## What If ?

Andrew Mathews Cartoon

These two little words are very powerful in teaching and learning Mathematics.

An Open Ended Question can easily lead to an investigation by simply saying:  “What if …….”

I encourage students to give more than one answer to an open ended question because:

1. I want them to THINK and do more Mathematics; and

2. I want them to stop thinking that Maths problems always have ONLY one answer.

### EXAMPLE QUESTION

Trevor from Tatura gets a pig for his birthday. Since it’s ok in Tatura to have pigs, he wants to build an enclosure for it in his back yard. The perimeter of his enclosure is 30 metres.

WHAT MIGHT ITS AREA BE?? WHAT WOULD THE LARGEST AREA BE??

Many students will assume a rectangular enclosure, so the teacher may have to scaffold by asking: “What if the enclosure is some other shape other than a rectangle?”

The first question is open ended because many answers are possible depending on the shape chosen.

WHAT IF the dimensions of the enclosure are all integers?

### WHAT IF  IN LESSON DESIGN

The power of Maths teachers blogging is in the sharing of ideas. This often results in a teacher taking another teachers idea and asking “What if………………..

Example 1

Rebecka Petersen‘s post: Math History – We’re all learning here, was read by Karen Fouss. She thought – what if I do the same thing with quotes? See her post titled Guilty Pleasures.

Example 2

In my previous post: Teaching in 2013 – I can’t wait, I adapted Paul Bogush’s script to make it more relevant to me.

So I wish that 2013 continues to be an excellent year for sharing ideas via Math blogs; and lets ask WHAT IF? often!