How to teach negative numbers

Grade 5 to Grade 6

Integers are the whole numbers extended below zero: ..., -3, -2, -1, 0, 1, 2, 3, ... Negative numbers describe amounts less than nothing, such as a temperature below zero, a debt, or floors below ground level. The number line is the single best model, because it makes 'less than zero' and the direction of each move visible.

How to teach it

1. Anchor to real contexts first: temperatures below zero, money owed, floors in a basement, points lost in a game.
2. Use a horizontal number line with zero in the middle. Moving right is adding, moving left is subtracting, whichever side of zero you start on.
3. Show that -5 is less than -2, because it sits further left. This reverses the intuition that a bigger digit means a bigger number.
4. Teach adding and subtracting as moves on the line: -3 + 5 lands on 2; -3 - 4 lands on -7.
5. Introduce multiplying signs last, with the rule that two negatives make a positive (-3 x -2 = 6) and a positive times a negative is negative.

Common mistakes

• Thinking -5 is greater than -2 because 5 is greater than 2.
• Losing track of the sign when subtracting a negative (5 - (-3) = 8, not 2).
• Assuming subtracting always makes a number smaller, which fails once negatives are involved.
• Confusing the minus sign for subtraction with the sign that marks a negative number.