Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Multiplication and Division Word Problems

Active learning helps children connect abstract concepts to concrete experiences, which is essential for multiplication and division word problems. When students manipulate objects, draw models, or act out scenarios, they build lasting understanding beyond memorized facts.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Geometry and Trigonometry - G.3.1

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Role Play
• 35 min · Small Groups

Small Groups: Manipulative Modelling

Distribute word problem cards focused on repeated groups or sharing. Each group uses counters or blocks to build models, draws their solution, and writes a number sentence. Groups present one strategy to the class.

What words in a problem tell you to multiply or divide?

Facilitation Tip

During Manipulative Modelling, circulate with guiding questions like 'Can you show me how dividing these counters changes your number sentence?' to push thinking.

What to look for

Provide students with a word problem, such as: 'Sarah has 3 bags of apples. Each bag has 5 apples. How many apples does Sarah have in total?' Ask students to write the number sentence and the answer, and to draw a picture to show their thinking.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 02

• Role Play
• 25 min · Pairs

Pairs: Story Swap Challenge

Partners write a short multiplication or division story using classroom objects. They swap papers, draw or use fingers to solve the partner's problem, then discuss and verify the answer together.

How can you use objects or a drawing to help you solve a multiplication or division problem?

Facilitation Tip

During Story Swap Challenge, provide sentence starters on cards ('We had ___, so we ___') to scaffold language for pairs who struggle to begin.

What to look for

Present a scenario: '12 cookies are shared equally among 4 friends. How many cookies does each friend get?' Ask students to hold up the correct number of fingers to represent the answer, or to write the answer on a mini-whiteboard.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Role Play
• 20 min · Whole Class

Whole Class: Clue Word Hunt

Project five mixed word problems on the board. Class chorally reads each, raises hands to spot multiply or divide words, votes on the operation, then shares a quick model.

Can you write a number sentence to match a real-life multiplication or division story?

Facilitation Tip

During Clue Word Hunt, ask students to justify why certain words signal one operation over another using their drawn examples.

What to look for

Pose the question: 'If you have 15 stickers and want to give 3 stickers to each friend, how many friends can you give stickers to?' Ask students to share their strategy, using words like 'groups of' or 'shared equally' in their explanation.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 04

• Role Play
• 30 min · Individual

Individual: Equation Match-Up

Provide cards with stories, drawings, and equations. Students match sets for multiplication or division problems, then create one new match to share with a neighbor.

What words in a problem tell you to multiply or divide?

Facilitation Tip

During Equation Match-Up, include problems with remainders so students see division as more than just whole-number quotients.

What to look for

Provide students with a word problem, such as: 'Sarah has 3 bags of apples. Each bag has 5 apples. How many apples does Sarah have in total?' Ask students to write the number sentence and the answer, and to draw a picture to show their thinking.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Teach this topic by letting students experience the inverse relationship between multiplication and division through hands-on reversal. Avoid starting with abstract rules or keyword memorization, as these can lead to confusion. Instead, focus on real-world contexts where students must decide between grouping or sharing, and use their own language to describe what they’re doing. Research shows that when children physically build and then dismantle arrays, they internalize the connection between repeated addition and equal sharing more deeply than with worksheets alone.

Successful learning looks like students confidently choosing between multiplication and division based on context clues, modeling problems with manipulatives or drawings, and explaining their reasoning using terms like 'groups of' or 'shared equally.' They should also recognize when a remainder is a natural part of the solution.

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Watch Out for These Misconceptions

• During Manipulative Modelling, watch for students who assume all 'groups' problems mean multiplication. Redirect by asking them to test both operations with the counters, using phrases like 'Show me how dividing these toys into equal sets changes your total.'

  During Story Swap Challenge, provide pairs with problems that use 'groups of' in multiplication and 'divide into groups' in division contexts. Ask them to present why the same phrase can signal different operations depending on the scenario.

• During Manipulative Modelling, watch for students who believe division always results in whole numbers. Redirect by using 7 counters and asking them to share equally between 2 friends, then discuss what happens to the leftover counter.

  During Clue Word Hunt, include problems like '11 pencils shared among 3 friends' and ask students to model the remainder with drawings or counters before writing the number sentence.

• During Manipulative Modelling, watch for students who treat multiplication and division as unrelated operations. Redirect by having them build an array for multiplication, then break it apart to model division, using language like 'undoing' or 'reversing.'

  During Equation Match-Up, include pairs of problems where the same numbers appear in both multiplication and division sentences, such as 4 x 3 = 12 and 12 ÷ 4 = 3, and ask students to explain how the drawings connect.

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Methods used in this brief

• Role Play