Integer: Addition and Subtraction
6 Minutes
Adding and subtracting integers for students, covering positive and negative numbers, games, and addition properties. A maths lesson in English.
- What integers are using natural numbers, zero, and sea level
- Adding and subtracting integers through a pit game and a car game
- Addition properties: closure, commutativity, and additive identity
What this lesson teaches
Integers are a complete set of numbers formed by combining whole numbers, including zero, with negative numbers. They allow quantities to be measured in opposite directions from a central zero point, such as heights above and below sea level.
Understanding positive and negative numbers
Natural numbers begin at one and continue upwards, and including zero turns them into whole numbers. Adding negative numbers in front of whole numbers creates the set of integers. On a number line, zero acts as the center, where positive numbers move in the forward direction and negative numbers move in the reverse direction. In real life, ground level or sea level is treated as zero, where positions above ground are positive and positions below ground or in a basement are negative.
Adding integers using elevation
- Starting at zero and going five steps down into a pit reaches minus five.
- Moving eight steps up from minus five equals plus three, because minus five plus eight equals three.
- Dropping down seven steps from positive three brings the position to minus four, since three minus seven equals minus four.
- Climbing four steps up from minus four reaches ground level again, showing that minus four plus four equals zero.
Subtracting integers with movement
- A car moving along a line goes forward for positive values and moves in reverse for negative values.
- A subtraction sign between two numbers causes the car to take a U-turn and face the opposite direction.
- Taking a U-turn and then driving in reverse produces forward movement, which proves that subtracting a negative number is equal to addition.
- For example, minus five minus negative three results in minus two, while minus seven minus positive five results in minus twelve.
Properties of integer addition
- The closure property means that adding any two integers will always result in another integer.
- Commutativity states that two integers can be added in any order without changing the final result.
- Associativity means that grouping or adding three integers like minus nine, seven, and minus two in any order gives the exact same value.
- Zero is called the additive identity because adding zero to any integer gives that exact same integer.