Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate

Students multiply larger numbers by one- or two-digit factors using partitioning, area models, written algorithms and compensation, selecting a method that fits the numbers and checking with estimation.

Multiplication of larger numbers can be decomposed into place-value partial products and recombined without changing the product.

Partition 326 and 24, find every partial product, then combine. The model shows why the written algorithm works rather than treating it as a digit rule.

Estimate first: 326 × 24 is about 300 × 25 = 7 500, so 7 824 is reasonable. A digital answer still requires a correct mathematical setup.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the problem
• Choose an efficient strategy
• Calculate accurately
• Interpret the context
• Estimate or use an inverse to verify

Content description: solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers.

• E1: solving multiplication problems such as 253 \times 4 using a doubling strategy; for example, 2 \times 253 = 506 and 2 \times 506 = 1012
• E2: solving multiplication problems like 15 \times 16 by thinking of factors of both numbers, 15 = 3 \times 5, 16 = 2 \times 8; rearranging the factors to make the calculation easier, 5 \times 2 = 10, 3 \times 8 = 24 and 10 \times 24 = 240
• E3: using an array to show place value partitioning to solve multiplication, such as 324 \times 8, thinking 300 \times 8 = 2400, 20 \times 8 = 160, 4 \times 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592 ; connecting the parts of the array to a standard written algorithm
• E4: using different strategies used to multiply numbers, explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers

Core idea: Multiplication of larger numbers can be decomposed into place-value partial products and recombined without changing the product.

Remember

• Represent the problem
• Choose an efficient strategy
• Calculate accurately
• Interpret the context
• Estimate or use an inverse to verify

Important questions

• Estimate 326 × 24. Explain using the model or evidence above.
• Find all partial products. Explain using the model or evidence above.
• Use compensation for 998 × 37. Explain using the model or evidence above.
• Solve 48 × 25 mentally. Explain using the model or evidence above.
• Check a digital result. Explain using the model or evidence above.

• A partial product is omitted — Record every place-value combination.
• Place values are misaligned — Track the value of tens and hundreds, not only digits.
• Calculator replaces reasoning — Formulate and estimate before using a tool.
• Estimate is treated as exact — Use it to check scale, not replace the product.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students multiply larger numbers by one- or two-digit factors using partitioning, area models, written algorithms and compensation, selecting a method that fits the numbers and checking with estimation.

Multiplication of larger numbers can be decomposed into place-value partial products and recombined without changing the product.

Partition 326 and 24, find every partial product, then combine. The model shows why the written algorithm works rather than treating it as a digit rule.

Estimate first: 326 × 24 is about 300 × 25 = 7 500, so 7 824 is reasonable. A digital answer still requires a correct mathematical setup.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the problem
• Choose an efficient strategy
• Calculate accurately
• Interpret the context
• Estimate or use an inverse to verify

Australian Curriculum Version 9.0

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