Research-based guidance and classroom activities for teachers of mathematics

Using algebra to reason

Using Algebra to reason is a theme within quantities and algebraic expressions. Links to relevant activities and resources are on the right hand side of this page. 

Algebra lets us apply additive and multiplicative relations to solve problems where we don’t know everything. For example:

  • If I have four more sweets than you have, then there is a method of equalising the amount so long as you know the relation of ‘difference’ – and we don’t have to know exactly how many sweets we have in total
  • If I know I run twice as fast as you on average, then I know I need half the time to run the distance - without knowing the total time or distance.
  • If I know that a + b = c, then: b + a = c      c = a + b      c = b + a    
    c – b = a     c – a = b     a = c – b     b = c – a
  • Associativity: a + (b + c) = (a + b) + c
  • Distributivity: a(b+c) = ab + ac
  • If I know that ab=c, then: ba=c, c = ab and c = ba, c/b=a and c/a=b
  • (a + d) – (b + d) = a – b
  • If a > b and b > c, then a > c
  • If a = 2b and b = 2c then a = 4c