Mathematical Practice Standards
Successful mathematical thinkers engage in specific practices that facilitate their problem solving.
1. Make sense of problems and persevere in solving them.
- What information do we need to begin this problem?
- What will we need to do first?
- How do you know if your answer is reasonable?
- What would be another way to do this?
- What connections can you make?
2. Reason abstractly and quantitatively.
- Can you create a picture to show that?
- Can you write that using symbols?
- Explain your picture/symbols. What do they mean in context?
3. Construct viable arguments and critique the reasoning of others.
- Why does this work?
- How do you know?
- Can you explain what he/she did?
- These approaches are different; why did they both work?
4. Model with mathematics.
- How does this picture/graph/table help us solve the problem?
- Is there a different model that we could have used?
5. Use appropriate tools strategically.
- What tool might be helpful in this problem?
- What would be the most efficient tool to use?
- Is your estimate too high or too low?
- Whose estimate do you think is closest to the actual answer? Why?
6. Attend to precision.
- Can you state that in a different way?
- Who can summarize what he/she said?
- How do you know your answer is accurate?
- Does the problem require an exact answer?
7. Look for and make use of structure.
- What patterns do you see? How are these helpful in this problem?
- What predictions can we make based on this pattern?
- What would come next?
8. Look for and express regularity in repeated reasoning.
- What rule can I use that will always work in this type of problem?
- Is there a more efficient way to do this?
- What algorithm did you develop?
- What algorithm did you use?
- How can patterns help you solve problems and explain rules?
- How can mathematical rules and shortcuts help you become a stronger mathematical thinker?