CCSS Standards for Mathematical Practice Flashcards
What are the CCSS Standards for mathematical practice?
Educators must incorporate these standards in instruction to enable students to achieve at a higher level. The goal of these standards is to develop mathematical expertise in students of all ages and academic abilities.
Make sense of _____________ and _____________ in solving them.
problems, persevere
- explain the meaning of a problem and actively look for ways it could be solved
- critically analyze the problem, think about the meaning of the solution, and form a pathway to get there
Construct _____________ _____________ and critique the _____________ of others.
viable arguments, reasoning
- consult definitions, theorems, and previously established results when constructing an argument
- use a logical progression of claims and examples to justify their conclusion
- differentiate between correct and flawed reasoning
Reason _____________ and _____________.
abstractly, quantitatively
- make sense of quantities and their relationships when problem solving
- use symbols to represent math situations
- use different properties of operations and objects flexibly
_____________ with mathematics.
model
- applying skills learned in math class to everyday life
Attend to _____________.
precision
- using math definitions clearly and accurately to explain reasoning
- precise about units of measurement and labeling axes
Use _____________ _____________ strategically.
appropriate tools
- identify which tool will be most helpful and use it appropriately
Look for and make use of _____________.
structure
- discern patterns and structures in math
Look for and express _____________ in _____________ _____________.
regularity, repeated meaning
- recognize when calculations are repeated and look for shortcuts
- as they work, students should reevaluate if they are on the right track
Examples: Make sense of problems and persevere in solving them.
Students are…
* Drawing pictures, diagrams, tables, or using objects to make sense of the problem
* Discussing the meaning of the problem with classmates
* Persisting in efforts to solve challenging problems, even after reaching a point of frustration.
Teachers are…
* Providing appropriate time for students to engage in the productive struggle of problem solving
* What information do you have? What do you need to find out? What do you think the answer might be?
* Can you draw a picture? How could you make this problem easier to solve?
Examples: Reason abstractly and quantitatively
Students are
* Using mathematical symbols to represent situations
* Taking quantities out of context to work with them (decontextualizing)
* Putting quantities back in context to see if they make sense (contextualizing)
Teachers are
* Providing a variety of problems in different contexts that allow students to arrive at a solution in different ways
* What does the number ____ represent in the problem? How can you represent the problem with symbols and numbers?
Examples: Construct viable arguments and critique the reasoning of others.
Students are
* Explaining and justifying their thinking using words, objects, and drawings
* Talking about and asking questions about each other’s thinking, in order to clarify or improve their own mathematical understanding.
Teachers are
* Providing many opportunities for student discourse in pairs, groups, and during whole group instruction
* How is your answer different than _____’s? What math language will help you prove your answer?
Examples: Model with mathematics
Students are
* Using mathematical models (i.e. formulas, equations, symbols) to solve problems in the world
* Using appropriate tools such as objects, drawings, and tables to create mathematical models
Teachers are
* Can you write a number sentence to describe this situation? What do you already know about solving this problem?
* Providing opportunities for students to solve problems in real life contexts/those that connect to students’ interests
Example: Use appropriate tools strategically
Students are
* Deciding which tool will best help solve the problem. Examples may include:
o Calculator
o Concrete models
o Digital Technology
o Pencil/paper
o Ruler, compass,
protractor
* Estimating solutions before using a tool (TKES 3)
* Comparing estimates to solutions to see if the tool was effective
Teachers are
* Making a variety of tools readily accessible to students and allowing them to select appropriate tools for themselves
* Which tool/manipulative would be best for this problem? What other resources could help you solve this problem?
Examples: Attend to precision
Students are
* Communicating precisely using clear language and accurate mathematics vocabulary
* Using appropriate units; appropriately labeling diagrams and graphs
Teachers are
* Requiring students to answer problems with complete sentences, including units
* Providing opportunities for students to check the accuracy of their work
* How do you know your answer is accurate? Did you use the most efficient way to solve the problem?
Examples: Look for and make use of structure
Students are
* finding structure and patterns in numbers, diagrams, and graphs
* sing patterns to make rules about math to help solve problems
Teachers are
* Allowing students to do the work of using structure to find the patterns for themselves rather than doing this work for students
* Why does this happen? How is ____ related to ____? Why is this important to the problem?
* What patterns do you see?
Examples: Look for and express regularity in repeated reasoning.
Students are
* Observing when calculations are repeated, and using these observations to take shortcuts
Teachers are
* Allowing students to do the work of finding and using their own shortcuts rather than doing this work for students
* How would your shortcut make the problem easier? How could this problem help you solve another problem?
