Expanded Column Method

Overview

This 45-minute lesson is Lesson 3 in the unit "Mastering Multiplication & Division," targeted at Year 4-5 students in New Zealand. It introduces the expanded column method for multiplication, helping students to visualise multiplication by breaking numbers into their place values. The lesson aligns explicitly with the New Zealand Curriculum Refresh and focuses on meeting the relevant learning objectives, standards, and competencies.

Curriculum Links and Learning Objectives

Number and Algebra - Operations (Years 4-5)
- Multiply multi-digit whole numbers, connecting to place value and the distributive property of multiplication over addition (e.g., 34 × 7 = 30 × 7 + 4 × 7).
- Explain and demonstrate the vertical-column method for multiplication, ensuring students connect the procedure with place value, known facts, and estimation.
- Develop strategies including partitioning and place value to multiply numbers.
Mathematical Processes
- Reasoning: Encourage students to explain and justify the steps they take and generalise from patterns.
- Communication: Use mathematical language related to multiplication, partitioning, and place value.
- Problem Solving: Decode and solve multiplication problems, and represent them as equations.
Key Competencies:
- Thinking, Using language, symbols and texts, and Managing Self (independent reasoning and recording) .

Lesson Title

Exploring Expanded Column Method

Learning Outcomes

By the end of this lesson, students will be able to:

Break two-digit numbers into place value components (tens and units) when multiplying.
Use the expanded column method to multiply two-digit by one-digit numbers.
Understand and visualise how the distributive property applies to multiplication.
Accurately calculate and record multiplication steps using expanded layout.
Use appropriate mathematical language (e.g., "partition," "product," "place value") in communicating their process.

Resources

Whiteboard and markers or interactive board
Place value blocks or base-ten materials (optional for demonstration)
Student worksheets with multiplication problems suited to expanded column method
Visual aids illustrating expanded form (place value charts)
Mini-whiteboards for student practice
Digital tools (optional) to model expanded column method

Lesson Breakdown

1. Warm-Up and Review (5 minutes)

Activity: Quick mental multiplication flashcards (multiplication facts for 4s, 6s, 7s, 8s), reinforcing recall.
Purpose: Activate prior knowledge of multiplication facts and jump into place value understanding.
Curriculum Link: Recall multiplication facts up to 10 × 10, and corresponding division facts.

2. Introduction to Expanded Column Method (10 minutes)

Explain: Introduce the expanded column method using 2-digit by 1-digit multiplication, e.g., 34 × 7.
Break 34 into 30 + 4 and multiply each by 7 separately, showing: 30 × 7 = 210 and 4 × 7 = 28.
Write these in columns to clearly show place values lining up, then add results to find the total product (210 + 28 = 238).
Use base-ten blocks or PV materials to visually demonstrate the partitioning and multiplication parts.
Key Vocabulary: Partition, place value, product, sum.

3. Guided Practice (15 minutes)

Activity: Students complete several problems on mini-whiteboards or worksheets, such as:
- 23 × 5
- 47 × 6
- 56 × 9
Encourage students to:
- Partition the 2-digit number into tens and units.
- Multiply each part by the single-digit multiplier.
- Write each product in the correct place value column.
- Add the partial products to get the total.
Teacher role: Circulate, scaffold where necessary, prompt use of correct vocabulary, ask “What happens if we change this digit?” to encourage generalisation.

4. Independent Practice and Problem Solving (10 minutes)

Activity: Present a real-life word problem that involves multiplying two-digit numbers by one-digit numbers (e.g., "If a school orders 34 packets of pencils, each packet contains 7 pencils, how many pencils in total?").
Students will:
- Use the expanded column method to solve the problem step-by-step.
- Write an equation showing their working (e.g., 34 × 7 = (30 × 7) + (4 × 7) = 210 + 28 = 238).
- Explain their reasoning orally or in writing using mathematical language.
Encourage students to estimate before calculating, reinforcing place value understanding and reasonableness of answers.

5. Reflection and Sharing (5 minutes)

Invite 2-3 students to share their solution and reasoning with the class.
Highlight good use of mathematical vocabulary and expansion method steps.
Discuss how the expanded column method helps visualize multiplication and why it links to place value.

Assessment for Learning

Observe and note students’ use of place value partitioning during guided and independent practice.
Review completed worksheets or mini-whiteboard work for correct expanded column method usage.
Listen for correct vocabulary use and reasoning in student explanations.
Use any misconceptions to guide subsequent lessons, especially future lesson 4 which might consolidate or introduce vertical-column multiplication fully.

Extension Ideas

Challenge students to try three-digit by one-digit multiplication through expanded methods or area models.
Explore connections to the distributive property in algebra using numerical examples.

Teacher Notes

The expanded column method supports understanding the vertical-column method by reinforcing place value and distribution of multiplication.
Emphasise connections to familiar multiplication facts and place value structures from earlier years.
Use culturally responsive pedagogy when explaining concepts—encourage students to share explanations in their first or heritage languages as appropriate, connecting with mathematical vocabulary.

This lesson actively supports the New Zealand Curriculum Refresh's focus on making mathematics meaningful and visual by connecting multiplication to place value structure and enabling students to reason and communicate mathematically with confidence and clarity .

Teaching Instructions