## Thursday, 17 October 2013

### Order of Oops-erations

We were going back over a few concepts that we thought it would be good to consolidate before the end of the school year and the kids move up to Year 7 and High School.

So we wanted to have a look at the order of operations - it's going to be an important understanding to have as the kids progress into the higher years.

## Intro to the Lesson

I wanted to start with some basic skills review so I put up 20 questions on the board. Here they are:

1 + 1 =

1 + 2 =

1 + 2 + 1 =

Subtraction questions

1 - 1 =

1 - 2 =

4 - 3 - 2 - 1 =

Combo of both

1 + 2 - 3 + 4 =

4 + 1 + 2 - 3 =

2 - 3 + 1 + 4 =

4 - 3 + 1 + 2 =

Multiplication questions

1 x 1 =

1 x 2 =

1 x 5 =

5 x 1 =

1 x 5 x 1 x 5 =

Division and multiplication questions

20 ÷ 5 =

20 ÷ 5 x 4 =

20 ÷ 4 x 5 =

20 ÷ 2 ÷ 2 x 5 =

20 ÷ 2 x 5 ÷ 2 =

I wanted to know, "Why do some of these questions have the same answers?" I was keen to explore the Associative Law and how it can be useful in the order of operations. I also wanted to see if the kids could identify how it was all related. And what problems they might encounter if they didn't follow the correct order of operations.

## BIDMAS, BODMAS, BIMDAS, PEMDAS?

I've seen all these variations of mnemonics to use to remember the order of operations. Lots of our kids had learned BIDMAS.

BIG MISCONCEPTION for our students – they are familiar with the terminology BIDMAS but 90% of the students believed that Division comes before Multiplication and that Addition comes before Subtraction.

Oops!

I think this is because they have only seen the acronym written horizontally.

So I decided to show it to them vertically:

B – brackets and other forms of parentheses
I - indices
DM – division and multiplication

Hopefully this helped them see that division and multiplication are equal, as are addition and subtraction.

## How many types of brackets are there?

I wasn't sure how familiar the kids were with brackets and parentheses so I asked the question.

One student replied, "Well on a computer you have the round ones, the square ones and the wiggly ones."

Good thinking.

We ended with a game of BIDMAS Bingo - and then had an argument about how 32  does not equal 6.

Oops!

1. Fascinating post, Bruce. I had a similar session with my class recently and found this video to be appropriate, The Order of Operations is Wrong: http://youtu.be/y9h1oqv21Vs

2. I really don't like that video - perhaps I didn't pay attention (Sunday afternoon beers!) BUT there is no doubt that the Order of Operations includes a very strong "From left to right"
So the first example in that video can be simplified by the youngest students!
In the USA we generally use the acronym PEMDAS. the P is for parentheses, but really it should be GEMDAS, grouping symbols come first!

I agree with you Bruce , writing the acronym vertically and stressing from left to right clarifies the order of operations.

Any comments you would like to make?