Mixing operations

Multi-step calculation problems are very common in daily life.

For example, you might purchase four T-shirts at $15.00 each and six pairs of socks at $5.00 per pair. To find the total cost of the items you need to do several things.

• Decide on the calculations you need to perform and the order you will do them in.
• Make strategic decisions about the best way to carry out the calculations.
  In multi-step problems there are often many choices of strategy.
• Find ways to 'park' the information so you can manage the memory load.

In the clothing example, you need to:

• realise that the total cost of the T-shirts can be found by using 4 $\times$ 15 = 60 and the total cost of the socks can be found by using 6 $\times$ 5 = 30 
• add these amounts to get a total cost.

This is not the only strategic choice you could make.

If you treat one T-shirt with one pair of socks as a combination you can solve the problem using 4 $\times$ (15 + 5) + 2 $\times$ 5 = $90.00.

Along the way to your solution you might jot down important information such as the result of each multiplication.

You can download a table of types of combined operations problems to create different problems for your students.