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.

• Year 5
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the product of two-digit numbers by two-digit numbers using the long multiplication algorithm.
2. Explain the purpose of the zero placeholder in the second step of long multiplication, relating it to place value.
3. Compare the efficiency of long multiplication with grid multiplication or short multiplication for solving specific two-digit by two-digit problems.
4. Construct a word problem that necessitates the use of two-digit by two-digit multiplication and solve it using long multiplication.

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

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.

Prepare & details

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

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Station Rotation: Multiplication Steps, 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.

Quick Check

During Pairs: Problem Construction Challenge, 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 before discussing in pairs.

Discussion Prompt

After Strategy Race, 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.' Have students discuss in small groups and share one reason with the class.

Extensions & Scaffolding

• Challenge: Create a word problem where the product exceeds 1,000 and solve using long multiplication, then verify with a calculator.
• Scaffolding: Provide a partially completed long multiplication grid with missing digits; students fill in the blanks to solve.
• Deeper: Compare long multiplication with grid or area models in a short written reflection on efficiency and accuracy.

Key Vocabulary

partial product	A product obtained during the process of multiplication, before the final sum is calculated. For example, when multiplying 34 x 21, the partial products are 34 and 680.
placeholder	A digit, usually zero, placed in a position to maintain place value. In long multiplication, a zero is used in the tens column when multiplying by the tens digit of the second number.
algorithm	A step-by-step procedure for solving a mathematical problem. Long multiplication is an algorithm for multiplying larger numbers.
place value	The value of a digit based on its position within a number. Understanding place value is crucial for correctly aligning numbers in long multiplication.