Exploring Multiplication Concepts

Focus Question

How can we use different strategies to multiply numbers and understand their relationships?

Big Idea

Multiplication is a way to combine equal groups to find the total, and understanding these strategies helps us solve real-world problems efficiently.

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Lesson Objectives

Aligned with IB Primary Years Programme (PYP) Mathematics Strand – Number: Number Operations and Relationships (M4)
By the end of the lesson, students will be able to:

• Use repeated addition and arrays to represent multiplication sentences (M4.2).
• Demonstrate the commutative property of multiplication by exchanging factors (M4.4).
• Apply multiplication strategies to solve word problems within 0–100 (M4.6).
• Communicate mathematical ideas clearly using appropriate vocabulary and representations (ATL skills: Communication).

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Assessment Style

• Formative Assessment: Observation during guided and independent practice with anecdotal notes.
• Peer Assessment: Students explain their reasoning to partners and provide feedback.
• Exit Ticket: A short written task applying multiplication in a new context.

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Academic Vocabulary

• Multiply, factor, product
• Array
• Equal groups
• Commutative property
• Repeated addition

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Higher-Level Thinking Questions

• What happens to the product if we change the order of the numbers we multiply? Why does that happen?
• How can we use arrays to help us solve multiplication problems?
• Can you think of real-life examples where multiplication helps us?
• If you do not know this multiplication fact, what strategy could you use to find the answer?

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Materials Needed

• Whiteboard and markers
• Grid paper for arrays
• Counters or small objects (e.g., blocks or beads)
• Student math journals
• Exit tickets (prepared worksheets)
• Chart paper with multiplication vocabulary and properties

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Lesson Timeline and Activities

1. Bell Ringer (5 minutes) – Activate Prior Knowledge

• Activity: Quick review of repeated addition with simple sums (e.g., 3 + 3 + 3).
• Differentiation:
  • Visual: Display addition sentences on whiteboard with pictures of objects.
  • Auditory: Read verbal repeated addition sentences aloud.
  • Kinesthetic: Students use counters to model repeated addition.

2. Introductory Hook (5 minutes) – Engage Through Storytelling

• Activity: Tell a story involving equal groups (e.g., planting 4 rows of flowers with 5 flowers each).
• Ask: “How many flowers are there in all? How might we find this quickly without counting all?”
• Differentiation: Use physical objects for kinesthetic learners, visuals for others.

3. Main Instruction (20-25 minutes) – Interactive Direct Instruction

• Part 1 (10 mins):
  • Introduce arrays as a visual multiplication strategy using grid paper and counters.
  • Model 4 × 5 by making an array and write the multiplication sentence.
  • Show repeated addition and connect to arrays.
  • Explain the commutative property with arrays (turn the array to show 5 × 4).
• Part 2 (10-15 mins):
  • Students work in pairs to create their own arrays with given factors.
  • Use questioning to prompt higher thinking: “Can you make arrays for both 3 × 6 and 6 × 3? What do you notice?”
  • Highlight language and communication: students explain their reasoning aloud or write brief reflections in math journals.
• Differentiation:
  • Visual: Emphasis on hands-on arrays and drawings.
  • Auditory: Students discuss in pairs and repeat key vocabulary.
  • Kinesthetic: Build arrays with counters and move them physically to see the commutative property.

4. Guided Practice (10 minutes)

• Worksheet with mixed multiplication problems involving arrays and word problems.
• Teacher circulates to provide scaffolding, asks probing questions, and identifies misconceptions.
• Encourage peer help for students needing support.

5. Independent Practice (10 minutes)

• Students solve multiplication problems independently using strategies learned.
• Students encouraged to choose the strategy that works best for them (array, repeated addition, skip counting).
• Provide manipulatives for those who benefit from kinesthetic support.

6. Closure (5 minutes)

• Review key concepts by discussing:
  • “What did we learn about multiplication today?”
  • “How can the commutative property help us?”
• Exit ticket: Solve one multiplication problem and write a sentence explaining the strategy used.

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Differentiation Summary

Learner Type	Supports and Strategies
Visual	Use of arrays, color-coded grids, visual examples on board and paper.
Auditory	Pair discussions, story-based hook, repetition of vocabulary, oral explanations.
Kinesthetic	Manipulatives (counters, beads), making physical arrays, moving objects to demonstrate properties.

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This lesson builds on the IB PYP transdisciplinary theme "How We Organize Ourselves" by connecting multiplication strategies to real-world systems like planting rows of flowers, enabling learners to see math in everyday contexts. The focus on communication encourages development of ATL skills, ensuring students not only calculate but articulate mathematical understanding.