The mathematics education group develops models and resources for professional development of in-service teachers.


Worksheets on Integers

One of the difficulties that children face is in interpreting negative numbers. What does ‘−2’ exactly
mean? There are broad senses in which negative numbers or more generally integers (positive,
negative numbers and zero) are interpreted.

1. As a change: Change includes increase or decrease, movement up or down (or forward and
backward) or positive or negative growth (for example, total annual sales of a company).
Think of situations which involve change and can therefore be described using integers. The
situations should be meaningful and interesting. Some suggested examples are given below.
Think of more such examples.

  • Increase/decrease: Make a table of the weight gained by a baby every week(may benegative, what does it indicate?).
  • Movement forward/backward or up/down: Change in tennis ranking of a tennisplayer, change in run rate from over to over.Make a presentation of such data in a way that would be interesting to students.

2. As a state: We can specify the state of something we are interested in using integers but
only when it is meaningful to talk about positive and negative states.
Think of such situations where integers represent sate. Some suggested examples are given
below. Think of more such examples.

  • Position of a lift in a building which also has basement floors
  • Temperature of water in a freezer
  • Again think of ways in which such situations can be presented in an interesting way to students.

3. As relation between numbers and quantities: An important point here is that this is a
directed relation. The relation makes sense if we distinguish the direction of the relationship
and use positive and negative numbers to indicate it.
Consider these two examples:

  • Me and my sister are standing in a queue to buy ice-cream. How far is my sisterfrom me?
  • Me and my sister are on different floors of a tall building with several basementfloor levels for parking. How far away is my sister from me?

Why is it meaningful to give the answers to these questions using integers? Is there any
difference between the two examples? Think of more examples where relations can be
represented using integers.

Worksheet on integers

Worksheet for problems to solve

Worksheet on integers: Data Intereptation

Lift Problem


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