AC9M4A02 • Year 4 Maths
recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
Fluent facts to 10 × 10 form a connected network. An array shows equal rows and columns; turning it, splitting it or making an equal copy helps explain a fact. The same product and factors also give related division facts.
Learning intention: Recall and explain multiplication and division facts, then use those facts to calculate efficiently with larger numbers without a calculator.
Learning routine: Recall a known fact → represent or connect it → choose a useful strategy → calculate mentally → check.
| Word | Meaning and example |
|---|---|
| factor | A number multiplied: 6 and 7 in 6 × 7. |
| product | The multiplication result: 42 in 6 × 7 = 42. |
| array | Equal rows and columns; 6 rows of 7 contain 42 objects. |
| inverse | Multiplication and division undo each other: 6 × 7 = 42, so 42 ÷ 6 = 7. |
| commutativity | Turning an array exchanges factors: 6 × 7 = 7 × 6. |
| distributive property | Split a factor and combine the parts: 6 × 7 = 6 × 2 + 6 × 5. |
Worked example: 6 × 2 = 12 and 6 × 5 = 30. Join the parts: 12 + 30 = 42, so 6 × 7 = 42. Read the same array as 42 ÷ 6 = 7 in each row and 42 ÷ 7 = 6 in each column.
Teacher asks: “What does the 6 count in both parts?” Students point to the six rows. If a learner adds 6 + 7, count one complete row and explain that there are six equal copies.
3 × 8 = 24. A second identical array adds another 24, so 6 × 8 = 48. The multiples 3, 6, 9, 12 double to 6, 12, 18, 24. Each pair keeps the same multiplier: 3 × 4 = 12 becomes 6 × 4 = 24.
Quick checkpoint: “If 3 × 7 = 21, what is 6 × 7, and why?” Answer: 42, because two copies of 21 make 42. Continue when students name the doubled group count; otherwise build the second copy.
3 × 8 = 8 × 3 = 24. For halving, 10 × 6 = 60; half the rows gives 5 × 6 = 30. Halving one factor halves the product. If one factor doubles while the other halves, the product stays equal: 25 × 8 = 50 × 4 = 100 × 2 = 200.
| Connection | Calculation |
|---|---|
| Turn the array | 8 × 7 = 56 |
| Related division | 56 ÷ 7 = 8 and 56 ÷ 8 = 7 |
| Double one factor | 14 × 8 = 112 and 7 × 16 = 112 |
| Scale one factor | 70 × 8 = 560: 56 tens |
One known fact supports commuted facts, inverse divisions, doubled facts and place-value extensions. Say which number changes and why the total changes or stays equal.
| Problem | Efficient worked thinking |
|---|---|
| 16 × 7 | 10 × 7 + 6 × 7 = 70 + 42 = 112. |
| 25 × 8 | 50 × 4 = 100 × 2 = 200; or 20 × 8 + 5 × 8 = 160 + 40 = 200. |
| 48 ÷ 6 | 6 × 8 = 48, so 48 ÷ 6 = 8. |
| 9 × 34 | 10 × 34 − 34 = 340 − 34 = 306. |
| 168 ÷ 7 | 140 ÷ 7 + 28 ÷ 7 = 20 + 4 = 24. Check 7 × 24 = 168. |
Choose a relationship that turns the unknown calculation into facts already known. Add all partial products or quotients. These are mental strategies; formal long multiplication, long division and calculator methods are not the target.
Content description: recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
E1: using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in the 10 × 10 multiplication facts; using the arrays to explain the related division facts
Teach and do: Build 4 rows of 7 with counters. Record 4 × 7 = 28 and 7 × 4 = 28, then 28 ÷ 4 = 7 and 28 ÷ 7 = 4. Add a fifth row: the total grows by 7 to 35. Students build a different array, label rows/columns/whole and explain one pattern and both divisions. Look for equal rows and a connection between whole and factors.
E2: using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity, and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6; recording and explaining the connections to the ×3 and ×6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …
Worked connections: Use 3 × 8 = 24 and double 24 to obtain 6 × 8 = 48; use 10 × 6 = 60 and halve 60 to obtain 5 × 6 = 30; turn 3 × 8 into 8 × 3; add one group of 6 to 6 × 6 = 36 to get 7 × 6 = 42; remove one group of 6 from 10 × 6 = 60 to get 9 × 6 = 54. Students show a chosen connection with an actual diagram and explain what changes.
E3: using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as “to multiply a number by 9 you multiply by 10 then take the number away”; 9 × 4 = 10 × 4 – 4, so 9 × 4 is 40 – 4 = 36; using multiple of 3 as “to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again”
Strategy menu: Build fours by doubling twos; sixes by doubling threes; sevens by joining fives and twos; eights by doubling fours; nines by subtracting one group from tens. For 9 × 5, either 50 − 5 = 45 or 3 × 5 = 15 then 3 × 15 = 45. In the second method there are three lots of three groups of 5, making nine groups. Ask students to compare two strategies for one fact, rather than memorise a rule without meaning.
E4: using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30 which is 42
Worked array: In 6 rows of 7, colour 2 columns blue and 5 gold. The parts give 6 × 2 = 12 and 6 × 5 = 30, so 6 × 7 = 42. Students create a sevens array of their own, show the 2+5 column split and write both partial products and the sum. If a learner writes 6 × 2 + 5, ask where the other five rows of gold counters went.
E5: using known multiplication facts up to 10 × 10 and the inverse relationship of multiplication and division to establish corresponding division facts
Worked inverse: From 7 × 8 = 56, there are 8 groups of 7 in 56 and 7 groups of 8 in 56. Thus 56 ÷ 7 = 8 and 56 ÷ 8 = 7. Distinguish “how many groups?” from “how many in each group?” With square facts the two division statements coincide: 6 × 6 = 36 gives 36 ÷ 6 = 6.
E6: designing, creating and playing instructive card games that involve the recall, recognition and explanation of the 10 × 10 multiplication facts and related division facts
Create and play: Use three multiplication facts with different products and factors 1–10. Make four cards per family: a multiplication, its product and two related divisions. Write rules: match a product, explain a mental strategy, then check a related division. Play three turns with a partner and keep a written record of the cards, strategy and division check. For 6 × 8, match 48, explain 3 × 8 = 24, so 6 × 8 = 24 + 24 = 48, then say 48 ÷ 6 = 8. The adult checks the actual 12 cards, rules and recorded play; varied correct games are welcome.
Use 6 × 9 = 54. Write the turned fact, two divisions, a doubled fact and a tens extension. Answers: 9 × 6 = 54; 54 ÷ 6 = 9; 54 ÷ 9 = 6; 12 × 9 = 108; 60 × 9 = 540. Explain which relation justifies each.
Solve 19 × 6, 32 × 4 and 15 × 8 without a calculator. Worked answers: 20 × 6 − 6 = 120 − 6 = 114; 30 × 4 + 2 × 4 = 120 + 8 = 128; 10 × 8 + 5 × 8 = 80 + 40 = 120. Students compare another valid strategy and explain which is easiest for them.
Partition 168 into 140 and 28. Divide both by 7:20 + 4 = 24. Check: 7 × 24 = 7 × 20 + 7 × 4 = 140 + 28 = 168. If a learner divides only 140, point to the unshared 28 and complete its share.
Use the creation and play steps in E6. Before playing, a partner verifies each family by drawing a small array or using a known fact. During play, a correct answer earns a match; a correct strategy and inverse check complete the turn. Record evidence of explanation, not only a score.
Core idea: Use connected facts and explain how each strategy changes equal groups.
Answer: 8 × 7 = 56; 56 ÷ 7 = 8; 56 ÷ 8 = 7. They use the same whole and factors.
Answer: 340 − 34 = 306. Remove one whole group of 34.
Answer: 140 ÷ 7 + 28 ÷ 7 = 20 + 4 = 24. Multiply 24 by 7 to check 168.
Answer: 10 × 7 + 6 × 7 = 70 + 42 = 112, or use 8 × 7 = 56 and double 56 to 112.
Answer: An equal copy of all the groups adds the original total again. The other factor stays unchanged.
Answer: Players must recall a fact, recognise its matching product and explain a strategy plus a related division; the game includes correct cards and rules that require those actions.
Read the topic guide and use the teacher slides for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.
Teacher resource
Use the fixed branded slide deck to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open Classroom ViewPrerequisites: Equal groups, arrays, repeated addition and place value in whole numbers. Must teach: facts through 10 × 10, inverse divisions, explanations with arrays, game creation and larger mental extensions. Useful informal support: turning and partitioning arrays. Boundary: Formal written multiplication/division algorithms and calculators are not this code’s target.
Answer: 10 × 7 − 7 = 70 − 7 = 63. Review hint: remove a group of 7, not one counter.
Answer: 32 tens ÷ 8 = 4 tens = 40; 8 × 40 = 320. Review hint: track the tens unit.
Answer: The model contains 35; 35 ÷ 5 = 7 and 35 ÷ 7 = 5. Review hint: use the whole 35 as the dividend.
Exit ticket: On paper, (1) derive 8 × 6 from 4 × 6 and explain; (2) give both division facts for 7 × 9 = 63; (3) find 18 × 5 mentally and show a check.
Answers and evidence: (1) 4 × 6 = 24, double 24 to 48 because there are twice as many rows. (2) 63 ÷ 7 = 9 and 63 ÷ 9 = 7. (3) 20 × 5 − 2 × 5 = 100 − 10 = 90; 90 ÷ 5 = 18 checks. Accept equivalent efficient reasoning. If a learner gives a result without the connection, revisit a matching array; if place value is lost, name the groups or units before calculating.
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M4A02 — recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator |
| Victoria | Victorian Curriculum F-10 | Year 4 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 2 Maths: closest content focus for Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator and related outcomes. |
| United States | Common Core / NGSS | Grade 4 Common Core Mathematics/ELA closest topic match for Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator. |
| England / UK | National Curriculum | Key Stage 2 / Year 4: closest programme-of-study match for Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator. |
| Canada | Provincial and territory curricula | Grade 4 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 2 Maths: closest achievement-objective topic for Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator. |
| India | NCERT / CBSE | Class 4 closest NCERT/CBSE topic match for Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator. |
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Before you watch:
Khan Academy — Use known multiplication facts to work out related facts.
As you watch: How can doubling a known fact help you find another product?
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Try it: Use 4 × 6 to explain 8 × 6, then write the related division facts.
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Mapped skill: recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M4A02 · Year 4 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M4A02 · Level 4 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA2-MR-01 + MA2-MR-02 · Stage 2 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 4 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 4 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 5, Key Stage 2 |
| India | NCERT / CBSE — Mathematics | Class 4 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M4A02 — AC9M4A02: Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
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