Mathematics · Year 5

Active learning ideas

Long Multiplication (2-digit by 2-digit)

Active learning works for long multiplication because students need to physically manipulate place values and partial products. When they rotate through stations, pair up to build problems, or race to solve, they see how the zero placeholder and column alignment affect the final result. This hands-on work makes abstract concepts concrete.

• National Curriculum Attainment Targets
• KS2: Mathematics - Multiplication and Division

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Multiplication Steps

Set up stations for each step: one for units multiplication with counters, one for tens with place value charts, one for adding partial products, and one for self-created problems. Groups rotate every 10 minutes, recording justifications at each. End with whole-class share-out.

Justify the steps involved in long multiplication, explaining the role of the 'zero' placeholder.

Facilitation Tip

During Station Rotation: Multiplication Steps, circulate to listen for students explaining the zero’s purpose aloud to peers.

What to look for

Provide students with the calculation 57 x 34. Ask them to solve it using long multiplication. On the back, have them write one sentence explaining why they placed a zero in the second line of their calculation.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Collaborative Problem-Solving
• 30 min · Pairs

Pairs: Problem Construction Challenge

Pairs create a two-digit by two-digit problem, solve using long multiplication, and swap with another pair to check and justify steps. Discuss the zero placehold's role. Teacher circulates to prompt comparisons with grid method.

Construct a multiplication problem that requires long multiplication and solve it.

Facilitation Tip

In Pairs: Problem Construction Challenge, give pairs exactly two minutes to compare their constructed problems and solutions before sharing with the class.

What to look for

Display the problem: 'A school is buying new library books. Each book costs $16, and they need to buy 25 books. How much will the books cost in total?' Ask students to show their working using long multiplication and circle their final answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 35 min · Whole Class

Whole Class: Strategy Race

Divide class into teams. Project problems; teams solve using long multiplication, grid, or short method and vote on most efficient. Debrief on when each works best, with students explaining choices.

Compare long multiplication with other multiplication strategies for efficiency.

Facilitation Tip

For Strategy Race, set a 60-second timer and insist students explain their first step verbally before moving to the next calculation.

What to look for

Pose the question: 'Imagine you need to calculate 42 x 53. Would you choose long multiplication, grid multiplication, or short multiplication? Explain why your chosen method is the most efficient for this specific problem and justify your steps.'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 25 min · Individual

Individual: Array Visualiser

Students draw arrays for given multiplications, then convert to long method on paper. Use coloured pencils to show partial products and zero shift. Share one with partner for peer feedback.

Justify the steps involved in long multiplication, explaining the role of the 'zero' placeholder.

What to look for

Provide students with the calculation 57 x 34. Ask them to solve it using long multiplication. On the back, have them write one sentence explaining why they placed a zero in the second line of their calculation.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach long multiplication by connecting it to base-10 understanding first. Use base-10 rods to show the shift when multiplying by tens, then transition to the written algorithm. Avoid rushing to abstract steps; anchor every new idea in visual or hands-on work. Research shows that students who articulate each step aloud develop stronger procedural fluency and fewer errors.

Students will explain why the zero placeholder is added when multiplying by tens and justify their calculations step-by-step. They will align partial products correctly and recognize long multiplication as a structured method, not just repeated addition. Clear articulation of reasoning shows true understanding.

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Watch Out for These Misconceptions

• During Station Rotation: Multiplication Steps, watch for students who omit the zero placeholder or add it without explanation.

  Pause at the station and ask students to use base-10 rods to multiply 10 x 23, then verbally connect the zero to the tens shift before returning to their written work.

• During Pairs: Problem Construction Challenge, watch for students who align partial products incorrectly or mix place values in the addition step.

  Have pairs place their calculations on a place value mat and use colored pencils to circle the tens and units columns before adding, then recheck alignment together.

• During Strategy Race, watch for students who treat long multiplication as a series of additions without structure.

  After the race, ask students to write a sentence comparing 23 x 45 as repeated addition versus long multiplication, focusing on how the algorithm organizes partial products efficiently.

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Methods used in this brief

• Stations Rotation
• Collaborative Problem-Solving