Ten daily mathematics lessons… | Year 5 Maths · T1 W3–4 · Lessons

Every day is a 25-minute core block. On Days 11–14 and 16–19, use 2-minute recall, 5-minute explicit model, 6-minute guided test, 7-minute learner route, 3-minute exit and 2-minute evidence note. Days 15/20 use a new 12-minute check inside the same total. Worked models, A/B/C learner cards, held-out checks, teacher key and optional extensions are separate. A child can reason with objects, tactile place cards, speech, AAC or writing; record what was prompted. Codes below are partial national links, not a year-level verdict.

Day 11 · Estimate the size before finding a product

Success: choose a benchmark for a larger-number product, calculate and explain why the exact result is plausible. Prepare: first model in MATERIALS, blank estimate mat. Codes: AC9M5N06, AC9M5N08.

Recall · 2 min. Ask if 50×20 is a useful scale for 48×19. Key: yes, about 1,000; it is not the exact seat count.
Model · 5 min. On the invented 48-by-19 stand, show 48×(20−1)=960−48=912. Both factors were rounded up for 1,000, so an answer above 1,000 would deserve a recheck. Say the original unit is drawn seats, not attendance.
Guide · 6 min. Compare 246×4 with 250×4=1,000. Partition 246×4=(200+40+6)×4=800+160+24=984. Ask which estimate is intentionally a little high and why.
Choose · 7 min. Offer one Day 11 A/B/C card. Ask for an estimate before exact multiplication, a visible method and one sentence comparing them.
Exit · 3 min. “Would 9,120 be reasonable for 48×19?” Key: no, about ten times a useful benchmark. Repair a misplaced zero with the bound.
Record · 2 min. Note estimate, exact value and explanation separately. A child's reasonable estimate can be sound even if their exact arithmetic needs reteaching.

Day 12 · Partition a larger number by one digit

Success: multiply hundreds, tens and ones by a single digit without losing a zero place. Prepare: 324×6 model, three place columns. Codes: AC9M5N06.

Recall · 2 min. Ask for 3×6 and 30×6, then why they differ. Key: 18 and 180; the second has tens.
Model · 5 min. Build 324×6=300×6+20×6+4×6=1,800+120+24=1,944. Circle the sum, not a concatenation of partial answers.
Guide · 6 min. Test 407×8 = 400×8 + 0×8 + 7×8 = 3,200+56=3,256. Ask whether 0 in the tens place can be silently turned into a 7 tens. Key: no.
Choose · 7 min. Day 12 A/B/C learner card. Permit place-value blocks, a typed table, vertical algorithm or spoken partitions; require each part to retain its value.
Exit · 3 min. “Which is a useful check for 324×6: near 1,800 or near 18,000?” Key: near 1,800. If 18,000, rebuild the hundreds group.
Record · 2 min. Mark arithmetic versus place-value error; a correct answer without inspectable strategy needs a question, not an automatic failure.

Day 13 · Twenty groups and three groups

Success: split a two-digit multiplier into tens and ones, then combine partial products. Prepare: partial-products mat or its text/tactile build. Codes: AC9M5N06.

Recall · 2 min. Ask what ×20 means. Key: twenty groups/two tens of the number, not merely ×2.
Model · 5 min. Write 128×23=128×20+128×3=2,560+384=2,944. Put 2,560 under the twenty groups row and 384 under three groups; align the sum by place. Compare with a loose 130×20=2,600, noting why the exact can be higher.
Guide · 6 min. Calculate 64×36 = 64×30 + 64×6 = 1,920+384=2,304. Ask child to audit the false partial 64×30=192 and restore the tens value.
Choose · 7 min. Day 13 A/B/C route: two-digit multiplication in a new fictional domain. Learner selects mat, expanded notation, grid or another efficient correct method and labels the tens product.
Exit · 3 min. “Would 294 be plausible for 128×23?” Key: no; 128×20 alone is 2,560. Ask for a lower bound.
Record · 2 min. Save the two partial products and the child's check, not only the final numeral.

Day 14 · Choose a strategy that helps

Success: use compensation, partitioning or a standard algorithm deliberately and explain a bound. Prepare: 247×18 model. Codes: AC9M5N06, AC9M5N08.

Recall · 2 min. Ask why 18 might be rewritten as 20−2. Key: 20 is easy to multiply by; subtract two extra groups.
Model · 5 min. Show 247×18=247×20−247×2=4,940−494=4,446. Check against 250×18=4,500; exact is 54 below because each of 18 groups has 3 fewer.
Guide · 6 min. Compare 125×32=(125×(4×8)) with 125×(30+2)=3,750+250=4,000. A learner may use 125×8=1,000 then ×4=4,000. Ask why either route is efficient here, and why 125×30 is 3,750 rather than 375.
Choose · 7 min. Day 14 A/B/C route with two possible strategies; child selects and defends one. Correct alternatives count if exact and inspectable.
Exit · 3 min. “Is 44,460 a reasonable result for 247×18?” Key: no; scale near 4,500, about ten times smaller. Revisit place alignment if needed.
Record · 2 min. Note choice, correctness and reasonableness separately; do not insist on one prescribed algorithm.

Day 15 · Fresh check A: product and bound

Success: transfer estimate, two-digit multiplication and explanation to an unseen count. Prepare: reveal Check A today only; keep worked key private. Codes: AC9M5N06, AC9M5N08.

Recall · 2 min. Ask from memory what makes an estimate useful. Key: nearby, justified and suited to the decision; do not preview the new digits.
Directions · 3 min. Explain response modes. Children may use paper mat or tactile place cards; if a calculator is allowed, record its role. Do not solve a parallel problem with check numbers.
Access · 3 min. Read the new fictional card once neutrally or provide a large-print/text copy. Check understanding of each and groups without suggesting an operation result.
Fresh response · 12 min. Learner estimates, calculates and checks Check A independently. A child needing more processing time finishes in a separately recorded continuation; time pressure is not the target.
Reflect · 3 min. Ask which part of their exact result agrees with their benchmark; collect before discussing a key.
Record · 2 min. Mark independent/prompted and method; secure named work under school policy. Offer after-check Day 15 routes only after collection.

Day 16 · A price needs an exact decision

Success: use multiplication and estimation in an invented budget, then state money left and the decision limit. Prepare: model $16 per kit, 28 kits, $470 available. Codes: AC9M5N06, AC9M5N08, AC9M5N09.

Recall · 2 min. Ask whether “about $450” is enough to say exactly how much remains from $470. Key: no.
Model · 5 min. State the complete fictional problem. Compute 28×$16 = 28×(10+6) = $280+$168=$448; $470−$448=$22. Rough 30×$15=$450 checks scale, but $450 does not replace exact payment. No actual shop price or family budget is claimed.
Guide · 6 min. Try $23 per item for 17 items with a $400 fictional limit: 23×17=23×(10+7)=230+161=391; $9 remains. Ask if $39.10 could be right for 17 items near $20 each. Key: no, scale near $340–$400.
Choose · 7 min. Day 16 A/B/C route. Learner writes/points to price × count → total → compare with given limit → money left, including the dollar unit. No discussion of real household spending.
Exit · 3 min. “If a rough estimate is close to the limit, what next?” Key: exact calculation and constraint check.
Record · 2 min. Note if child chose the operation and interpreted the $ difference; arithmetic alone is not the whole modelling target.

Day 17 · Check with the inverse, then a second route

Success: use multiplication/division as inverse facts and a bound to inspect a product. Prepare: 468×7 model. Codes: AC9M5A01, AC9M5N06, AC9M5N08.

Recall · 2 min. From 6×7=42, ask for a related division fact. Key: 42÷7=6 or 42÷6=7.
Model · 5 min. Compute 468×7=400×7+60×7+8×7=2,800+420+56=3,276. Divide back 3,276÷7=468; compare with 470×7=3,290. Distinguish inverse and estimation checks.
Guide · 6 min. Let class audit 324×8=2,592. Ask what division statement would undo it and what rough product 300×8=2,400 predicts. If a child says 259.2, use place-value scale.
Choose · 7 min. Day 17 A/B/C product plus inverse fact, using a fact family, manipulatives or selected equation cards. No child must perform long division as the only evidence; a valid inverse multiplication check is accepted.
Exit · 3 min. “Why is 32,760 implausible for 468×7?” Key: near 3,290, about one zero too many.
Record · 2 min. Note whether the child understands which number is group size/count; copied reverse digits alone are not an inverse explanation.

Day 18 · Find the missing group count

Success: solve a multiplication equation with an unknown, then check by substitution. Prepare: 24×?=720 card. Codes: AC9M5A02, AC9M5A01.

Recall · 2 min. Ask what 24×10 and 24×3 are. Key: 240 and 72.
Model · 5 min. 24×?=720: use inverse 720÷24=30 or note 24×3=72 then tenfold to 720. Substitute: 24×30=720. Name ? as number of equal groups in this model.
Guide · 6 min. Solve ?×16=672: 16×40=640, 16×2=32, total 672, so ?=42. Check with 672÷16=42. Correct a plausible ?=4.2 by scale.
Choose · 7 min. Day 18 A/B/C unknown-value route; child may use related facts, an area model, division or trial and refinement. Require a substitution check.
Exit · 3 min. “Would 3 or 30 fit 24×?=720?” Key: 30; 24×3=72. Ask why the zero changes the total.
Record · 2 min. Note strategy and check rather than speed or preferred symbol format.

Day 19 · Equal totals can hide different constraints

Success: formulate and compare two multiplicative plans, then choose the one that meets a stated limit. Prepare: 24×36 versus 32×27 paper-bundle model. Codes: AC9M5N09, AC9M5N06, AC9M5N08.

Recall · 2 min. Ask if equal totals guarantee equal practicality. Key: no; another constraint can differ.
Model · 5 min. Both invented arrangements hold 864 cards: 24×36=864 and 32×27=864. If the fictional workspace allows at most 30 bundles, only 27 bundles fits. Do not invent a price, environmental impact or real policy.
Guide · 6 min. Compare 18×42=756 with 27×28=756 under at most 30 bundles. The 28-bundle arrangement fits; 42 does not. Let children state the multiplication equation and constraint separately.
Choose · 7 min. Day 19 A/B/C route. Require two products, constraint test and a recommendation limited to the supplied facts; a learner may challenge missing information.
Exit · 3 min. “Can we name the cheapest option from these numbers?” Key: no, no prices were given. If a child asserts a cost, ask which source supplies it.
Record · 2 min. Note product, constraint and limit to conclusion as separate evidence. A correct total with unsupported recommendation needs feedback.

Day 20 · Fresh check B: multiply, check and decide

Success: transfer a two-digit product, benchmark, inverse and context decision to a new unseen arrangement. Prepare: reveal Check B only now; staff key remains private. Codes: AC9M5N06, AC9M5N08, AC9M5N09, AC9M5A01.

Recall · 2 min. Ask what a complete recommendation needs: product, bound and stated constraint. Do not preview card values.
Directions · 3 min. Explain accessible response routes and that every quantity is fictional; provide no worked parallel solution using test digits.
Access · 3 min. Read the card once neutrally or supply the text/tactile version; record any adult paraphrase.
Fresh response · 12 min. Learner calculates a new product, gives a useful estimate, checks inversely and judges a stated package limit. Finish later with a recorded continuation if access/time requires it.
Reflect · 3 min. Ask what evidence in the card supported the recommendation. Collect initial and revised work before feedback.
Record · 2 min. Mark calculation, estimation, inverse and interpretation separately; no whole-year grade follows from this check. After collection, optional Day 20 routes are available.