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Number lines

This activity uses eighths, but can be adjusted to use other fractions and diagrams. Examples of same denominator problems are available.

Together the class constructs a number line from 0 to 2, labelled with eighths. The line should be labelled with both improper fractions and mixed numbers.

Present a contextual problem.

The family bought some pizzas. I ate \(\frac{4}{8}\) of the pepperoni pizza and \(\frac{3}{8}\) of the ham and pineapple pizza. How much pizza did I eat?

  • Ask students to predict whether the answer will be less than, equal to, or more than one, and explain their reasons.
  • Use questioning to scaffold the modelling of the problem with circles partitioned into eighths to represent the pizzas.
  • On the number line, mark the two jumps to \(\frac{7}{8}\). Display the equation \(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\).
Number line between 0 and 1,divided into eighths, showing ‘jumps’ from 0 to 4/8 then a further 3/8 to 7/8.

Student work sample showing addition of fractions with related denominators.

Extend the problem.

Later I ate \(\frac{2}{8}\) of the vegetarian pizza. How much pizza had I eaten altogether?

  • Ask students to predict the answer, then model with the circle diagrams and the extra jump on the number line. Discuss the equivalence of \(\frac{9}{8}\) and 1\(\frac{1}{8}\).
  • Display the equation: \(\frac{4}{8}\) + \(\frac{3}{8}\) + \(\frac{2}{8}\) = \(\frac{9}{8}\) = 1\(\frac{1}{8}\).
  • In pairs, students work on a few similar problems, recording their diagrams and solutions. You might find the recording template useful.

As a class, review the solutions and discuss strategies for completing similar additions without the use of diagrams or number lines.

A similar approach can be used with subtraction problems.