Negative Numbers Worksheets Generator

Two kinds of question

Arithmetic gives adding and subtracting problems involving negative values. Compare gives two numbers and asks for the right symbol between them. Mixed is half of each.

The range runs from −20 to 20 by default, twenty questions, answer key included.

Comparison first, always

It looks like the easier mode and it is the more important one.

Nearly every mistake with negative numbers comes back to a broken mental picture of where they sit. A pupil who thinks −8 is bigger than −3, because 8 is bigger than 3, will get arithmetic questions wrong in ways that look random and are not. Comparison work fixes the picture, and the arithmetic gets easier by itself afterwards.

Draw a number line on the board and leave it there. Further left is smaller. That is the entire rule and pupils need to see it several hundred times.

Subtracting a negative

The step everyone stumbles on, and the tricks people teach for it are mostly bad.

"Two minuses make a plus" is true here and false for multiplication in the pupil's head three weeks later. Better to keep it concrete: subtracting means taking away, and taking away a debt leaves you better off. 5 − (−3) is 8 because removing a debt of 3 from a balance of 5 gives you 8.

Money and temperature are the two contexts that reliably work. Both go below zero in ordinary life and both have a direction pupils already feel.

Setting the range

Ten either side is enough for first work, and it is small enough that the number line can be drawn along the top of the page.

Twenty is the default and covers most classroom needs. A hundred is stretch work and mostly tests arithmetic rather than the concept — if the negatives are understood at 20 they are understood at 1000, and the extra difficulty is in the adding.

Where it shows up next

Coordinates in all four quadrants. Temperature and elevation. Bank balances. Any algebra at all, where a mis-signed term propagates through six lines of working.

The pupils who struggle with algebra at fourteen are very often pupils who never quite secured negatives at eleven, and this is the cheapest place to fix that.

Level

Introduced around ages ten to eleven and worth revisiting every year afterwards. Twenty questions a day for a week costs almost nothing and settles it.