Unit 6: Integers

It can be -17 degrees C in Greenland while Male' is a warm 27 degrees C - that minus sign in front of 17 is what makes it an integer. In this unit you'll add and subtract integers, and build patterns with them.

Two friends chat on the phone. One wears 3 layers of clothing because it's freezing. The other is going for a swim to cool down! In Antarctica the temperature can drop to -88 degrees C, while in the Libyan desert it can rise to 58 degrees C. Integers help us talk about both.

A thermometer is a vertical number line. Numbers above 0 are positive (warm), numbers below 0 are negative (cold). Look where the liquid reaches - that's the temperature.

On a number line, numbers get bigger as you move right and smaller as you move left. So -3 < -1 because -3 is further left. Use this to compare and order integers.

Number patterns work the same way with integers - find the rule, then continue the pattern. Example: -15, -12, -9, ___, ___ - the rule is +3 each step, so the next terms are -6 and -3.

Integers are whole numbers and their opposites. They are either positive, negative or zero - and they do NOT have fractions or decimals. So 5, 0, -7 and -100 are all integers, but 1/2 and 2.5 are not.

A bird flies 3 ft above the ground, then goes up 5 more feet. Its new height is 3 + 5 = 8 ft. On a number line: start at 0, jump 3 right, then 5 more right. Adding positives = move right.

It is -5 degrees C and the temperature drops 2 degrees C more. Show -5 with five -1 discs, then add two more -1 discs. Altogether you have 7 -1 discs -5 + -2 = -7. Same signs? Add the numbers and keep the sign.

To add integers with like (same) signs:

Examples:

An addend is any number being added to another number.

Let's add 4 + (-6). Use 4 blue +1 discs and 6 red -1 discs. Pair them up - each pair (+1 and -1) cancels to zero. Four pairs cancel out, leaving 2 red discs - 4 + (-6) = -2.

Use arrows on a number line:

For 4 + (-6): start at 0, jump 4 right (to 4), then 6 left (to -2). So 4 + (-6) = -2.

Look at a number-line picture and write the matching sentence:

The arrows tell you the sign and size of each jump.

Find the rule first, then keep applying it. Sequence -20, -15, -10, ___, ___ - the rule is +5 each step.

The next two terms are -5 and 0.

Use +1 and -1 discs to picture each sum. Match up pairs that cancel to zero, then count the discs that are left.

Try these using a number line:

Try these real-life integer problems:

Three-step rule:

Then follow the addition rule. Example: -5 - (-3) -> -5 + (+3) = -2.

Quick reference for sign changes:

Example: 2 - 8 = 2 + (-8). Two +1 discs cancel two -1 discs, leaving 6 -1 discs -> -6.

Solve -10 - 6. Rewrite as -10 + (-6). Show -10 with ten -1 discs, add six more -1 discs -> 16 negative discs in total -> -16.

Remember: Subtracting an integer is the same as adding the opposite of that integer.

Solve 4 - 5 = 4 + (-5). Start at 0, jump 4 right (to 4), then 5 left (to -1) -> -1.

Real life: An aeroplane rises 350 ft then descends 129 ft -> 350 - 129 = 221 ft still in the air.