8 Common Core Math Practices
1. Make sense of problems and persevere in solving them.
Understand the meaning of the problem and look for entry points to its solution Analyze Information (givens, constraints, relationships, and goals) Make conjectures and develop a plan to solve it Monitor and evaluate progress and change course if necessary Check answers to problems and determine if the answer makes sense 2. Reason abstractly and quantitatively Make sense of quantities and relationships in problem situations Represent abstract situations symbolically (i.e. equations, expressions) and understand the meaning of quantities Create a coherent representation of the problem at hand Consider the units involved Flexibly use properties of operations 3. Construct viable arguments and critique the reasoning of others. Use definitions and previously established causes/effects (results) in constructing arguments Make conjectures and use counter-examples to build a logical progression of statements to explore and support their ideas Communicate and defend mathematical reasoning using objects, drawings, diagrams, actions Listen to or read the arguments of others Decide if the arguments of others make sense and ask probing questions to clarify or improve the arguments 4. Model with mathematics Apply prior knowledge to solve real world problems Identify important quantities and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas Make assumptions and approximations to make a problem simpler Check to see if an answer makes sense within the context of a situation and change a model when necessary Some Detailed Explanations...
1. Make sense of problems and persevere in solving them. Students need to understand problems, figure out how to solve them, and then persevere until they're finished. Common Core standards encourage students to work with what they already know. As they use their skills to solve problems, they check their understanding. We can see if they're making sense of the problem (and their perseverance) by giving them problems above their skill level. Students need to focus on the process (of solving the problem) rather than just getting the correct answer. Here's another way to understand this practice... To make sense of problems, students need to know what a problem means and look at how to solve it. They analyze the facts that are given, whatever limits solving the problem, how the facts are related, and the goals of the problem (what they need to solve). They guess at the form of the solution and plan the steps to solving it (rather than just jump into trying any way to solve it). To gain insights in how to solve it, they might create a simpler form of the original problem, or look for a problem that is similar to it. They check their work, monitoring and evaluating their progress (and changing course if needed). Students can explain how equations, verbal descriptions, tables and graphs correspond to each other. They can draw diagrams of important features and relationships in a problem, graph data, and look for trends (regularities). Younger students may use concrete objects (like manipulatives) to better understand and solve a problem. Students can use a different method to check their work. They continually ask themselves, "Does this make sense?" They can understand how other students approached solving complex problems, and see how those different approaches correspond with each other. 2. Reason abstractly and quantitatively
There are multiple ways to break apart problems when we look for a solution. Students can symbols, pictures or other representations to describe different sections of a problem. This allows students to use skills that apply to the context of a problem rather than simply use standard algorithms (a series of steps that is taught to solve a problem, like long division). Another way to understand this practice... Make sense of quantities and their relationships Represent symbolically (i.e: Equations, expressions) Manipulate equations (attends to the meaning of the quantities, not just computes them) Understand and use different properties and operations Students recognize that a number represents a specific quantity. They connect quantities to written symbols and create logical representations of problems, considering appropriate units and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Teachers can support student reasoning by asking questions such as these: “What do the numbers in the problem represent?”“What is the relationship of the quantities?” Students write simple expressions that record calculations with numbers and represent or round numbers using place-value concepts. For example, students use abstract and quantitative thinking to recognize, without calculating the quotient, that is of. |
5. Use appropriate tools strategically.
Make sound decisions about the use of specific tools. Examples might include: Calculator Concrete models Digital Technology Pencil/paper Ruler, compass, protractor Use technological tools to visualize the results of assumptions, explore consequences and compare predictions with data Identify relevant external math resources (digital content on a website) and use them to pose or solve problems Use technological tools to explore and deepen understanding of concepts 6. Attend to precision. Communicate precisely using clear definitions State the meaning of symbols, carefully specifying units of measure, and providing accurate labels Calculate accurately and efficiently, expressing numerical answers with a degree of precision Provide carefully formulated explanations Label accurately when measuring and graphing 7. Look for and make use of structure Look for patterns or structure, recognizing that quantities can be represented in different ways Recognize the significance in concepts and models and use the patterns or structure for solving related problems View complicated quantities both as single objects or compositions of several objects and use operations to make sense of problems 8. Look for and express regularity in repeated reasoning Notice repeated calculations and look for general methods and shortcuts Continually evaluate the reasonableness of intermediate results (comparing estimates) while attending to details and make generalizations based on findings TeacherStep article explaining the 8 Math Practices |