4 mistakes learners make with adding and subtracting negatives, each one named and explained.
The sign is part of the number, and every operation is a walk along the number line in one direction or the other.
A temperature rising from minus 6 by 9 degrees is given as minus 3.
Working with a negative starting point makes it unclear which way rising moves you.
Question. -6 degrees rising by 9 degrees
A common answer. -3
The answer. 3
Why. Rising 6 degrees reaches zero, and the remaining 3 takes it above.
Draw the number line and step along it. Rising always moves right, whatever you start from.
Asked to order -3, -1.5 and -0.2 you put -0.2 first, then -1.5, then -3.
Three is bigger than two, and it takes a while for the number line to overrule that.
Question. -3 and -0.2
A common answer. -0.2 is smaller, because 0.2 is smaller than 3
The answer. -3 is smaller
Why. -3 is further left on the line, and further left always means smaller.
For negatives, the bigger the digits the smaller the number. Draw the line if there is any doubt.
-3 - -2 is answered as -5.
Two minus signs look like more taking away, so the total gets pushed further down.
Question. -3 - -2
A common answer. -5
The answer. -1
Why. Taking away a debt of 2 leaves you better off, so you move up the line rather than down it.
Taking away something negative sends you the other way.
-5 + 3 is answered as 8, or as 2 with the sign left off.
The digits are the familiar part, so the minus sign gets treated as decoration rather than as part of the number.
Question. -5 + 3
A common answer. 8
The answer. -2
Why. You start 5 below zero and move 3 steps towards it, which leaves you 2 below.
The sign is part of the number, not a label stuck on the front of it.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.