Formal Multiplication: Grid Method

Active learning works well for the grid method because it turns abstract place value ideas into visible steps. Students see how 20 x 7 differs from 3 x 7 when they draw and label each section of the grid. Movement and collaboration help cement these connections better than silent worksheets.

• Year 4
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Calculate the product of a two-digit number and a one-digit number using the grid method.
2. Calculate the product of a three-digit number and a one-digit number using the grid method.
3. Explain how partitioning a multiplicand into tens and ones (or hundreds, tens, and ones) simplifies the multiplication process within the grid method.
4. Justify the accuracy of the grid method by demonstrating how it accounts for all parts of the multiplicand.
5. Compare the steps of the grid method to other multiplication strategies, identifying its advantages for specific calculations.

Peer Teaching

⏱ 25 min·Pairs

Pairs: Grid Relay Challenge

Pair students and provide problem cards like 45 x 8. One partner draws the empty grid and partitions the numbers; the other fills partial products and adds. Switch roles for the next problem, then compare answers. Circulate to prompt explanations.

Prepare & details

Analyze how the grid method breaks down a multiplication problem into simpler parts.

Facilitation Tip: During the Grid Relay Challenge, set a timer and circulate to listen for math talk that shows students are linking partial products to place value.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

Peer Teaching

⏱ 40 min·Small Groups

Small Groups: Multiplication Market

Give groups shopping lists with two-digit prices and a one-digit multiplier as quantity. They create grids to calculate subtotals, then totals. Groups pitch their 'bills' to the class for verification.

Prepare & details

Construct a grid to solve 23 x 7, explaining each step.

Facilitation Tip: In the Multiplication Market, ask each group to explain why they priced an item a certain way using their grid calculations.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

Peer Teaching

⏱ 35 min·Whole Class

Whole Class: Human Grid Demo

Select students to represent grid cells holding place value cards (e.g., 100s, 10s, 1s). Multiply by demonstrating partial products with additional students, then 'add' by combining. Class records on boards.

Prepare & details

Justify why the grid method helps prevent errors in multiplication.

Facilitation Tip: During the Human Grid Demo, move deliberately between stations so every student has a chance to model a partial product.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

Peer Teaching

⏱ 20 min·Individual

Individual: Grid Puzzle Sheets

Provide differentiated sheets with half-completed grids and missing steps. Students finish them, self-check with answer keys, then create their own problem to swap with a partner.

Prepare & details

Analyze how the grid method breaks down a multiplication problem into simpler parts.

Facilitation Tip: For Grid Puzzle Sheets, provide colored pencils so students can trace the connection between partitioned numbers and grid cells.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

Teaching This Topic

Start with base-10 rods or place value counters to show why 23 x 7 becomes 20 x 7 and 3 x 7. Avoid rushing to the written grid before students can verbalize the value of each part. Research shows that students who practice explaining their partitioning before writing tend to make fewer place value mistakes later. Keep the grid layout consistent so students build automaticity in how they position tens and ones.

What to Expect

Successful learning looks like students partitioning numbers accurately, filling grids with correct partial products, and adding totals without place value errors. They should explain their steps aloud and check each other’s work during group tasks.

Watch Out for These Misconceptions

Common Misconception

During the Pairs: Grid Relay Challenge, watch for students who omit the zero in partial products such as writing 2 x 7 instead of 20 x 7.

What to Teach Instead

Have partners stop at the first mislabeled cell and use base-10 rods to rebuild that row, asking ‘What does the 2 in the tens place really represent here?’ before continuing.

Common Misconception

During the Small Groups: Multiplication Market, watch for students who add partial products without lining up place values (e.g., 140 + 21 = 161).

What to Teach Instead

Ask the group to lay their partial product cards on a place value mat so they see how 140 and 21 must align before adding.

Common Misconception

During the Whole Class: Human Grid Demo, watch for students who treat the grid as simple repeated addition without recognizing the partitioned structure.

What to Teach Instead

Have the student modeling 30 x 4 physically group 30 counters into three groups of 10 before adding four copies, prompting the class to articulate what each row represents.

Assessment Ideas

Exit Ticket

After the Pairs: Grid Relay Challenge, give 34 x 6 as an exit ticket. Ask students to draw the grid, show partial products, and write a sentence explaining the role of the zero in each partial product.

Quick Check

During the Small Groups: Multiplication Market, circulate with a clipboard and ask pairs to explain their grid for 125 x 4, focusing on how they partitioned 125 and why they placed each partial product where they did.

Discussion Prompt

After the Whole Class: Human Grid Demo, pose the question: ‘How does the grid method help us avoid mistakes when multiplying larger numbers?’ Have students refer to their Human Grid Demo posters to justify their answers.

Extensions & Scaffolding

• Challenge: Provide a three-digit by one-digit problem and ask students to extend the grid to four partial products.
• Scaffolding: Give students pre-partitioned numbers on sticky notes so they focus on grid layout rather than partitioning.
• Deeper: Ask students to compare the grid method with the standard algorithm, writing about which they find easier and why.

Key Vocabulary

Grid Method	A multiplication strategy where a grid is drawn to represent the partial products of a calculation, making it easier to manage larger numbers.
Partition	To break a number down into its place value components, such as breaking 23 into 20 and 3.
Partial Product	The result of multiplying one part of a partitioned number by the multiplier. For example, in 23 x 7, 20 x 7 is a partial product.
Place Value	The value of a digit based on its position within a number (e.g., the '2' in 23 represents twenty).