Multiplying integers: the lift in a building
A lift is at floor 5. It moves up or down a number of floors each minute. Find where it will be in a few minutes, or where it was a few minutes ago, and discover the rules for multiplying positive and negative numbers.
Core concept
The product of two integers with the same sign is positive and of two with different signs is negative: (+) × (+) = +, (−) × (−) = +, (+) × (−) = − and (−) × (+) = −
Topic: Integers
A lift in a tall building is at floor 5 right now. Its rate is how many floors it moves each minute: +2 means 2 floors up each minute, and −2 means 2 floors down. Time can be positive (minutes from now) or negative (minutes ago). The change in floors is rate × time. Going up at +2 for +3 minutes, it will be 6 floors higher: (+2) × (+3) = +6. Going down at −2 for +3 minutes, it will be 6 floors lower: (−2) × (+3) = −6. But where was a lift that is going down, 3 minutes ago? Higher up: (−2) × (−3) = +6. Floors below 0 are the basement.
What you will learn
- Multiply positive and negative integers.
- State the sign rules for multiplication and division of integers.
- Explain why the product of two negative numbers is positive.
Before you start
- Know how to add and subtract integers on a number line.
Materials
- A number line drawn up the side of a page, like floors
Equipment
- A counter to move up and down
Procedure
- Record (+2) × (+3): going up, in 3 minutes.
- Record (−2) × (+3): going down, in 3 minutes.
- Record (+2) × (−3): going up, 3 minutes ago.
- Record (−2) × (−3): going down, 3 minutes ago.
How this simulation is simplified
- The lift is at floor 5 now and keeps the same rate the whole time.