A Parent’s Guide to the Common Core Georgia Performance Standards: A Closer Look at Mathematical Practice The Common Core Georgia Performance Standards (CCGPS) are a natural fit with Gwinnett’s rigorous, world-class AKS curriculum and its long-standing focus on problem-solving. The CCGPS emphasize problem-solving as well as a conceptual understanding of mathematical processes. As a result, the learning experience in math classrooms in Gwinnett include plenty of application opportunities, a teaching strategy that Gwinnett County teachers have been using all along. One way in which GCPS teachers are ensuring that students have the 21st century skills to be successful is to emphasize the development of eight mathematical practices or “behaviors” that promote math success. Read on to learn more about these practices, some math terminology, and the content standards at your student’s school level. Make Sense of Problems and Persevere in Solving Them— When given a problem, students think about a problem and make a plan to solve it using available strategies. They predict results, and monitor and evaluate their progress, changing course or trying new tactics if needed. They test out theories, and check their answers using a different method. Students ask themselves the question “Does this make sense?” Younger students might rely on concrete objects or pictures to help “visualize” and solve a problem. Questions to Develop Mathematical Thinking— How would you describe the problem in your own words? Talk me through your steps so far. What are some other strategies you might try? How might you use a previous problem to help you begin? Reason Abstractly and Quantitatively— Students use numbers and words to help make sense of problems. With quantitative relationships, they decontextualize (use and manipulate symbols represented in the problem) and contextualize (make meaning of symbols in a problem). They understand the meaning of quantities and are flexible in using operation and properties. They attend to the meaning of quantities, not just how to compute them. Questions to Develop Mathematical Thinking— What do the numbers used in the problem represent? How is _______________ related to _______________? What does ________________ mean to you? (symbol, quantity, diagram) What properties might you use to find a solution? Construct Viable Arguments and Critique the Reasoning of Others— Students can explain their thinking and respond to the mathematical thinking of others. They understand and use definitions when justifying results. They communicate and defend their reasoning, using objects, drawings, diagrams, actions, examples and non-examples, and verbal and written communication. They recognize both correct and flawed logic. They can decide if arguments make sense, and ask useful questions to clarify or improve arguments. Questions to Develop Mathematical Thinking— What evidence would support your solution? How did you decide to try this strategy? Will it still work if…? How did you test whether your approach worked? Words Matter: Terminology in Mathematics Procedural Fluency is a student’s skill in completing math procedures flexibly, accurately, efficiently, and appropriately. Think of it as “muscle memory” for the brain. Conceptual Understanding reflects a student’s functional understanding of mathematical concepts, operations, and relations. An example might be that a student understands that the equation “2x5” can be expressed visually like this— • • • • • + • • • • • Coherence is the progression of content across grade levels and courses, which allows students to build new understanding and make connections extending from their previous learning. Because math skills build upon one another, it’s important that a student have a firm foundation in counting before progressing to addition and subtraction, in addition and subtraction before moving to multiplication and division, and so on. Application and Modeling describes the ability to apply mathematics and analyze resulting data in real-world scenarios. Students are able to use strategies from the classroom in everyday life, work, and decision-making. For example, a high school student might use geometry skills to solve a design problem, while a middle schooler might set up a flowchart to plan a school event. Domains are the overarching ideas that connect topics across grade levels. Examples are Counting; Numbers and Operations; Algebra; Geometry; and Functions. (See the box on the other side for domains by level.) Model with Mathematics— Students use familiar math strategies to solve problems that come up in everyday life. They may apply assumptions and approximations to simplify complicated tasks. They use tools (diagrams, two-way tables, graphs, flowcharts, and formulas) to tackle everyday problems. They interpret results to see if they make sense. Younger students may use pictures, symbols, objects, or words to express the problem and find a solution. Questions to Develop Mathematical Thinking— What are some ways to represent the quantities? What formula might apply in this situation? How would it help to create a diagram, graph, table…? What equation or expression matches the diagram, number line, chart, table…? Use Appropriate Tools Strategically— Students use certain tools, including technology, Standards: About Domains and Clusters These performance standards outline the specific skills and knowledge that students need to be successful at each grade level, building grade to grade, organized into domains: Elementary School Content Domains Students build a strong foundation in numbers and operations: Counting and Cardinality (K) to explore and deepen their math understanding. They have a math “toolbox” of both tools (such as ruler, calculator, manipulatives, protractor, etc.) and strategies. They are familiar with the tools that are appropriate for their grade/course. They consider available math tools and know how and when to use each tool. They detect possible errors by using estimation. Operations and Algebraic Thinking (K–5) Questions to Develop Mathematical Thinking— What mathematical tools could you use to visualize and represent the situation? What information do you have? What information do you need? In this situation, would it be helpful to use a __________________? Geometry(K–5) Numbers and Operations in Base Ten (K–5) Numbers and Operations – Fractions (3–5) Measurement and Data (K–5) Middle School Content Domains Students explore more complex operations and applications: Ratios and Proportional Relationships Attend to Precision— Students are precise when solving problems and clear when sharing The Number System mathematical ideas. They use correct math vocabulary, symbols that have meaning, accurate labels, consistent and appropriate units of measure, and accurate and efficient calculations. Expressions and Equations Questions to Develop Mathematical Thinking— What mathematical terms apply in this situation? How did you know your solution was reasonable? What symbols or mathematical notations are important in this problem? How are you showing the meaning of the quantities? Geometry ? < •/•• Look for and Make Use of Structure— Students see and understand how numbers and shapes are organized and put together as parts and wholes. They look closely to find patterns or structure, and step back for an overview of the whole. They see how complicated things are composed of single objects or several smaller objects. They apply general math rules to specific situations. Questions to Develop Mathematical Thinking— What observations can you make about…? What parts of the problem can you eliminate or simplify? What are other problems similar to this one? How can you use previous knowledge to solve this problem? Functions Statistics and Probability High School Content Clusters Students build knowledge, skills, application, and communication through the study of advanced mathematical content in preparation for college and career: Number and Quantity Algebra Geometry Functions Probability and Statistics Modeling Look for and Express Regularity in Repeated Reasoning— Students notice when calculations are repeated. For instance, 5 x 2 = 10 is the same as adding 2 five times, counting five rows of two blocks, or making five hops of 2 on a number line. They look for both generalizations and shortcuts in solving a problem. They see number patterns across applications. They understand the broader application of patterns and see the structure in similar situations. Questions to Develop Mathematical Thinking— How does this strategy work in other situations? Is this always true? Sometime true? Never true? What predictions or generalizations can this pattern support? What would happen if…? 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