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!**

I love it! What if questions have begun some of the richest and deepest thinking in my classroom! I find even normally quiet students want to share their opinion about a effective question like this.

Thanks for the reminder!