Operations with Integers: Multiplication & DivisionActivities & Teaching Strategies
Active learning helps students move beyond memorizing sign rules by letting them see patterns emerge. When students manipulate models and work through problems in real time, abstract rules become concrete. This approach builds confidence and reduces reliance on rote memory for operations with integers.
Learning Objectives
- 1Calculate the product of two negative integers, explaining the resulting positive sign.
- 2Compare the sign rules for integer multiplication with the sign rules for integer division.
- 3Analyze a given scenario to determine if division of negative integers is applicable.
- 4Construct a real-world problem that requires dividing negative integers to find a solution.
Want a complete lesson plan with these objectives? Generate a Mission →
Chip Model: Sign Patterns
Provide two-color counters (red for negative, yellow for positive). Students model multiplication like (-3)×2 by pairing 3 red with 2 yellow groups, flipping pairs to positives. Discuss results, then extend to division by separating into equal groups. Record patterns in journals.
Prepare & details
Explain the pattern that emerges when multiplying two negative integers.
Facilitation Tip: During Chip Model: Sign Patterns, circulate and ask pairs to explain why removing negative pairs results in positive totals.
Setup: Groups at tables with case materials
Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template
Number Line Relay: Mixed Operations
Mark number lines on floor with tape. Teams solve multiplication/division problems by jumping to represent integers, e.g., start at -4, multiply by -2 to reach 8. Relay passes marker; first accurate team wins. Debrief sign rules as class.
Prepare & details
Analyze how the sign rules for division relate to those for multiplication.
Facilitation Tip: For Number Line Relay: Mixed Operations, ensure each team member verbalizes the sign change before moving the counter.
Setup: Groups at tables with case materials
Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template
Contextual Problem Stations
Set up stations with scenarios: debts, elevations, temperatures. Students solve using rules, draw models, and create their own problems. Rotate stations, share solutions whole class. Emphasize pattern application.
Prepare & details
Construct a real-world scenario where dividing negative integers is necessary.
Facilitation Tip: In Contextual Problem Stations, provide calculators only after students have set up the equation using integer rules.
Setup: Groups at tables with case materials
Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template
Pattern Hunt Cards
Distribute cards with integer pairs and products/quotients. Pairs sort into pattern groups (++, +-, --, -+), justify rules. Create posters displaying findings for class gallery walk.
Prepare & details
Explain the pattern that emerges when multiplying two negative integers.
Setup: Groups at tables with case materials
Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template
Teaching This Topic
Start with visual models to establish the foundations of sign rules, then transition to number lines to reinforce consistency. Avoid rushing to abstract rules before students see the patterns for themselves. Research shows that students retain integer operations better when they construct the rules through guided discovery rather than direct instruction.
What to Expect
Successful learning looks like students using models to justify their answers, not just stating them. They should connect multiplication and division rules through shared patterns and apply these rules accurately in contextual problems. Discussions should include clear explanations of why signs behave as they do.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Chip Model: Sign Patterns, watch for students who assume the rules are the same as for addition and subtraction without testing the model.
What to Teach Instead
Ask students to physically remove negative pairs and observe the positive outcome before recording the rule. Have them explain the visual transformation to the group.
Common MisconceptionDuring Number Line Relay: Mixed Operations, watch for students who treat division as unrelated to multiplication.
What to Teach Instead
After each relay round, have teams present how reversing a multiplication step led to the division result, emphasizing the shared sign pattern.
Common MisconceptionDuring Contextual Problem Stations, watch for students who treat zero as a negative or positive number in context.
What to Teach Instead
Use zero-pair counters during the activity to model how adding and subtracting zero does not change the value, reinforcing the identity property for integers.
Assessment Ideas
After Chip Model: Sign Patterns, present three multiplication problems: (-4) x (-5), 6 x (-3), and (-7) x 2. Ask students to write the answer and explain the sign rule, referencing their chip model visuals.
After Contextual Problem Stations, give students a card with the problem: 'A company lost €1000 over 5 days. What was the average daily loss?' Ask them to write the calculation using integers, state the answer, and explain their sign choice.
During Number Line Relay: Mixed Operations, pause the relay and pose the question: 'How are the rules for multiplying integers similar to the rules for dividing integers?' Facilitate a quick group discussion, inviting students to use examples from their relay steps to support their reasoning.
Extensions & Scaffolding
- Challenge early finishers to create three original word problems using integer multiplication and division with negative values, then solve and trade with peers.
- Scaffolding for struggling students: provide partially completed chip models where only one side is filled, asking them to predict the result before completing the model.
- Deeper exploration: invite students to research historical contexts where negative numbers were first used in mathematics, then present how sign rules were justified at the time.
Key Vocabulary
| Integer | A whole number, positive or negative, including zero. Examples include -3, 0, and 5. |
| Product | The result of multiplying two or more numbers. For example, the product of 4 and 5 is 20. |
| Quotient | The result of dividing one number by another. For example, the quotient of 10 divided by 2 is 5. |
| Sign Rule | A specific rule that determines the sign (positive or negative) of the result when performing multiplication or division with integers. |
Suggested Methodologies
Planning templates for Foundations of Mathematical Thinking
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Number Systems and Operations
Integers: Representation and Ordering
Students will represent and order integers on a number line, understanding their relative values and real-world applications.
3 methodologies
Operations with Integers: Addition & Subtraction
Students will perform addition and subtraction of integers, using various models and understanding the concept of absolute value.
3 methodologies
Fractions: Equivalence and Simplification
Students will understand equivalent fractions, simplify fractions to their lowest terms, and compare their values.
3 methodologies
Operations with Fractions: Addition & Subtraction
Students will add and subtract fractions with like and unlike denominators, including mixed numbers.
3 methodologies
Operations with Fractions: Multiplication & Division
Students will multiply and divide fractions, including mixed numbers, and solve related word problems.
3 methodologies
Ready to teach Operations with Integers: Multiplication & Division?
Generate a full mission with everything you need
Generate a Mission