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.

Hey look! They've got the same answer!

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!