Introduction to algebra

Algebraic thinking - part 1

Genuine algebraic thinking starts in the exploration of number patterns in the early years of primary school. Below are some examples of things that children up to the age of 8 years might do that are the beginnings of thinking algebraically.

  • Explore and discuss patterns in odd and even numbers
  • Understand a statement like ‘all numbers ending in 5 or 0 can be grouped into fives’ and check whether this is true in particular cases, using counters
  • On a grid 3 squares wide, colour in the numbers 1, 4, 7, 10, 13 16 … and describe the pattern that emerges (see Figure 20.1)
  • Recognise the relationship between doubling and halving
  • Put the numbers from 1 to 10 into a ‘double and add 1’ rule and discuss the pattern of numbers that emerges

Examples such as these, none of which uses letters for numbers, are about making generalisations. This, as we shall see, is the essence of algebra.