Mathematics · Class 1

Active learning ideas

Dividing Integers

Active learning helps students grasp the abstract rules of dividing integers by making the sign rules concrete and visual. Moving beyond rote memorisation, these activities engage students in reasoning, peer discussion, and real-world applications to build lasting understanding of integer division.

• CBSE Learning Outcomes
• NCERT: Class 7, Chapter 1, Integers

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

Activity 01

• Mystery Object
• 30 min · Pairs

Number Line Relay: Sign Rule Races

Draw number lines on the floor with tape. Pairs take turns jumping to model divisions like -10 ÷ 2, noting the quotient sign. Switch roles after each problem, recording results on a class chart. Discuss patterns as a group.

Analyze the relationship between integer multiplication and division.

Facilitation Tip

During Number Line Relay, ensure each team member physically jumps to demonstrate the direction and count of steps for both positive and negative divisors.

What to look for

Present students with three division problems on the board: 1. 36 ÷ (-9), 2. -45 ÷ (-5), 3. -56 ÷ 7. Ask them to write down the answer and the sign of the quotient for each problem on a small whiteboard or paper.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 02

• Mystery Object
• 45 min · Small Groups

Chip Model Division: Manipulative Stations

Provide two-colour counters (red for negative, yellow for positive). Small groups model divisions by pairing chips, e.g., 12 red ÷ 3 yellow = -4. Rotate stations for different problems, then share models with the class.

Explain the rules for dividing integers with different signs.

Facilitation Tip

For Chip Model Division, provide red and yellow chips and instruct students to group negative chips first to see how pairing affects the quotient's sign.

What to look for

Give each student a slip of paper. Ask them to solve one problem: 'If a team lost 24 points over 6 rounds, what was the average points lost per round?' Then, ask them to write one sentence explaining how they determined the sign of their answer.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 03

• Mystery Object
• 25 min · Pairs

Error Hunt Game: Peer Correction

Distribute cards with division problems and wrong answers. Pairs identify sign errors, explain corrections using multiplication check, and create their own tricky problems. Whole class votes on the best ones.

Evaluate the outcome of various integer division problems.

Facilitation Tip

In Error Hunt Game, ask students to write corrections directly on the problem sheets and explain their reasoning in pairs before moving to the next station.

What to look for

Pose the question: 'Is dividing a negative integer by a positive integer the same as dividing a positive integer by a negative integer? Explain your reasoning using examples.' Facilitate a class discussion where students share their answers and justifications.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 04

• Mystery Object
• 40 min · Small Groups

Real-Life Division Scenarios: Group Posters

Assign scenarios like dividing profits or debts. Small groups solve using rules, illustrate with diagrams, and present posters explaining sign decisions. Class discusses applications.

Analyze the relationship between integer multiplication and division.

What to look for

Present students with three division problems on the board: 1. 36 ÷ (-9), 2. -45 ÷ (-5), 3. -56 ÷ 7. Ask them to write down the answer and the sign of the quotient for each problem on a small whiteboard or paper.

• Understand
• Analyze
• Evaluate
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach sign rules by linking them to multiplication, as research shows this strengthens conceptual fluency. Avoid teaching rules in isolation; instead, have students derive them through patterns in number line jumps or chip pairings. Emphasise verification through multiplication to build confidence in their answers and catch errors early.

Successful learning looks like students confidently applying sign rules, explaining their reasoning with examples, and verifying results through multiplication. Students should also correct errors collaboratively and connect division to real-life contexts with clear sign determination.

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Watch Out for These Misconceptions

• During Chip Model Division, watch for students pairing negative chips and assuming the quotient is negative.

  Remind students to count the number of negative pairs formed and note how even pairs result in a positive quotient, using the phrase 'negatives pair to make positives' to reinforce the rule.

• During Number Line Relay, watch for students ignoring the direction of jumps when the divisor is negative.

  Have them repeat the relay with a negative divisor, asking them to explain why the jumps move left and how this affects the quotient's sign.

• During Chip Model Division or Error Hunt Game, watch for students stating that zero divided by any integer equals zero.

  Ask them to model 0 ÷ 5 with chips and discuss what 'no chips to pair' means, linking it to the undefined nature of division by zero.

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Methods used in this brief

• Mystery Object