Often the most difficult part of problem-based teaching is knowing which questions to ask. This questions is designed to be a starting place for a great source of questions. I hope that teachers will email their own great questions in so that we can add them to this bank. In addition to this, make sure that you read the section on Asking Questions before using this questions bank. It contains many different question types, and examples of where each is used.

Questions that Tierney asked in a recent lesson on Fractions:

*Questions to begin a lesson and to help students to take risks:*

- Do I care if you’re wrong anyway?
- Can you see the amount of thinking that you did?
- Can you tell me what stuff you already know about …?

*Questions to elicit prior knowledge about a topic and to consolidate understanding:*

- Do you know what that would be the same as?
- How come?
- What do you mean? Give me an example …
- Why can’t I call it…?
- Do you know what that would be?
- Like what?
- I’m confused … tell me again … Like that?
- What do you mean? Tell me about your thinking.
- Does that look right to you?
- What have we worked out?

*Leading Questions on a specific topic (e.g. 1/3 + 1/5):*

- If I have a cake and I eat 1/3 of it and then I ate 1/5 of it, how much did I eat? Draw a picture.
- Is that a third (student drew picture of uneven sized thirds)? Imagine that this is a very yummy chocolate cake. This one is my third! Does that seem ok to you? Is that fair?
- So what do you know about fractions? (They need to be equal sizes)
- I ate 1/5 of the cake and then ate another 2/5s of the cake. How much did I eat? What happened to the numbers? So do you think it’s ok if I eat 1/3 of the cake and then 1/5 of the cake and that makes 2/8 of the cake?
- It’s a bit tricky fitting all the pieces on when they are different sizes! Do you think I can decide that since it’s not really fitting that I could just get another whole cake and eat a fifth of that one instead? (went back to example of ½ + ¼ being on the whole cake)
- So are you adding 1/3 and 1/5
^{th}any more when there are 2 cakes? - How should I have done it? Just cutting it differently?
- Can we have 2 different cakes?
- Who’s finding circles difficult? Is there a different shape you could use? Ok, let’s all try it with rectangles instead.
- What’s the problem with what I did? Can you see the problem here?
- Is it OK to have different size bits?
- Started with a rectangle broken into 3 parts and then added 2 more wedges (to “turn it into fifths”). What do you think? Is this still 1/3 if I get extra bits?
- Do you think you could get extra cake because the fifths won’t fit?
- Is there a way that you could cut it differently to get all the pieces on the one cake?
- Is there a different way I could cut the cake to show thirds?
- Can you draw a picture that shows thirds in a different way?
- You have your cake with thirds, how could you cut it to now show fifths?
- How else could you show fifths on the same cake? Remember that you need to have the same sized pieces.
- Can you see a problem here? Yes, you ate that piece twice. That seems really messy to me! So what could you do instead?