Middle school maths, year 1 · unit 2
Integers and Rational Numbers
Basement level 2, three degrees below freezing. Numbers below zero are already all around us. Call the ground 0, call up + and down −, and that is all there is to it. We start by riding a lift down below the ground.
There are numbers below zero
A board to adjustThe ground is floor 0. Going up: +1, +2. Going down: −1, −2. Drag the lift to change floors.
One red and one blue make 0
A board to arrangeA red chip is +1, a blue chip is −1. When they meet they cancel out. Drag chips onto the mat.
Why is a negative times a negative positive?
A board to adjustWater rising is +, draining is −. Later in time is +, earlier is −. Drag the gold handle to run time forwards and backwards.
There are numbers between the integers too
A board to adjustTemperatures do not only come in whole numbers. There is such a thing as 1.5 below zero. Drag the gold handle to set the temperature.
Try it yourself
Use what you found on the boards. The numbers change every time and the easy questions come first. Get three right and the lamp lights.
What to take away from this unit
- Numbers above 0 are positive (+) and numbers below 0 are negative (−). 0 is neither. The further right (or up) on the number line, the bigger the number. That is why −4 is less than −1.
- The distance from 0 is the absolute value. +3 and −3 point in opposite directions, but both have absolute value 3.
- Adding is gathering chips. Same signs simply pile up; different signs cancel in pairs and the larger side is left over. Subtracting is the same as adding with the sign flipped. (+2) − (−3) = (+2) + (+3) = +5.
- Multiplying gives + when the signs match and − when they differ. Rewind (−) draining water (−) and it rises (+), so (−) × (−) = (+).
- A number that can be written as a fraction is a rational number. Integers are rational too, and between any two integers there are endlessly many rationals such as −1.5 and −½.