## Saturday, September 29, 2012

### Just Warming Up, Backwards

This past week I posted a warm-up for the students as they came into class. It read:
This is the second line of an 'order of operations' question.
What might the first line be?
=26 - 84 ÷ 3

The students had reached a certain comfort in their Order of Operations ability and had seen most questions that I had already planned on presenting to them. But for this warm-up I thought I might try something that Marian Small often suggests. Give them the answer (or in this case the second line) and not the question.

Examples of this technique are scattered throughout her book,
Good Questions: Great Ways to Differentiate Mathematics Instruction.

I have a copy on my desk for quick inspiration when I'm looking to start building something new.

This was not the first "work backwards" warm-up I've given my students. But some still looked at it for a minute before diving in. But then answers (or questions rather) were being offered with some ease. Very few students (about one per class) actually misjudged the warm-up and simply solved the next two lines.

• it was open and offered lots of options (thanks Marian)
• it gave them a new look at and old question. After all, they saw bedmas last year didn't they? (pemdas for those in the US)
• they were impressed by the number of solutions and quickly understood that there were infinite solutions
• it didn't take much time and provided lots of discussion including some valuable mistakes

Are there any other points that make this warm-up useful?
What can I do to improve it? Or make them see bedmas without the same old question?