Most times, we give students questions to answer. They seldom get to ask the questions – except to indicate confusion or lack of understanding. Last year, I wrote a post on another blog Becoming a Better Math Teacher, about how to engage students in problem solving from the start. It is through the method of “I Notice…” and “I Wonder…”.

This was taken from NCTM’s Palette of Problems in the September 2014, Vol. 20, Issue 2.

*Justine works at a clothing store that is having a one-day 60% off sale. A customer presents a coupon for an additional 40% off a single item, which is a dress she has picked out. She expects to receive the dress for free. *~~How should Justine convince the customer that the dress is not free? What percentage of the original price of the dress should the customer have to pay?~~

**I Notice…**

*there are two discounts 60% and an additional 40%*
*Justine thinks she will get the dress for free*

**I Wonder…**

*how much was the actual discount?*
*does it make a difference if the dress is $100 or $200?*
*if the price will be the same if the order of the discounts is changed?*

Here is another problem that we could edit. This one is from the University of Waterloo Problem of the Week, 5/6.

*Moe helps out the seniors Larry and Curly by mowing their lawns during the summer. He can mow a square lawn with side 30m in 45 minutes. **If he mows at the same rate, how long would it take Moe to mow a square lawn with a side length of 60 m?*

*I Notice…*

*Moe can mow a square lawn with side length 30 m in 45 minutes*

**I Wonder…**

*how long would it take for him to mow a rectangular lawn that is 20 m x 30 m?*
*how much area can he mow in an hour?*
*how many square lawns with side 20m can he mow in an hour?*

As you can see, the possibilities are vast. Students might need some guidance at first when asking questions. In the end, students take more ownership and are more likely to answer questions that they have asked.

Good luck with that and let me know if you have tried this and you can share how you edited the original problem to come up with interesting questions to answer.

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