Introducing Multiplication

Learning Objectives

By the end of this 45-minute lesson, Year 3 students will be able to:

• Understand multiplication as repeated addition and equal grouping.
• Represent simple multiplication problems using arrays and grouping objects.
• Model multiplication problems with number sentences and diagrams.
• Use mental strategies and visual aids to solve basic multiplication problems.
• Communicate their mathematical thinking clearly.

Australian Curriculum Alignment

This lesson addresses the following Australian Curriculum (Version 9) content descriptions and elaborations for Year 3 Mathematics:

• AC9M3N04: Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies.
• Elaboration examples used: Applying arrays and various visual models to represent multiplication sentences, and understanding multiplication as repeated addition or equal grouping.
• AC9M2N05: (extension reference from Year 2) Multiplying by one-digit numbers using repeated addition, equal grouping, and arrays to support strategies.

Lesson Plan Outline (45 minutes)

Materials Needed

• Counters or small objects (25 sets of 10 each for group work)
• Pre-prepared array mats or grid paper
• Whiteboard and markers
• Multiplication Think Boards or blank sheets
• Visual aids (posters or slides showing arrays and grouping)
• Number sentence cards

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1. Introduction and Engagement (7 minutes)

• Begin by revisiting addition with the class: "What does 3 + 3 + 3 mean?"
• Introduce the idea that multiplication is a quicker way to add the same number repeatedly.
• Show a simple repeated addition example: 3 + 3 + 3 + 3 and write the multiplication sentence alongside: 4 × 3 = 12
• Explain multiplication as "4 groups of 3" using everyday language and relate to objects easily found in the classroom.

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2. Explanation and Modelling (8 minutes)

• Use counters to create 4 groups of 3 counters each on the whiteboard or a document camera.
• Count together with the class to reinforce repeated addition connection: 3 + 3 + 3 + 3 = 12 counters.
• Introduce the concept of arrays using a grid (e.g., 3 rows and 4 columns) and explain how the total is found by multiplying the rows by columns.
• Draw an array on the whiteboard and write the multiplication sentence for it (3 × 4 = 12), emphasising how multiplication relates to both rows and columns (3 groups of 4 or 4 groups of 3).
• Use a Think Board or sketch diagrams to represent simple multiplication scenarios, highlighting the connection between the picture and number sentence.

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3. Guided Practice in Small Groups (12 minutes)

• Divide students into small groups (3-5 per group), providing each group with counters and an array mat.
• Give the groups multiplication tasks such as "Make 5 groups of 2," "Make 3 groups of 4," etc.
• Encourage students to:
• Build arrays with the counters.
• Write repeated addition sentences.
• Write multiplication sentences.
• Explain their thinking to peers in the group.
• Circulate and assist groups, prompting students with questions about the grouping and totals.
• Provide challenge cards for quick extension, e.g., creating arrays for the number 12 in different ways (3×4, 4×3, 6×2).

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4. Independent Visual and Mental Multiplication Activity (10 minutes)

• Students individually complete a worksheet or use their notebooks to:
• Draw an array of a given multiplication problem (e.g., 4 × 3).
• Write the repeated addition number sentence.
• Solve simple multiplication problems mentally or with drawings.
• Incorporate an engaging question such as "If you have 7 baskets with 5 apples each, how many apples do you have? Draw and show how you know."
• Encourage use of skip counting as a mental strategy (e.g., count in 5s for the baskets example).

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5. Assessment and Discussion (8 minutes)

• Bring the class together and ask students to share how they solved one multiplication problem.
• Use quick formative assessment:
• Ask individuals simple questions such as "What is 3 groups of 4?" and "How do you know?"
• Use thumbs up/down or mini whiteboards for students to show answers to quick multiplication questions using arrays or repeated addition.
• Check for understanding by having students explain the connection between repeated addition and multiplication verbally or in writing.
• Provide corrective feedback and reinforcement if misconceptions appear.

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6. Conclusion and Reflection (optional 5 minutes if time allows)

• Recap the lesson’s key points: multiplication is repeated addition, arrays show multiplication visually, and multiplication sentences represent groups.
• Highlight real-world examples (e.g., groups of fruit or toys).
• Encourage students to look for multiplication in everyday situations.
• Set a small home connection activity such as finding “groups” of objects at home and expressing them as multiplication sentences.

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Innovative Teaching Notes for Engagement

• Utilise digital tools or interactive whiteboard apps (if available) to create virtual arrays.
• Engage students in a quick "Multiplication Dance" where they form groups physically and count (linking to First Nations Australians' cultural dance stories related to numbers and balance if culturally appropriate).
• Introduce multiplication games using cards or dice to form groups quickly.

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This lesson plan is designed to be dynamic and hands-on, supporting Year 3 students’ understanding by linking concrete materials (counters), visual representations (arrays), and symbolic representations (number sentences) — all within the framework of the Australian Curriculum's arithmetic stage for multiplication introduction.