Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

Problem Solving with Multiplication and Division

Active learning turns abstract multiplication and division problems into concrete challenges that build reasoning skills. Students move from reading words to visualizing actions, which strengthens their ability to choose operations and sequence steps accurately.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Problem Solving

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 25 min · Pairs

Pair Relay: Operation Sequences

Pairs read a multi-step word problem and solve the first operation together using counters. They pass the model to the next pair for the second operation, repeating until complete. Pairs then explain their full solution to the class.

Analyze a word problem to determine the appropriate operation(s) to use.

Facilitation Tip

During Pair Relay: Operation Sequences, provide each pair with a problem strip and a blank strip to write the next step, ensuring they physically construct the sequence.

What to look for

Provide students with a word problem like: 'A class of 28 students is going on a field trip. Each bus can hold 12 students. How many buses are needed? If each ticket costs €5, what is the total cost for all students?' Ask students to write down the steps they took and their final answer.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Inquiry Circle
• 35 min · Small Groups

Small Group Bar Model Challenge

Provide groups with word problems printed on cards. Groups draw bar models to represent each step, solve using multiplication or division, and label units. Groups swap models to check and critique another group's work.

Construct a mathematical model to represent a complex multiplication and division problem.

Facilitation Tip

For Small Group Bar Model Challenge, give groups colored markers to label each bar with the operation it represents, making thinking visible.

What to look for

Present a problem on the board: 'Sarah bought 3 packs of pencils with 12 pencils in each pack. She wants to share them equally among 4 friends. How many pencils does each friend get?' Ask students to show their work using a chosen strategy (e.g., drawing a diagram, writing an equation) and hold up their answer.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Inquiry Circle
• 40 min · Small Groups

Whole Class Strategy Carousel

Display 4-5 multi-step problems around the room. Students rotate in groups, solving one per station with a chosen strategy and noting it. Final rotation allows groups to review and select the most efficient method.

Critique different strategies for solving a multi-step problem.

Facilitation Tip

In Whole Class Strategy Carousel, post sample problems on large sheets so students can annotate with arrows and notes as they rotate.

What to look for

Pose a problem: 'A factory made 150 toys. They need to pack them into boxes that hold 6 toys each. If they have 20 boxes, will they have enough boxes? Explain your reasoning.' Facilitate a class discussion where students share their solutions and compare different methods for solving.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 04

• Inquiry Circle
• 20 min · Individual

Individual Model Builder

Students receive a word problem and build a personal model using paper strips or drawings. They solve independently, then pair up briefly to compare models and operations before sharing one with the class.

Analyze a word problem to determine the appropriate operation(s) to use.

Facilitation Tip

Have Individual Model Builder students write a one-sentence justification under each diagram to connect their visual model to the problem’s story.

What to look for

Provide students with a word problem like: 'A class of 28 students is going on a field trip. Each bus can hold 12 students. How many buses are needed? If each ticket costs €5, what is the total cost for all students?' Ask students to write down the steps they took and their final answer.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teachers approach this topic by asking students to narrate the problem as a story before modeling it mathematically. They avoid rushing to equations, instead guiding students to draw quick sketches or arrays that match the language of sharing, grouping, or totaling. Research shows that students who verbalize before calculating make fewer order-of-operations errors and better connect symbols to real situations.

Students will confidently select operations based on context, model solutions using diagrams, and explain each step aloud. They will compare strategies with peers and adjust models until their answers match the problem’s conditions.

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Watch Out for These Misconceptions

• During Pair Relay: Operation Sequences, watch for students applying operations in a fixed order without reading context clues.

  Have pairs build their operation strips side by side, then read the problem aloud while pointing to each step in the strip to reveal why context dictates order.

• During Small Group Bar Model Challenge, watch for students skipping remainders or ignoring them in final answers.

  Prompt groups to place actual counters on the remainder section of their bar model and discuss whether the extra items are shared or left over.

• During Whole Class Strategy Carousel, watch for students reusing the same numbers across all steps without parsing unique values.

  Ask stations to highlight each number used in a different color and label which operation it belongs to before solving.

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Methods used in this brief

• Inquiry Circle