Representating the denominator as a thing

The number at the bottom of the fraction is the “sort of thing” that the fraction represents. If that number is a 2, then the “thing” is a semicircle; if that number is a 4, then the “thing” is a quadrant; if that number is a 8, then the “thing” is a pizza slice; if the number is a 10, then the “thing” is a slimmer pizza slice.
Teaching children to imagine fraction in terms of these shapes relieves them from the abstract nature of numbers. When adding fractions this approach allows the pupils to see why it is allowable to have some numbers in the denominator of the answer, but not others. Puppet Maths presents children with these pictures so that they can imagine what their calculations are asking of them.