The Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all students in Grades K12. Below are the standards and a few examples of how these Eight Practices may be integrated into problem solving tasks.
1. Make sense of problems and persevere in solving them. 1. Make sense of problems and persevere in solving them. Solve real world problems through the application of arithmetic, algebraic, statistical and geometric concepts. These problems involve addition, multiplication, subtraction, division, ratio, rate, area, volume and statistics. — Seek the meaning of a problem and look for efficient ways to represent and solve it. — You may check your thinking by asking, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”. — Explain the relationships between equations, verbal descriptions, tables and graphs. — When mathematically proficient check answers to problems using a different method. Learn to ask yourself: How can this information be used? 2. Reason abstractly and quantitatively. Represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. — Analyze to understand the meaning of the number or variable as related to the problem — Manipulate symbolic representations by applying properties of operations. Learn to ask yourself: What is a situation that could be represented by this equality? 3. Construct viable arguments and critique the reasoning of others. Learn to ask yourself: Will that method always work? 4. Model with mathematics. Learn to ask yourself: Why is that a good model for this problem? 5. Use appropriate tools strategically. Consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, you may decide to represent figures on the coordinate plane to calculate area. — Number lines are used to understand division and to create dot plots, histograms and box plots to visually compare the center and variability of the data. — Additionally, you might use physical objects or applets to construct nets and calculate the surface area of threedimensional figures. Learn to ask yourself: What could I use to help me solve this problem? In grade 6, you continue to refine their mathematical communication skills by using clear and precise language in your discussions with others and in their own reasoning. — You use appropriate terminology when referring to rates, ratios, geometric figures, data displays, and components of expressions, equations or inequalities. Learn to ask yourself: How do I know my answer is reasonable? 7. Look for and make use of structure. You routinely seek patterns or structures to model and solve problems. For instance, you recognize Learn to ask yourself: How did I discover that pattern? 8. Look for and express regularity in repeated reasoning. .You use repeated reasoning to understand algorithms and make generalizations about patterns.. During multiple opportunities to solve and model problems, you may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm your generalization. — You connect place value and your prior work with operations to understand algorithms to fluently divide multidigit numbers and perform all operations with multidigit decimals. — You informally begin to make connections between covariance, rates, and representations showing the relationships between quantities. Ask yourself: What do I remember about…? Revised: 01/17/13
