Guiding Questions

Tips for Starting:

After observing students and the work/creations they have made, select 2-3 exemplars of student thinking to share with the entire group:

*Basic - ‘reachable’ for most students and a strategy that perhaps many others thought of or tried.

*More advanced - stretches thinking a bit for the group and introduces another strategy for the group to try/think about.

*Most advanced - stretches thinking even further, but may not make sense to most kids right away.

*Sharing may be in one day or spread over several days.

Teacher talk is minimal - it is only to guide the discussion.

Promote a community of learners that listens actively without evaluation.

Provide lots of wait time.

Summarize main ideas and identify future problems. Questions can clarify children's ideas, emphasize reasoning, or encourage student-student dialogue. See below for some questions to try that have been gathered from a variety of source such as Taking Shape, Becoming the Math Teacher You Wish You Had, and more.

"Experienced math teachers have mastered the art of keeping their faces curious and interested - but neutral - so students can't use them as answer keys." (Tracy Zager, Becoming the Math Teacher You Wish You Had, 2017, pg 68)

Click here to print these questions out for easy reference.

Effective guiding questions...

• • What math do you see in this design? project? structure?

  • How did you decide what to do?

  • Can you tell us more?

  • Did anybody look at (x) in a different way?

  • What can you tell us about (today’s topic)?

  • Do you have more questions after doing this? What are you wondering about now?

  • Can you explain in your own words what _____ just said/was thinking?

  • Raise your hand if you used a similar strategy.

  • How could we give them a clue to figure it out without telling them the answer?

  • Can someone explain what is the same about Group 1 and Group 2’s thinking/strategies?

  • Is there another way we could do this? Solve this?

  • Which strategy made sense to you? Why?

  • What problems did you have? How did you overcome them? How did you figure out that it was not going to work?

  • Explain how you know that your answer is correct.

  • Can you give an example?

  • Do you agree or disagree with ___? Why?

  • What if..?

  • Why does it make sense to ____?

  • Who has a question for ___?

  • Turn to your partner and explain why you agree or disagree with ____

  • Talk with ____ about how your strategy relates to hers.

  • How can you put the problem into your own words?

  • Was there something in this problem that reminded you of another problem we’ve done?

  • Can you show us what you were thinking with the materials? Can you draw a picture to help think about the problem? Can you write an equation to go with it?

  • What does _____have to do with _______?

  • Does it work? Always? Sometimes? Never? Why?

  • Let's all try to solve a problem using Max's method so we can see if we understand the way he did it.

  • I have a lot of people that are confident in their answer, and I've got some people who are kind of on the fence. And so I want to hear some thoughts.

  • What are you reasoning through?

  • Does anyone see anything they disagree with?

Spatial Language to consider...

• • Positional Language (describes relative locations of objects/people). Examples: over, under, on top, above, below, beneath, in front of, outside, between, up, down, along, through.

  • Spatial Dimensions (describes distance, height, width, depth, length). Examples: far, close, wide, narrow, near, short, tall.

  • Spatial Features/Properties (describes features of shapes/objects). Examples: curve, point, angle, line, edge, corner, vertex, base, face, parallel, vertical, horizontal, diagonal.

  • Names of Shapes (use proper names to describe 2D and 3D shapes). 

  • Spatial Transformations (describes actions applied to objects). Examples: flip, turn, slide, reflection, rotation, turn it around, you have to cut it in half, put that piece on top of that one, face it this way, clockwise.

  • Representational Gestures (movements with body/hands to communicate thinking). Examples: bringing both hands toward each other to represent 'together', throwing one hand to the side to show 'subtraction', moving hand in a way to show movement/shape of object.

Spatial Questions to ask...

• • Do you see symmetry in this design? (think line and rotational symmetry)

  • In what ways do you think that the two sides are the same?

  • What would happen if I cut _____ down this line and tried to put on half on top of the other?

  • How can you tell your finished design is symmetrical?

  • What was the trickiest part of your design to create? Explain.

  • Do you think all your pieces will fit or will you run out of space?

  • Do you have a strategy to fit ____ pieces/shapes together?

  • What might happen to your design if you rotated/flipped/slid _____ your shape?

  • What does (this shape/design etc.) remind you of?

  • How would you describe that motion? (example: flip, turn, rotate)

  • What shapes do you see within this design?

  • How many (name a shape) can you see in this design? Where do you see them?

  • How many (name a shape) do you think it will take to cover (name a shape/collection of shapes)?

  • In how many different ways do you think we can cover this shape?

  • What if we take away (name a shape)? Are there other shapes that could be used to cover the space?

  • How many blocks do you predict will cover the shape?

  • How can you cover/build this shape/design using the fewest/most pattern blocks? How many would that be?

  • What do you notice when you are looking at (name a shape/this design)?

  • What did you do first? How did you decide to do that?

  • What do you predict will happen if we...made this twice as big? Flipped the design? Stretched the design so it was longer?

  • How are you able to hold in your mind the image of...while you...?

  • How can you describe the easiest way to build your structure to someone else?

  • How can you describe your structure to someone else?

  • Were certain shapes/objects easier/more difficult to build than others? Why do you think that's so?

  • Are these 2 shapes/objects the same or different? How do you know?

  • How do you know that these 2 shapes/objects are different, even though they might look the same?

  • Is there anything you can do to this shape/object to make it look and go the same way as this one (point to other shape/object)? 

  • Take a close look at your structures/designs and pick your favorite one. Explain why it is your favorite.

  • Did you close your eyes to help you 'picture' the shape/structure? Do you think this strategy helps? Why?

  • Did you use your hands to act out building the structure? Do you think this strategy helps? Why?

  • Where did you start?

  • Did anyone get stuck at any point and then suddenly figure out a new way to... (build/create)? What was your trick?

  • Do you think we have build/found all the possible shapes/structures? Is there a way that we can prove it?

  • What would you do differently next time?

  • How many moves did it take to get from the green square to the red square (think items on a grid)? Is there a shorter path? How do you know it is shorter? Is there another route? How many moves would it take? Did you visualize your pathway before you started? Would you rather make a longer or shorter path?

  • What change do you (the coder) think you need to make to the code so the pathway the code checker follows matches yours?

  • Can you build something that looks like...when viewed from the top? What might it look like from the front and sides? Do these views look the same? What are you doing with your body to see that (front, side, top) view? Might there be other side views?