Order of Operations

Years 2 - 6

Summary

Children discover that all calculators don't give the same answer - and, in fact, that many calculators give wrong answers. Further discussion leads to building a Poly Plug model of how the different types of calculators do their calculations.

Materials

  • At least one MathMaster calculator (or other brand that gives correct 'order of operations' answers) and at least one simple four function calculator
  • One Poly Plug per child
Note
To discover whether a calculator has the Algebraic Operating System (AOS) built in press these buttons in this order: [2] + [3] x [5] [=] ... The correct answer is 17. If your calculator gives the answer 25, which is wrong, then it will give wrong answers to every calculation that mixes +/- with x/÷.		 MathMaster
All calculators are not the same.
Read our advice here.

Procedure

Ask children to enter an equation such as the following into their calculator in the order shown:
6] [+] [3] [x] [4] [=]
Write it on the board as you say it.

Create a bit of drama by asking them to call out their answer at the same time. Notice that there appear to be two answers in the room.

I heard two answers. That can't be right. Let's try that again.
Again there will be two answers, so write them both as answers with question marks.
Only one of these answers can be correct. So which one is it???
 

Content

Listed alphabetically.
Primary content in bold.
  • mathematical conversation
  • operations - whole number
  • order of operations
  • recording - written
  • using brackets
  • visual & kinaesthetic representation of number
After discussion, explain that long ago mathematicians had to decide what to do about a situation like this. They decided that multiplication (and its partner division) should be more important than addition (and its partner subtraction). Challenge the children to make a picture with their Poly Plug of how each machine is calculating. For example:

ORDINARY
CALCULATOR

  ORDER OF OPERATIONS
CALCULATOR

Suppose we only had an ordinary calculator. How could we use it to get the correct answer to our calculation?
This will lead to discussion of how using brackets avoids confusion in a written calculation and how the memory buttons could be used with the ordinary calculator to break a calculation into smaller parts. Encourage students to think of situations (number stories) where it would be appropriate to use (6 + 3) x 4 and others where it would be appropriate to use 6 + (3 x 4).
NB: Please share examples from your classroom of children's interpretations of these expressions.

Return to Calculating Changes Activities

Calculating Changes ... is a division of ... Mathematics Centre