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Grids and jumps

Work through at least one example with the class (e.g. \(\frac{1}{6}\) + \(\frac{2}{3}\)) demonstrating the construction of an appropriate labelled grid diagram, a number line showing the jumps and an equation.

Examples of addition and subtraction of fractions with related denominators using grids and number lines

Student work sample.

Focus on identifying the multiplicative relationship between the denominators. For example, if working with sixths and thirds, recognising that 2 \(\times\) 3 = 6 leads to constructing a 2 \(\times\) 3 grid to show both the sixths and the thirds.

Although using a 6 \(\times\) 3 grid will also lead to a correct solution, encourage the students to find the smallest factor pair (making the smallest grid).

Select and prepare several sets of the task cards.

  • Pairs of students select a task card and work together to present a solution.
  • Grid paper can be used to support the construction of diagrams and number lines.
  • Pairs who have worked on the same task cards can compare solutions and explain any differences.

As a class, discuss strategies for solving the addition or subtraction tasks without supporting diagrams.

In small groups students discuss the following scenario.

Someone in the class gave this solution: \(\frac{3}{10}\) – \(\frac{1}{5}\) = \(\frac{2}{5}\).

How would you explain why the answer is incorrect? Share some explanations as a class.

Curriculum links

Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators