Math look fors (updated)
•
1 like•1,819 views
The document discusses the seven Mathematical Practices from the Common Core State Standards and provides examples of what these practices may look like for both students and teachers in the classroom. The seven practices are: 1) Make sense of problems and persevere in solving them, 2) Reason abstractly and quantitatively, 3) Construct viable arguments and critique the reasoning of others, 4) Model with mathematics, 5) Use appropriate tools strategically, 6) Attend to precision, and 7) Look for and make use of structure. For each practice, examples are given of how teachers can support the practice and what behaviors students may demonstrate when applying the practice.
Report
Share
Math look fors (updated)
- 1. Mathematical Practices Look-fors MP.1: Make sense of problems and persevere in solving them. REGIONAL EDUCATIONAL SERVICE AGENCY Laura Chambless Assistant Director, K-8 Math and Science ©2013 St. Clair County RESA (problem solving) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Analyzes information given • Looks for different ways to solve the problem (i.e. situation vs. solution) • Knows and uses different representations (i.e. equation vs. table or graph) and/or manipulative • Evaluates progress and changes plan if needed • Explains using both pictures and words • Makes connection to the way they solved the problem and how others solved the problem • Uses basic fact fluency or fact strategies • Promotes visible thinking using pictures and equations • Gives time for students to discuss with others or class • Encourages students to keep trying and builds supportive math community • Uses explicit and precise language when using representations and definitions and expects students to do the same in their discussions • Helps students make connections between representations, equations, and student thinking • Engages students in metacognition • Models problem situation, not problem solution. MP.3: Construct viable arguments and critique the reasoning of others. (math talk) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Communicates by using mathematical reasoning with objects, drawings, diagrams, equations … • Justifies solutions • Makes connections between their own thinking and that of others • Demonstrates actively listening by asking questions of others • Makes statements to prove or disprove concepts or presented ideas • Students understand different forms of reasoning (ie. deductive reasoning) and when to apply them • Uses accurate vocabulary • Promotes math talk and the critiquing of presented solutions • Asks higher-order questions to facilitate discussion and presses for justification • Gives time for students to construct their own ideas before small or large group discussions • Expects students to be explicit and precise when using representations, definitions, and symbols • Builds a supportive math community • Helps make connections between the reasoning of students and content standard
- 2. Mathematical Practices Look-fors REGIONAL EDUCATIONAL SERVICE AGENCY Laura Chambless Assistant Director, K-8 Math and Science ©2013 St. Clair County RESA MP.2: Reason abstractly and quantitatively. (number sense) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer Task explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Makes sense of quantities and their relationship in problem situations • Recognizes that quantities can be represented in different ways • Uses numbers and words to make sense of a problem • Gives attention to the meaning of the numbers and knows which operation to choose • Performs operations flexibly, accurately, and efficiently • Uses multiple representations • Connects numbers, symbols or units to quantities • Justifies solutions • Makes connections to how they solved a problem and how others solved the problem • Reasons with attributes of geometric figures • Promotes visible thinking using pictures and equations • Uses physical representations (manipulatives, drawings) to model what happens to a variable when it changes and how that effects the other variable • Gives time for students to discuss with others or class • Encourages students to keep trying • Uses explicit and precise language when using representations and definitions and expects students to be the same in their discussion • Builds a supportive math community • Helps make connections between representations, equations, student thinking, and content standard MP.6: Attend to precision. (vocabulary, labeling, answers) The Math Task: The Student: The Teacher: • Is an interesting problem • Uses appropriate math vocabulary • Has more than one solution path • Uses clear definitions in discussion which may be unpredictable • Calculates accurately and efficiently • Creates discussion • Explains their reasoning with • Requires cognitive effort accurate mathematical language • Connects to real world • Uses proper unit labels with • Relates to grade level CCSS measuring • Builds student understanding of • Uses appropriate labels when grade level standard graphing and solving story problems • Leads students to look back and • Determines when different levels reflect on answer of precision are needed and how • Explicitly asks for justification or precision affects results explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Communicates precisely using clear definitions • Emphasizes the importance of precise communication • Emphasizes the importance of precision of measurement • Helps make connections between vocabulary, student thinking, unit labels, calculations, and content standard
- 3. Mathematical Practices Look-fors REGIONAL EDUCATIONAL SERVICE AGENCY Laura Chambless Assistant Director, K-8 Math and Science ©2013 St. Clair County RESA MP.4: Model with mathematics. (representations and graphs) The Math Task: The Student: The Teacher: • Is an interesting problem • Identifies important elements and • Has more than one solution path quantities needed for a model which may be unpredictable • Describes relationships of models • Creates discussion and equation • Requires cognitive effort • Chooses a representation • Connects to real world • Applies formulas/equations • Relates to grade level CCSS • Uses models to draw conclusion • Builds student understanding of • Explains why it is a good model for grade level standard the problem • Leads students to look back and • Recognizes and uses parts of a graph reflect on answer (i.e. title, labels, symbols, key) • Explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Expects students to justify their choice in models • Gives students opportunity to evaluate the appropriateness of their model and that of others • Helps make connections with the relationships between representation, equation, answer, student thinking, and content standard MP.5: Use appropriate tools strategically. (calculators, rulers, manipulative) The Math Task: The Student: The Teacher: • Is an interesting problem • Uses mental computations fluently • Has more than one solution path • Knows which tools are appropriate which may be unpredictable for the task • Creates discussion • Knows when to use a tool • Requires cognitive effort • Understands and uses properties of • Connects to real world operations • Relates to grade level CCSS • Uses estimation to find errors and • Builds student understanding of check answer for reasonableness grade level standard • Justifies tool selection • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Allows students to choose appropriate learning tools • Uses appropriate tools to represent, explore and deepen student understanding • Models how different representations are tools • Uses technology tools to deepen students’ understanding of a concept • Helps make connections between tool, equation, student thinking, and content standard
- 4. Mathematical Practices Look-fors REGIONAL EDUCATIONAL SERVICE AGENCY Laura Chambless Assistant Director, K-8 Math and Science ©2013 St. Clair County RESA MP.7: Look for and make use of structure. (how numbers and shapes are organized) The Math Task: The Student: The Teacher: • Is an interesting problem • Recognizes that quantities can be • Has more than one solution path represented in different ways which may be unpredictable • Uses properties of operations to make • Creates discussion sense of problems • Requires cognitive effort • Recognizes how numbers and shapes • Connects to real world are organized • Relates to grade level CCSS • Looks for patterns and structures in • Builds student understanding of the number system grade level standard • Justify strategy for basic facts • Leads students to look back and • Uses models to prove equations reflect on answer • Recognize how symbols help • Explicitly asks for justification or represent relationships and can be explanation applied to new situations (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Gives students time to discuss connections • Brings students back to the rule or properties being used • Helps students look for patterns and structures in the number system • Helps make connections between the structure used, equation, student thinking, and content standard • Helps make connections to real world MP #8: Look for and express regularity in repeated reasoning. (number pattern) The Math Task: The Student: The Teacher: • Is an interesting problem • Notices number patterns • Has more than one solution path • Notices if calculations are repeated which may be unpredictable • Applies more efficient computation • Creates discussion strategies using number patterns • Requires cognitive effort • Looks both for general methods and • Connects to real world for shortcuts • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) • Encourages students to connect task to prior concepts taught • Helps make connections between pattern, equation, student thinking, and content standard Compiled from multiple resources where links can be found within the “8 Mathematical Practices” tab on: Laura Chambless’ Protopage