How to teach negative numbers

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, money owed, or floors below ground level. The number line is the clearest model for them.

Negative numbers are usually introduced in Grade 5 and Grade 6. Students start with real contexts like temperature and debt, use a number line to order and add and subtract integers, and later meet multiplying with signs.

Because -5 sits further to the left on the number line than -2, and further left always means smaller. This reverses the whole-number intuition that a bigger digit means a bigger number, which is why thinking -5 is greater than -2 is such a common mistake.

A horizontal number line with zero in the middle makes 'less than zero' visible and shows the direction of each move. Moving right adds and moving left subtracts, wherever you start. This turns abstract sign rules into concrete jumps that children can see and follow.

Subtracting a negative is the same as adding, so 5 minus negative 3 equals 8, not 2. On the number line, taking away a negative move sends you to the right. Losing track of the sign here, and getting 2, is one of the most common integer errors.

When multiplying, a negative times a negative gives a positive, so negative 3 times negative 2 is 6, while a positive times a negative is negative. This sign rule is taught last, after adding and subtracting on the number line are secure, because it is more abstract.

In temperatures below zero, money owed or a bank balance in the red, floors below ground in a lift, and points lost in a game. Anchoring integers to these familiar contexts first makes 'less than nothing' concrete before the number-line work begins.