 Know and use the order of operations including brackets

Examples of what pupils should know and be able to do
Find mentally or use jottings to find the value of:
$\begin{array}{cccc}16\xf74+8& & =& 12\\ 16+8\xf74& & =& 18\\ 14\times 7+8\times 11& & =& 186\\ \frac{100}{4\times 5}& & =& 5\\ 32+13\times 5& & =& 97\\ ({3}^{2}+{4}^{2}{)}^{2}& & =& 625\\ \frac{({5}^{2}7)}{({2}^{2}1)}& & =& 6\end{array}$
 Secondary mathematics exemplification: Use the order of operations, including brackets
 Assessment example: Factors and multiples: Anand (PDF720 KB) Attachments
Probing questions
 What clues do you look for when you are reading a calculation and deciding the order of operations?
 What rules do you follow?
What if pupils find this a barrier?
The most common mistake is for pupils to read from left to right and to 'ignore' the order of operations.
Give pupils practice in 'reading' a calculation. Get pupils to talk through what a calculation is asking them to do.
Use a basic and a scientific calculator and explore the different answers given to questions such as $2+4\times 3$.
 Check a result by considering whether it is of the right order of magnitude and by working the problem backwards

Examples of what pupils should know and be able to do
 Secondary mathematics exemplification: Checking results
 Assessment example: Multiplication and division revision: Pauline (PDF123 KB) Attachments
Probing questions
 Roughly, what answer do you expect to get? How did you come to that estimate? Do you think your estimate is higher or lower that the real answer? Explain why.
 How would you use inverse operations to check that a calculation is correct?
What if pupils find this a barrier?
It can be helpful to give pupils some worked examples to mark and to identify the mistakes.
Encourage pupils to approximate first before working out answers.