S TANDARDS FOR M ATHEMATICAL P RACTICE In the classroom

F ORTUNE C OOKIES Take a fortune cookie. Find an educator from another table to visit with. Open and read your fortune aloud adding one of these endings. …at school. …at home. …with the common core standards. …outside. Listen to your partners fortune and selected ending.

SMARTER B ALANCED A SSESSMENT C ONSORTIUM (SBAC) To achieve the goal that all students leave high school ready for college and career, SBAC is committed to ensuring that assessment and instruction embody the CCSS and that all students, regardless of disability, language, or subgroup status, have the opportunity to learn this valued content and show what they know and can do.

SBAC C LAIMS Claims are the broad statements of the assessment system’s learning outcomes, each of which requires evidence that articulates the types of data/observations that will support interpretations of competence towards achievement of the claims SBAC has 4 claims for mathematics

SBAC C LAIMS Mathematics Claim #1 CONCEPTS AND PROCEDURES Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

SBAC C LAIMS Mathematics Claim #2 PROBLEM SOLVING Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

S MARTER B ALANCED A SSESSMENT C ONSORTIUM Mathematics Claim #3 COMMUNICATING REASONING Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

S MARTER B ALANCED A SSESSMENT C ONSORTIUM Mathematics Claim #4 MODELING AND DATA ANALYSIS Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

Claim #1 Claim #4 Claim #3 Claim #2

Claim #1 Claim #4 Claim #3 Claim #

MP1 MP5 MP7 MP8 MP3 MP6 MP4 MP2 MP5 MP5 MP6 MP7 MP8 Claim #1 Claim #2 Claim #3 Claim #4

S TANDARDS FOR M ATHEMATICAL P RACTICE 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing

CCSS AND I NSTRUCTION In what ways do these practices fit into lessons we teach? How do these practices look in action? What do students do? What do teachers do? How might our instructional materials help us teach the practices?

S TANDARDS FOR M ATHEMATICAL P RACTICE 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing

M ATHEMATICAL P RACTICES IN ACTION Seeing structure and generalizing  Practice 7: Look for and make use of structure  Practice 8: Look for and express regularity in repeated reasoning

M ATHEMATICAL P RACTICES IN ACTION Practice 7: Look for and make use of structure Mathematically proficient students use structures such as place value, the properties of the operations, other generalizations about the behavior of the operations, attributes of shapes, and symmetry to solve problems. In many cases, they have identified and described these structures through repeated reasoning (MP 8). (Working Draft 9/29/11, Illustrative Mathematics Project, CCSSM)

M ATHEMATICAL P RACTICES IN ACTION Practice 8: Look for and express regularity in repeated reasoning Mathematically proficient students look for regularities as they solve multiple related problems, then identify and describe these regularities. As students explain why these generalizations must be true, they construct, critique, and compare arguments (MP 3). As they apply these regularities in new situations, they are making use of structure (MP 7). (Working Draft 9/29/11, Illustrative Mathematics Project, CCSSM)

M ATHEMATICAL P RACTICES IN ACTION Practice 8: Look for and express regularity in repeated reasoning Practice 7: Look for and make use of structure At your tables, talk about what students will do to learn and demonstrate these practices. Also consider what teachers will do to help students become better at these two practices.

M ATHEMATICAL P RACTICES IN ACTION S EEING S TRUCTURE AND G ENERALIZING Watch and listen to second graders explain their thinking about Listen for and record evidence of students using structure and generalizing. Listen for and record evidence of instruction to help students use structure and generalizing = ________

M ATHEMATICAL P RACTICES IN ACTION S EEING S TRUCTURE AND G ENERALIZING

M ATHEMATICAL P RACTICES 7 AND 8 Discuss with a partner: Where did you see evidence of students “looking for and making use of structure” or “looking for and expressing regularity in repeated reasoning”? How many times did you see evidence of students practicing standards 7 and 8? Each person will enter the total number of times they saw or heard evidence of MP7 and MP8.

E VALUATING C URRICULUM “Since the Mathematical Practices describe the essence of ‘doing mathematics,’ mathematics curriculum materials that align with the CCSSM must also provide teachers support in incorporating these Mathematical Practices into their lessons, thereby providing students ample opportunities to engage in the Practices.” CCSSM Curriculum Analysis Tool, p. 7

C URRICULUM AS A TOOL FOR P ROFESSIONAL D EVELOPMENT  In what ways does the curriculum support teachers in implementing the Mathematical Practices?  Dialogue Box with Teacher notes  Session  Implementation guide

S TANDARDS FOR M ATHEMATICAL P RACTICE 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing

M ATHEMATICAL P RACTICES IN INSTRUCTION Modeling and using tools  Practice 4: Model with mathematics  Practice 5: Use appropriate tools strategically

M ATHEMATICAL P RACTICES IN A CTION Practice 4: Model with mathematics When given a contextual situation, mathematically proficient students express the situation using mathematical representations such as physical objects, diagrams, graphs, tables, number lines, or symbols. They operate within the mathematical context to solve the problem, then use their solution to answer the original contextual question. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. (Working Draft 9/29/11, Illustrative Mathematics Project, CCSSM)

M ATHEMATICAL P RACTICES IN A CTION Practice 5: Use appropriate tools strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

M ATHEMATICAL P RACTICES IN ACTION Practice 4: Model with mathematics Practice 5: Use appropriate tools strategically As you watch a 2 minute of RCAS 3 rd graders consider how tools and models help them make sense of the mathematics while arranging chairs.

M ATHEMATICAL P RACTICES IN A CTION

S ESSION 1.8A, “S TORY P ROBLEMS WITH M ISSING P ARTS ”  With a partner highlight and label places in session (CC62-CC68) that illustrate or support Mathematical Practices 4 and 5  Enter the number of times you saw evidence of instruction designed to help students practice MP4 and MP5?  Discuss in small groups  How are students using these Practices?  How is the teacher supporting the use of these practices?  What other Mathematical Practices seem evident?

S TANDARDS FOR M ATHEMATICAL P RACTICE 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing

S TANDARDS FOR M ATHEMATICAL P RACTICE Which standards for mathematical practice do you understand fairly clearly? a.MP1 and MP6 b.MP2 and MP3 c.MP4 and MP5 d.MP7 and MP8 Which standards for mathematical practice are becoming more familiar? a.MP1 and MP6 b.MP2 and MP3 c.MP4 and MP5 d.MP7 and MP8 For which mathematical practices will you want more time and study to understand? a.MP1 and MP6 b.MP2 and MP3 c.MP4 and MP5 d.MP7 and MP8

S TANDARDS FOR M ATHEMATICAL P RACTICE 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 1.Make sense of problems and persevere in solving them 6. Attend to precision Overarching habits of mind of a productive mathematical thinker. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning 4. Model with mathematics 5. Use appropriate tools strategically Reasoning and explaining Modeling and using tools Seeing structure and generalizing