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.


pig-thumbTrevor 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.


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?


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.

math quote

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!


About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
This entry was posted in Problem Solving, Teaching Ideas and tagged , , . Bookmark the permalink.

One Response to What If ?

  1. Kevin Cunningham says:

    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!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s