Mathematics · Grade 4

Active learning ideas

Multiplying by One-Digit Numbers

Active learning helps students grasp the abstract nature of division and multiplication by connecting them to real-world tasks. When students act as feast coordinators or use counters, they see how numbers represent objects and groups, making calculations meaningful and memorable. This hands-on approach reduces errors in place value and remainders by grounding abstract concepts in concrete experiences.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.NBT.B.5

• 20–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 35 min · Small Groups

Simulation Game: The Feast Coordinator

Students are given a set number of 'bannock pieces' (counters) and must divide them among different numbers of guests. They must decide what to do with remainders in different contexts: cutting them into fractions, giving them away, or needing an extra plate.

Design a strategy to multiply a four-digit number by a one-digit number.

Facilitation Tip

During The Feast Coordinator simulation, circulate with counters to prompt students who remainders are still shareable.

What to look for

Present students with the problem: 'A school orders 1,234 pencils for each of its 4 grades. How many pencils are ordered in total?' Ask students to solve it using the standard algorithm and show their work. Check for correct calculation and understanding of place value.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Division Strategies

Set up stations for different division methods: one for repeated subtraction, one for using arrays, and one for partial quotients. Students solve the same problem at each station to see which method feels most efficient for them.

Evaluate the efficiency of different multiplication strategies (e.g., area model vs. standard algorithm).

Facilitation Tip

For Station Rotation, model each strategy at the first station before letting students rotate independently.

What to look for

Pose the question: 'Imagine you need to multiply 3,456 by 7. Which strategy would you choose, the area model or the standard algorithm, and why? Explain the advantages and disadvantages of each for this specific problem.'

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

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: The Remainder Riddle

Give a word problem where the remainder must be handled differently (e.g., 'rounding up' for buses vs. 'ignoring' for leftover change). Students discuss their decision with a partner and justify why their answer makes sense in the real world.

Predict the product of a multi-digit number and a one-digit number using estimation.

Facilitation Tip

During The Remainder Riddle, provide sentence starters like 'The remainder must be... because...' to guide discussions.

What to look for

Give students a multiplication problem, such as 2,500 x 5. Ask them to first estimate the product, then calculate the exact product using any strategy they prefer. Collect their responses to gauge understanding of both estimation and calculation.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach division by linking it to multiplication facts students already know, using arrays and area models to visualize equal groups. Avoid rushing to the standard algorithm; instead, let students explore strategies like partial quotients or repeated subtraction to build a strong conceptual foundation. Research shows that students who develop multiple strategies before standard algorithms make fewer procedural errors and understand remainders better.

Students will confidently divide two-digit numbers by one-digit numbers with and without remainders, explaining their process using at least two strategies. They will interpret remainders in real-world contexts and justify their decisions with clear reasoning. Missteps will be caught during peer discussions, showing growing accuracy and understanding.

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Watch Out for These Misconceptions

• During The Feast Coordinator simulation, watch for students who declare extra items as leftovers without redistributing them into new groups.

  Prompt students with counters to physically move one extra item to each group until no more groups can receive a whole item, then ask how many groups received one more and how many items are still left.

• During Station Rotation: Division Strategies, listen for students who say dividing always makes the number smaller without considering the context.

  At the sharing station, have students compare dividing 12 cookies among 3 friends versus dividing 12 cookies among 12 friends, asking which situation results in smaller portions and why that matters.

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Methods used in this brief

• Simulation Game
• Stations Rotation
• Think-Pair-Share