Step 9

Examples of what pupils should know and be able to do

Add and subtract more complex fractions, e.g. $\frac{11}{18}+\frac{7}{24}$, including mixed numbers.

Solve problems involving fractions, e.g. In a survey of 24 pupils $\frac{1}{3}$ liked football best, $\frac{1}{4}$ liked basketball, $\frac{3}{8}$ liked athletics and the rest liked swimming. How many liked swimming?

• Secondary mathematics exemplification: Calculate fractions of quantities; add, subtract, multiply and divide fractions

Probing questions

See also probing questions for Step 8.

• If I divide one fraction by another I will always get a smaller answer – true/false? Why? Explain.
• Give pupils some examples of addition, subtraction, multiplication and division of fractions with common mistakes in them. e.g.$\frac{2}{8}+\frac{3}{6}=\frac{5}{14}$. Ask them to talk you through the mistakes and how they would correct them.
• The answer is:$\frac{3}{8}$. What is the question?

What if pupils find this a barrier?

Ask pupils, in pairs, to discuss and create their own concept maps for fractions. You may wish to provide key words, such as: equivalence, fractions as operators, cancelling.

Discuss the important components of the concept map as a whole class (or with a targeted group). Help them to identify areas of weakness. Either support pupils in their own research to address weaknesses or refer back to appropriate steps to explore strategies to overcome them.