Inverse Operations & Problem Solving

ST Name: Kym Fox

ST Number: 40036679

Class Level: 2nd & 3rd Class

Date: 9/5/25

Subject: Maths

Time: 10:40

Duration of Lesson: 60 Minutes

Number of Pupils: 20

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Strand(s)

Number

Strand Unit(s)/Element(s)

Sets and Operations

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Learning Outcomes / Content Objectives

• To understand and apply flexibly the four operations; and the relationships between operations.
• Specifically, children will recognise and explain the inverse relationship between multiplication and division.
• Children will solve two-step word problems involving division, using multiplication/division facts to aid problem solving.

Aligned to Primary Curriculum Framework for Mathematics, 2015 (NCCA), Number strand, Strand Unit ‘Sets and Operations’, learning outcome for 3rd class: “use the inverse relationship between multiplication and division in calculations”, and problem-solving strand unit “solve problems in meaningful contexts”.

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Learning Objectives

1. The child should be enabled to: recognise and explain the inverse relationship between multiplication and division.
2. The child should be enabled to: solve two-step word problems involving division, by applying multiplication and division facts.

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Assessment

Method	Assessment of	To be Recorded
Teacher questioning	Understanding of inverse operations and accuracy in solving 2-step division problems	Anecdotal notes, individual student responses, and written work in book/worksheet

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Teacher Questioning

Lower Order Questions (Closed)

1. What is the answer to 3 × 4?
2. If 12 ÷ 4 = ?, what does this mean?
3. If I multiply 6 by 2, what number do I get?

Higher Order Questions (Open)

1. How can we check our division answer using multiplication?
2. Can you explain why multiplication and division are ‘opposite’ operations?
3. In the two-step word problem, what should we do first, and why?

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Language Development Opportunities

• Use mathematical vocabulary: inverse, multiplication, division, ‘undo’, product, quotient, factor, operation, two-step problem.
• Encourage verbal mathematical explanations and group discussions.
• Promote sentence starters such as: “Multiplication and division are inverse because...”

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Literacy Development Opportunities

• Reading comprehension through word problems.
• Writing clear mathematical sentences to explain reasoning.
• Use of keywords such as multiply, divide, twice, equal parts, shared equally.

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Teaching Methodologies

• Using cognitively challenging tasks
• Promoting Maths Talk
• Fostering productive disposition
• Encouraging playfulness
• Emphasising mathematical modelling

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Introduction (10 minutes)

Stimulus

• Show a number sentence on the board: 4 × 3 = 12.
• Write the division sentence 12 ÷ 3 = ? beside it.

Elicit Prior Knowledge

• Ask children what 4 × 3 means.
• Ask if they have seen the division number sentence before and what they think it means.
• Invite children to recall times tables facts they know.

Share Learning Intention

• “Today we will explore how multiplication and division are ‘opposite’ or inverse operations.”
• “We will also solve two-step word problems that involve division.”

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Development (40 minutes)

1. Discussion & Explanation (10 minutes):

   • Teacher explains that multiplication and division undo each other.
   • Use examples:
     • 4 × 3 = 12 and 12 ÷ 3 = 4
     • Ask, “How do these sentences show the inverse relationship?”
   • Draw a “math fact family” triangle on the board with numbers 4, 3, 12 to visually represent the link between multiplication and division.

2. Multiplication Dice Game (10 minutes):

   • Pupils work in pairs. Each pair gets two dice.
   • Pupils roll the dice, multiply the two numbers shown, and say the product aloud.
   • Rotate pairs to encourage peer interaction & maths talk.

3. Two-Step Division Word Problems (15 minutes):

   • Present and read aloud two word problems where division is involved in two steps, for example:
     • “There are 24 sweets shared equally into 3 bags. Then each bag is divided between 2 children. How many sweets does each child get?”
   • Discuss with the class how to solve step by step, relating to inverse multiplication where possible.
   • Pupils solve problems individually or in pairs with concrete materials (like counters or cubes if needed).

4. Math Talk and Modelling (5 minutes):

   • Select some children to explain their thinking aloud to the class, encouraging use of terms like ‘inverse’ and ‘undo’.
   • Display student explanations on the board or wall for reference.

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Conclusion (10 minutes)

Cognitive:

• Recap how multiplication and division relate as inverse operations.
• Summarise key maths vocabulary learned.
• Invite one or two pupils to explain the inverse relationship again in their own words.

Social:

• Choose names from the name jar to collect and put away all concrete materials.
• Reflect on the importance of working together and explaining maths to friends.

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Universal Design for Learning

Pupil(s)	Reason(s)	Method(s)	Additional Comments
Pupils with learning difficulties	Need support breaking down 2-step problems	Use visual aids, manipulatives (counters) and paired work	Extra prompts and simplified language may help
EAL Learners	May require vocabulary support	Pre-teach key words, use visuals, gestures	Encourage peer support and oral repetition
Advanced Pupils	Need extension challenge	Challenge with creating own inverse problems or 3-step problems	Provide open-ended tasks to deepen understanding

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The Learning Environment

Resources:

• Whiteboard and markers
• Two dice per pair
• Counters or cubes for concrete modelling
• Word problem cards/printed worksheets
• Name jar for classroom organisation
• Visual aids showing “math fact families” and inverse operation diagrams

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This lesson plan rigorously follows the Mathematics strand of the IE Primary Curriculum, balancing conceptual understanding, practical application, and language development, reinforced through active learning methodologies designed to engage 20 third-class pupils.