Lessons · Teaching · negative numbers and the number line
Negative numbers are directions, not smaller positives
A negative number is a position to the left of zero on the number line. Adding moves right, subtracting moves left, and subtracting a negative moves right because you are removing a debt. Multiplying two negatives gives a positive because you are reversing a reversal.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Temperature, elevation, and an overdrawn account are all the same line, and a pupil who can walk the line can answer every question on it without a rule. The rules are what people forget in an examination hall; the line is what they can rebuild.
How to think about it
Draw the line and walk it. Start at the first number, face right for plus and left for minus, then walk the second number, turning around if it is negative. For multiplication, count the negative signs: an even count gives positive, an odd count gives negative.
Worked example
-3 + 5: start at -3, move 5 right, land on 2Crossing zero is the step that feels wrong and is not.
4 - 7 = -3: start at 4, move 7 left, land three past zeroThe answer being below zero is not an error.
5 - (-3) = 5 + 3 = 8: removing a debt of 3 leaves you 3 better offTwo minus signs next to each other become a plus.
-2 x -6 = 12, because two negative signs cancelAn even number of negatives gives a positive, an odd number a negative.
Your turn
Name the direction on a number line that subtraction moves you.
Subtracting moves you to the
Solve one, graded on the server
The trap
Reading -5 as bigger than -2 because five is bigger than two. On the line, -5 is further left, so it is smaller. In a cold week, minus five degrees is the colder day.