The 8 Mathematical Practices
Practice QUestions and Prompts
Mathematical Practice 1
I can make sense of problems and not give up when trying to solve them.
I can make sense of problems and not give up when trying to solve them.
- Retell the problem in your own words.
- Can you think of similar problems we have solved? How might that help?
- We know __________. What do we not know?
- What have you already tried?
- Can you think of another strategy to try?
- Can you try the same problem using smaller numbers?
- Does your answer make sense? Why or why not?
Mathematical Practice 2
I can use words, numbers, logic, and reasoning skills to help me solve problems.
I can use words, numbers, logic, and reasoning skills to help me solve problems.
- Can you write an expression or equation to represent your thinking?
- What do these numbers represent? What does __________ stand for?
- What is the relationship between __________ and __________?
- Can you describe how these numbers can break apart and be put back together in different ways?
- Does your solution answer the question? How do you know?
- What is the unit of measure being used?
- Can you explain your steps for working through this problem?
- Can you identify a mathematical relationship with any of these numbers?
- Does your expression or equation make sense in the context of a real life problem?
Mathematical Practice 3
I can justify my strategies and evaluate if the ideas of others make sense.
I can justify my strategies and evaluate if the ideas of others make sense.
- Convince us that your solution makes sense.
- Did you test whether your method worked?
- Does __________'s solution make sense to you? Why or why not? Do you have any follow-up questions to ask them?
- Are you making any assumptions? If so, what are they?
- What things that you already know are helping you?
- Were you able to follow __________'s explanation and reasoning? Which part could use clarifying?
- Can anyone explain this in a different way?
- Do these different solutions express the same or different ideas? Explain any connections.
- How can such different solutions both or all be correct?
- Tell us why you think this solution is correct or incorrect.
- Are these statements logical?
- Are these statements connected?
- Is the solution plausible?
- Have you sufficiently supported your answer and shown your work?
- Does anyone have a counterargument?
Mathematical Practice 4
I can clearly show my work using diagrams, words, symbols, and pictures.
I can clearly show my work using diagrams, words, symbols, and pictures.
- Can you draw a picture or model as a visual representation of what you are thinking?
- How could you visualize or organize your thinking? (E.g. using physical objects, symbols, or diagrams)
- What are the important quantities or numbers in the problem?
- What mathematics applies to this situation?
- Can you break this problem into chunks to create a mathematical model of the situation?
- In what ways can you simplify pieces of this problem?
- Is your mathematical model limited in any way? If so, how is it limited?
Mathematical Practice 5
I can select and use appropriate tools to help me solve problems.
I can select and use appropriate tools to help me solve problems.
- What math tools can you use to solve the problem?
- Which tools will be most efficient and effective with this particular situation?
- Which tool do you think will be the most helpful for you?
- Would a __________ or __________ make more sense to use?
- Which of the tools that you have will take the least amount of time to use right now?
- Why did you decide to use __________?
- Is there a better tool available that you know of?
- How might estimation help you?
Mathematical Practice 6
I can review my calculations and strategies to see if they are correct.
I can review my calculations and strategies to see if they are correct.
- Remember to use precise mathematical language in your written explanation
- Remember to label all diagrams with quantities, units of measurement, axes, etc. so everyone understands exactly what they are looking at.
- What precisely are you trying to say?
- Is there precise mathematical vocabulary that might help you explain your thought process more clearly?
- Have you checked over your data, reasoning, and conclusion for clarity and precision?
- Have you tested the accuracy of your answer? How?
- Will everyone understand the labels and language you have used?
- What does the equal sign tell you here?
Mathematical Practice 7
I can use the structure of a problem to help me find the answer.
I can use the structure of a problem to help me find the answer.
- Do you notice a certain structure in the numbers or shapes as you work? How can this help you?
- Can you think of a problem we have solved before that looked like this?
- How can you use the structure of another similar problem to help you work backwards?
- How can you be sure that your interpretation of the problem is correct?
- Will this always be true? Sometimes be true? Never be true?
Mathematical Practice 8
I can find and use mathematical patterns to help me solve a problem.
I can find and use mathematical patterns to help me solve a problem.
- What pattern(s) can you see?
- What does the pattern or repetition tell you?
- Can you predict what happens next? And after that?
- What if you worked backwards? Would the same pattern be true?
- Can you make a conjecture about __________ that will always be true?
- Why does this always work the same way?
- Do you notice any relationship(s) between the patterns you have found?
- Is there a summary or shorthand way of expressing these recurring patterns?