Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

Operations with Integers: Multiplication and Division

Active learning works for multiplication and division of integers because these operations rely on concrete understanding of grouping, sharing, and patterns. Students need to move beyond rote rules and see the logic behind signs and remainders, which hands-on tasks make visible.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1
• NCCA: Junior Cycle - Number - N.2

• 25–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Role Play
• 35 min · Small Groups

Role Play: The Party Planner

Students are given a set number of 'guests' (counters) and 'tables' (paper plates). They must divide the guests and decide what to do with the remainders. Does the 'leftover' guest need a whole new table, or do they just miss out?

Explain the rules for multiplying and dividing integers with different signs.

Facilitation Tip

During The Party Planner, circulate with counters and explicitly ask students to show how many more groups could be made when they have a remainder.

What to look for

Present students with three multiplication problems: 5 x -3, -7 x -2, and -4 x 6. Ask them to write the answer and circle the sign they applied. Review answers as a class, focusing on the sign rule used for each.

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

Activity 02

• Inquiry Circle
• 25 min · Pairs

Inquiry Circle: The Remainder Race

Give pairs a set of division problems. They must sort them into three categories: 'Ignore the remainder,' 'Round up the answer,' and 'The remainder is the answer.' They must justify their choices to another pair.

Predict the sign of the product or quotient of multiple integers.

Facilitation Tip

In The Remainder Race, have pairs verbalize each step of their sharing or grouping process aloud to catch misconceptions in real time.

What to look for

Give each student a card with a division problem involving integers, such as -24 ÷ 8 or -36 ÷ -6. Ask them to solve the problem and write one sentence explaining how they determined the sign of their answer.

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Division Strategies

Set up stations for different methods: one for repeated subtraction on a number line, one for 'chunking' using multiplication facts, and one for physical grouping with cubes. Students rotate to find which method they find most reliable.

Construct a pattern that demonstrates why a negative number multiplied by a negative number results in a positive number.

Facilitation Tip

Set a timer for Station Rotation so students rotate before losing focus, and post expected strategies at each station for quick reference.

What to look for

Pose the question: 'If we know that 3 x 4 = 12, and we also know that 3 x 0 = 0, how can we use this pattern to figure out what -3 x -4 should be?' Facilitate a discussion where students explore the pattern of decreasing the first factor by 1 and observe the corresponding change in the product.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach integer multiplication by starting with patterns on a number line or grid, then connect to real-world debts and temperature changes. For division, use physical objects to contrast sharing (equal distribution) with grouping (how many equal sets fit). Encourage students to verbalize the meaning of each number in the problem rather than just computing.

Students will confidently explain why negative times negative makes a positive, and interpret remainders in context. They will use sharing and grouping language to describe division, and connect division to multiplication as inverse operations.

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Watch Out for These Misconceptions

• During The Party Planner, watch for students who ignore the remainder or treat it as part of the quotient without checking if another group can be formed.

  Have students physically place counters into cups or plates labeled with the divisor, and prompt with 'Can you make one more equal group with what’s left? What does that extra counter mean in your story?'

• During The Remainder Race, watch for students who treat the remainder as a separate answer without connecting it to the context of the problem.

  Ask each pair to explain their final result using the race scenario: 'Does the remainder mean another lap? A partial lap? How do you decide?'

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Methods used in this brief

• Role Play
• Inquiry Circle
• Stations Rotation