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.

Curriculum links

Year 6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers