · 2 min. Ask whether 24 can make 5 equal rows of whole counters. Accept “let's test”.
Model · 4 min. Arrange 1×24 and 2×12; turn each rectangle to show a rotated pair is not a new factor pair.
Guided arrays · 5 min. Make 3×8 and 4×6. Test 5×? and explain why no whole row length works.
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.
Completeness check · 4 min. Ask why stopping at 4×6 is enough: swapped pairs then repeat. Do not demand formal square-root terminology.
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. (AC9M5N02)

Warm · 2 min. Count by fours to 20; ask what a multiple means.
Model · 4 min. List positive multiples of 4 and 6 to 36. Circle 12, 24, 36 as common values.
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.
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.
Check method · 4 min. Partners swap lists, circle an error, and verify it with multiplication rather than agreement.
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)

Recall · 2 min. Ask whether a factor pair gives a division fact. Example 4×6=24 gives 24÷6=4.
Model · 4 min. Arrange 36 into six equal rows: 36÷6=6. Test five rows: five groups of seven use 35, one remains.
Guided compare · 5 min. Check divisibility of 36 by 4, 9 and 5 with facts: 4×9, 9×4, and no whole factor 5.
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.
Explain · 4 min. Learners compare a quick rule with an array or inverse multiplication check. Teacher looks for reasoning, not a memorised slogan.
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)

Frame · 2 min. Read the constraint: six boxes available, capacity eight each. This is an invented problem.
Model · 4 min. Put six books in each available box: 6×6=36, 6≤8, so equal sharing and capacity both work.
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.
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.
Partner audit · 4 min. Partners ask whether the plan fits every stated condition. No prices have been supplied, so no one can calculate cheapest.
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. (AC9M5N02, AC9M5N09)

Set task · 2 min. Explain that values are new and the goal is reasoning; allow arrays, number facts or text.
Read card · 4 min. Present 42 cards and 7 trays; do not point out the solution. Clarify that cards stay whole.
Plan · 5 min. Learners select an array, multiplication fact family or systematic factor list.
Independent response · 7 min. Answer all items, including a sentence about a five-tray plan. Record supports.
Reasonableness check · 4 min. Learners multiply back and check whether their plan uses all 42 cards.
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.