Grid Method Practice

Context

This 45-minute lesson is lesson 2 of 20 in the unit "Mastering Multiplication & Division" for Year 4–5 students in New Zealand. It focuses on practising the grid method of multiplication — a strategy aligned with the New Zealand Curriculum Refresh to develop student fluency, understanding, and problem-solving skills in multi-digit multiplication.

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Learning Objectives

Aligned to the New Zealand Curriculum Refresh (Te Mātaiaho Maths, Phase 2 for Years 4 and 5), the lesson aims for students to:

• Recall multiplication facts to at least 10×10 and corresponding division facts (to support calculations).
• Multiply two-digit by one-digit numbers and connect multiplication to place value using the grid (area) method, representing the distributive property (e.g., 34×7 as (30×7) + (4×7)) .
• Use strategies to make estimates and mental calculations by connecting to place value, partitioning, and known facts.
• Solve multiplication problems involving real-life contexts, representing these as equations.
• Develop mathematical competencies: thinking, reasoning, managing self, relating to others, and using language, symbols, and texts (as per NZC key competencies).

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Equipment

• Whiteboard and markers
• Prepared grids worksheets (partially completed) with multiplication problems (e.g., 34×7, 23×5)
• Counters or base-ten blocks for manipulatives
• Mini whiteboards for pairs
• Timer or clock

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Lesson Outline

1. Starter & Recap (5 minutes)

• Goal: Activate prior knowledge of multiplication facts and introduce the grid method.
• Quickly rehearse times tables facts (4s, 6s, 7s, 8s, 9s) with choral counting or flashcards.
• Demonstrate a simple grid method example on the whiteboard (e.g., 23 × 4):
  • Partition 23 into 20 + 3
  • Multiply each by 4 separately
  • Add results (80 + 12 = 92)
• Verbally highlight how this uses place value and the distributive property.

2. Modelling & Explanation (8 minutes)

• Work through another example, this time with a 2-digit × 1-digit number (e.g., 34 × 7).
• Use a stepwise approach:
  • Draw the grid on the board.
  • Partition 34 into 30 and 4.
  • Multiply each by 7 (30×7=210 and 4×7=28).
  • Add partial products to get the final answer (210 + 28 = 238).
• Ask students to explain why this method helps break down complex multiplication.

3. Collaborative Practice (15 minutes)

• Students work in pairs with mini whiteboards and counters or base-ten blocks.
• Provide a set of multiplication problems (e.g., 45×6, 23×8).
• First, pairs use manipulatives to model the multiplication in the grid method physically.
• Then, they write the grid partition and calculation on their mini whiteboards.
• Teacher circulates to prompt thinking, question reasoning, and support where needed.
• Encourage students to verbalise their thinking and check each other’s work.

4. Independent Practice (12 minutes)

• Hand out grid method worksheets with problems increasing in difficulty:
  • Start with 2-digit by 1-digit multiplications.
  • Include word problems requiring setting up the grid method.
• Students complete these individually, applying the method practiced.
• Teacher scaffolds and supports as necessary, encouraging estimates and mental calculations prior to full calculation.

5. Plenary & Reflection (5 minutes)

• Invite several students to share their solutions on the board, explaining their grid partition and multiplication steps.
• Discussion prompts:
  • How does the grid method help with understanding multiplication?
  • When might you choose to use this method?
• Reinforce the connection between grid method, place value, and distributive property.
• Highlight progress in fluency and problem-solving.

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Assessment & Feedback

• Formative assessment via observing students’ use of the grid method during collaborative and independent tasks.
• Listen for oral explanations to assess conceptual understanding.
• Review worksheet answers to check accuracy and application.
• Provide immediate corrective feedback or extension prompts.

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Differentiation

• Support: Use manipulatives and visual aids, work in pairs, provide simpler problems.
• Extension: Challenge capable students with 2-digit by 2-digit multiplication using grids or word problems involving combinations (e.g., “If you have 4 tops and 3 shorts...”).

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Curriculum Alignments

• Mathematics and Statistics Learning Area — Number and Algebra Strand

  • Achievement objectives:
    • Number and Algebra - Level 3-4
      • Understand and recall multiplication facts, use multiplicative strategies involving place value and distributive property in problem situations.

• Competencies from NZC (key to maths learning):

  • Thinking: Students extend understanding and apply concepts to new problems.
  • Using language, symbols, and texts: Represent multiplication with symbolic and graphical methods like the grid.
  • Relating to others: Peer collaboration strengthens reasoning.

• This lesson supports fluency, understanding, and problem-solving in mathematics, per the refreshed curriculum's focus on building robust mathematical foundations aligned with real-world applications .

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If you need further detailed activities or explanations for any part, feel free to ask!