Teacher Guide: Multiplying and Dividing Integers
Learn the rules for multiplying and dividing positive and negative numbers.
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Class quiz
10 questions on Negative Numbers. Students join with a name, you see everyone's score.
For Teachers
- Apply sign rules to multiply integers correctly
- Apply sign rules to divide integers correctly
- Determine the sign of a product or quotient before calculating
- Solve real-world problems involving integer multiplication and division
- • Understanding of negative numbers and the number line
- • Addition and subtraction of integers
- • Basic multiplication and division facts
- 1. Why do you think mathematicians decided that negative times negative should be positive?
- 2. Can you think of a real-life situation where you multiply a negative by a negative?
- 3. What patterns do you notice when multiplying three or more negative numbers?
- 4. How can you quickly tell if a product of many integers will be positive or negative?
Two negatives always make a positive
Division sign rules are different from multiplication
For Struggling Students:
- • Use color coding: green for positive results, red for negative
- • Start with single-digit integers only
- • Provide a sign rule reference card for every problem
For On-Level Students:
- • Include mixed multiplication and division problems
- • Add word problems with temperature and money contexts
- • Practice with two and three integer products
For Advanced Students:
- • Explore patterns with longer chains of multiplication
- • Introduce division with remainders
- • Challenge with algebraic expressions using variables
- 7.NS.A.2 (CCSS.MATH.CONTENT.7.NS.A.2)
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers
- 7.NS.A.2a (CCSS.MATH.CONTENT.7.NS.A.2a)
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations
- visualSign Rule Chart
Color-coded reference showing all sign combinations
- activityInteger Product Game
Match expressions to their correct products
- worksheetTemperature Word Problems
Apply integer operations to real scenarios
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
| Operation | Result |
|---|---|
| Positive | |
| Positive | |
| Negative | |
| Negative |
- Same signs → Positive result
- Different signs → Negative result
Worked Examples
Calculate:
Identify the signs
Both numbers are negative: and → Same signs
Apply the sign rule
Same signs → positive result → Answer will be positive
Multiply the absolute values
→
Apply the sign
Positive result →
Answer:
Common Mistakes
Thinking
Why it's wrong: Students forget that multiplying two negatives gives a positive result.
Correct: Same signs → positive:
Confusing with
Why it's wrong: Both give the same answer! Different signs → negative in both cases.
Correct: and . Order does not matter.
Forgetting the sign when the answer is positive
Why it's wrong: When two negatives multiply, students may write out of habit.
Correct: Always check: same signs = positive, different signs = negative.
Why It Matters
- Temperature changes: If temperature drops 3 degrees per hour for 5 hours, the total change is degrees
- Finance: A monthly debt payment of 200 euros over 6 months means euros total
- Gaming: Losing 5 points per wrong answer over 4 questions gives points
- Elevation: Descending 10 meters per minute for 8 minutes means meters
Real World Applications
Temperature Changes Over Time
Meteorologists calculate temperature changes using integer multiplication.
Example:
If the temperature drops 2 degrees every hour, after 6 hours the change is degrees.
A freezer cools food by dropping 5 degrees every 10 minutes. How much does the temperature change in 40 minutes?
What is the total temperature change?
Step 1: Write the mathematical expression
Calculate: number of 10-minute periods
Stock Market Changes
Investors track daily gains and losses over multiple days.
Example:
A stock loses 3 euros per day for 5 days: euros total loss.
An investor reverses a bad trade. They undo a loss of 8 euros that happened 3 times. What is the net effect?
What is the total change when reversing these losses?
Step 1: Write the mathematical expression
Undoing a loss is like:
Key Takeaways
- 1Same signs (both positive or both negative) → positive result
- 2Different signs (one positive, one negative) → negative result
- 3These rules work for both multiplication AND division
- 4When multiplying many integers: odd number of negatives → negative, even → positive
- 5Always calculate with absolute values first, then apply the sign rule
Frequently Asked Questions
Why does a negative times a negative equal a positive?
Does the order matter when multiplying integers?
What about zero?
Glossary
- Integer
- A whole number that can be positive, negative, or zero
- Absolute value
- The distance from zero, always positive.
- Product
- The result of multiplication
- Quotient
- The result of division
- Sign rule
- The rule that determines if the result is positive or negative based on the signs of the operands
Formula Card
Positive × Positive
Positive times positive equals positive
Negative × Negative
Negative times negative equals positive
Positive × Negative
Positive times negative equals negative
Negative × Positive
Negative times positive equals negative