Adding and subtracting integers
Temperatures drop below zero and scores fall behind. How do you add and subtract numbers that can be negative?
Where you are 2 inside
What this area is about
An integer carries a size and a direction. Adding two of them combines two moves that may point opposite ways, so one can partly cancel the other. Subtracting asks for a difference even when the number taken away is negative. This area makes both work for every pair of integers, not only for whole numbers.
How these fit together
A procedure. Adding integers reads each integer as a move along the number line, then as counters that cancel in pairs, and turns both pictures into a rule. When the signs differ, the sum is the larger absolute value minus the smaller, with the sign of the number farther from zero.
A concept. Subtracting integers shows that a - b = a + (-b) for all integers a and b, so every subtraction becomes an addition. It then uses differences to find distances on the number line and changes in height and money.
A path through it
Adding first, then subtracting, since the second turns every subtraction into a sum of the first kind.
Finish here and you are ready for multiplying and dividing integers, order of operations with negative numbers, combining like terms with negative coefficients, and temperature changes below zero.