Questions we ask . . .
. . . to promote problem solving:
- What do you need to find out?
- What information do you already have?
- What strategies do you plan to use?
- Will you do it mentally, or with pencil and paper?
- Do you plan to use a number line, tape diagram, or another visual representation?
- What tools do you think you will you need?
- What do you predict or estimate the solution will be? Where did your prediction come from?
- How do you see or imagine the problem in your mind?
. . . to help when we feel stuck:
- How would you describe the problem in your own words?
- Can you break the problem into smaller parts that you can understand?
- Are there any details that you know for sure?
- What details are you still unsure about?
- Where could you start?
- Could you try it with a simpler number? Fewer numbers?
- Have you tried using a number line, tape diagram, or table?
- Would it help to draw a picture or another visual representation?
- Can you guess and check?
- What have you already tried?
- Have you compared your work with anyone else? What did other members of your group try?
. . . to make connections among ideas and concepts:
- How does this method relate to . . . ?
- What ideas that you have learned before were useful in solving this problem?
- What uses of mathematics have you noticed out in the world lately?
- Can you find an example of . . . ?
- Have you made a discovery like this before?
- Where have you seen symbols like this before?
. . . to encourage reflection:
- How did you arrive at your answer?
- Does your answer seem reasonable? Does it make sense? Why or why not?
- Did you make any interesting mistakes?
- Can you explain your method and why it works?
- What if you started with ___________ rather than ___________ ?
- How else could you have . . . ?
- What have you learned or discovered today?
- What are you still confused about?
- Did you learn any new words today? What do they mean? How do you spell them?
- What are the key points or big ideas from the lesson?
- Why is that true?
- How can you prove it?
- Can you prove it visually?
- How did you reach your conclusion?
- Can you make a model to show what you are saying?
- Is that true for all cases, or can you think of a counterexample?
- What assumptions are you making?
- How did you know which . . . ?
- How did you know when . . . ?
- How did you know where . . . ?
. . . to think about the progress we are making:
- Can you explain what you have done so far? What else is there to do?
- Why did you decide to use this method?
- Can you think of another method that might have worked?
- Is there a more efficient strategy?
- What do you notice when . . . ?
- Why did you decide to organize your results like that?
- Do you think this would work with different numbers?
- Have you thought of all the possibilities? How can you be sure?
. . . to collaborate and bring our ideas together:
- What do you think about what ___________ said?
- Do you agree? Why or why not?
- Does anyone have the same answer, but a different way to explain it?
- Are there any other ways to solve this problem?
- Do you understand what ___________ is saying?
- Can you convince the rest of us that your answer makes sense?
- Can you justify your thinking?
- How can that idea be represented in different ways?
. . . to promote curiosity and imagination:
- Can you predict what would happen if . . . ?
- What would you do if ___________ changed?
- Do you see a pattern? Can you explain the pattern?
- What are some possibilities here?
- Can you predict the next value? What about the last one?
- What decision do you think they should make?
- If I ___________ , what will happen?
Prompts we use . . .
. . . to share multiple representations:
- I decided to use a ___________ to show . . .
- A [graph, table, picture, diagram, etc.] shows this the best because . . .
- I could make this a little clearer by using . . .
- The math vocabulary that would help someone understand what I did are . . .
- The way I see this in my mind is . . .
. . . to reflect on our work:
- A question I had was . . .
- I was feeling really . . .
- I decided to ___________ because I was thinking . . .
- I found ___________ challenging because . . .
- The most important thing I learned from this is . . .
. . . to make connections:
- This new math idea or concept is like . . .
- I did something like this before when . . .
- We do this at home when . . .
- I remember when we . . .
. . . to share feelings, attitudes, and beliefs:
- What I like best about mathematics is . . .
- The hardest part of this has been . . .
- I need help with ___________ because . . .
- Mathematics is like ___________ because . . .
- Today, I felt . . .
- My favorite part of ___________ was . . .
. . . to explain our thoughts and ideas:
- I solved the problem by . . .
- The steps I followed were . . .
- My strategy was successful because . . .
- Pretend you are explain to a fifth grader, or someone who was absent from class
- Draw a picture to show how you solved the problem
. . . to prove our process and our reasoning:
- I know this is true because . . .
- My answer makes sense because . . .
- This would work with different numbers because . . .
- Let me show you how I did it!
- Before, I used to think ___________ but now I understand differently that . . .
- I was able to prove my original estimate of ___________ by . . .