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 $\frac{4}{8}$ + $\frac{3}{8}$ = $\frac{7}{8}$.

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.