Open-ended maths questions!

Last week I taught my class about open and closed questions, and also had my maths observation where I then immediately tried to implement some of the feedback.

Today I combined both of those things, and gave my class an open-ended maths question.

One of the pieces of feedback I was given was to move onto broader, group word problems as my class was ready and able to do them now they have begun talking about their thinking and working collaboratively with confidence. 

Every maths problem I have ever seen and used in maths are closed questions, where one particular answer is sought, so using an open-ended question was quite different for me and I wasn't sure how the students would respond.

My word problem was 

Miss Ashley wants to order pizza to share. If each of her friends will eat 1/4 of a pizza, how many pizzas does she need to order?

Immediately, a student asked 'Miss how many friends is there?'. We broke down the problem (ala the other piece of feedback I have implemented) and talked about why I didn't tell them how many friends I had on purpose. I asked them 'what kind of question is this' and they could instantly tell me it was an open question because there was more than one answer. So proud! 

Building on their understanding of open questions, they knew they could find more than one answer, and were eager to give it a try.

 It was interesting to see the different strategies they used. As you can see, 

- one group got distracted by Miss Ashley's friends and spent maybe a bit too much time drawing pictures of the friends (bless them!)

-most groups drew the pizzas or represented them by squares with four sections to show the quarters and counted out a quarter for each person until they had enough pizzas for the friends. 

-one group drew the pizzas, labeled each quarter, then had to 'name' each piece of pizza with an initial of one of the friends to ensure they didn't miss anybody.

-one group didn't draw any pizzas, and used their knowledge of doubles and their 4x tables. They knew that you need 4 pieces of pizza/1 whole pizza per 4 people, so they found one quarter of the number of people as their number of pizzas required.

 We came back together and shared all our different answers. I felt that the students were more open to sharing their thinking with an open ended question, as there wasn't as much chance they would be 'wrong' (compared to a closed question, where there was only one answer that could be right.)

Every group shared at least one answer, and the group who used their multiplicative knowledge could explain to the rest of the class what they did as well which was awesome!

I also loved how this activity cemented and demonstrated what the students have been learning about fractions for the past six weeks. Most of them instantly knew that 1/4 means you need 4 equal groups, they knew that 4 quarters made one whole pizza, and that you could have lots of quarters that then made lots of whole numbers.

Next time I use an open-ended question, I think I will use one that does reinforce what they have been learning, but frames it in a different way so they are challenged more by it. 

This could even be the wording the problem uses.