Step 9 Objective

Use efficient methods to add, subtract, multiply and divide fractions.

Examples of what pupils should know and be able to do

Add and subtract more complex fractions, e.g. Eleven eighteenths + Seven twenty fourths, including mixed numbers.
Solve problems involving fractions, e.g. In a survey of 24 pupils One third liked football best, One quarter liked basketball, Three eighths liked athletics and the rest liked swimming. How many liked swimming?

 

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.

Two eighths + Three sixths = Five fourteenths

Ask them to talk you through the mistakes and how they would correct them.
The answer is:

Three eighths

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.