CCSS MODULE 3 MATH By Marcia Torgrude

OUTCOMES Day 1  What are the 6 shifts in math and how do they connect to the 8 SMP?  Experience the 8 Standards for Mathematical Practice in Action  Practice and utilize mathematical discourse  Connect the 8 SMP to SmarterBalanced Assessments Day 2  Modeling the 8 SMP in individual classrooms

THE 6 SHIFTS IN MATHEMATICS  Focus  Coherence  Fluency  Deep Understanding  Application  Dual Intensity Rigor

 Focus THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Spend more time thinking and working on fewer concepts. Make conscious decisions about what to excise from the curriculum and what to focus on Being able to understand concepts as well as processes (algorithms). Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic. Think about how the concepts connect to one another Build knowledge, fluency and understanding of why and how we do certain math concepts.

 Coherence THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Build on knowledge from year to year, in a coherent learning progression Connect the threads of math focus areas across grade levels – Vertical Alignment Connections are discovered by the student by using known math in new ways Connect to the way content was taught the year before and the years after – Avoid Misconceptions Focus on priority progressions

 Fluency THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Spend time practicing with intensity and skills in class and at home Prepare opportunities for students to create and use invented strategies through tasks and questioning Focus on the listed fluencies by grade level Prepare opportunities for students to learn derived fact strategies for transition Determine your in-class and out-of-class structure for time spent practicing Push students to know basic skills at a greater level of fluency

REQUIRED FLUENCY

 Deep Understanding THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Show, through numerous ways, mastery of material at a deep level Ask yourself what mastery/proficiency really looks like and means – do proficient students recreate or create? Use mathematical practices to demonstrate understanding of different material and concepts Plan for progression of levels of understanding. Spend the time to gain the depth of the understanding – Keep Learning! Become flexible and comfortable in own depth of content knowledge.

DEEP UNDERSTANDING

 Application THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Apply math in other content areas and situations, as relevant Apply math including areas where its not directly required (i.e. in science) Choose the right math concept to solve a problem when not necessarily prompted to do so Provide students with real world experiences and opportunities to apply what they have learned – match the real world problem with the math they know Incorporate more student-centered problems into class time.

APPLICATION

 Dual Intensity THE 6 SHIFTS IN MATHEMATICS What the Student Does..What the Teacher Does… Practice math skills with an intensity that results in fluency Find the dual intensity between understanding and practice within different periods or different units Practice math concepts with an intensity that forces application in novel situations Be ambitious in demands for fluency and practice, as well as the range of application Pursue a rigorous level of conceptual understanding, procedural skill and fluency, and application with equal intensity.

 Table talk:  Affirmation of what you are already doing  Big aha’s to begin to focus on  Questions – What is meant by…., THE 6 SHIFTS IN MATHEMATICS

 Table talk:  Create a list of what you are already doing well  Create a list of focus areas  Create a list of questions  Share one confirmation per table  Share one aha per table  Share one question per table  Round Up – Whole Group THE 6 SHIFTS IN MATHEMATICS

Standards for Mathematical Practice

8 SMP - COMPARING TASKS Martha’s Carpeting Task vs The Fencing Task  Read through both tasks  Think about how you would solve each task  Share at your table  What are the similarities and differences?

8 SMP IN ACTION  Elementary and Middle/High School Tasks  Brownie Problem or The Basic Student Budget  Do the task alone – PRIVATE THINK TIME  Compare strategies for solving the problem with your table.  Discuss all strategies and determine if all are viable methods and if they would work for all problems of this type.

8 SMP IN ACTION  Brownie Problem Brownie Problem  The Basic Student Budget The Basic Student Budget  Find evidence of the 8 SMP  Large group share out

MAKING SENSE OF ALGORITHMS MULTIPLICATION 8 SMP IN ACTION Ma and Pa Kettle Multiplication and Division

MAKING CONNECTIONS THROUGH DIAGRAM – 23 X Virtual Tools -

 Array Model for Fractions  MULTIPLYING FRACTIONS

CONCRETE ALGEBRA MULTIPLICATION

Connecting Number System to Algebra (20 + 3)( )

MAKING SENSE OF ALGORITHMS DIVISION Captain Hook Scaffolding Three children went trick or treating and when they got home, mom said you have to divide the candies equally. How much candy will each child get if there were 67 pieces of candy? Partial Quotient Division

American Idol had 6 stops across the nation. They selected a total of 750 participants. How many participants came from each city? Use Partial quotient division to solve this problem.

WHAT STANDARDS FOR MATHEMATICAL PRACTICE DID WE FOCUS ON?  SMP 4 – Model with mathematics  SMP 5 – Use appropriate tools strategically

ROLE OF DISCOURSE IN THE MATH CLASSROOM   discussion discussion Why use Talk in Mathematics Classrooms? Your big ideas Your concerns

ROLE OF DISCOURSE IN THE MATH CLASSROOM  Mentally Solve the following problem: 301 – x 102

MATH-TALK LEVELS TOOL: WHERE ARE YOU? Individually:  Do a quick ranking of yourself and your students using the tool (all four categories).  You do not have to share this information.

 What skills do students need to have to work effectively in cooperative groups?  Video clip: “How to Teach Math as a Social Activity”Jot down the big ideas as you watch (8.5 minutes)  Teaching Math as a Social Activity Teaching Math as a Social Activity  High-Leverage Practices that Impact Student Achievement  Questions to support effective discussions Cooperative Group Learning - Discourse Social-Emotional Learning

COOPERATIVE GROUP LEARNING  Read the handout “Cooperative Learning—Direct Instruction”  Read (scan) “Fifteen Common Mistakes in Using Cooperative Learning and What To Do About Them”  “Using student self-assessment…”

COOPERATIVE GROUP LEARNING  Practicing the “fishbowl”  Tangram math activity Work alone on this activity: If the whole square is equal to one unit, what fraction of the whole is each piece? Form a circle around people who will talk about how they found the fractional parts of the tangram. Listen to the strategies. Being a good listener is a major part of mathematical discourse. People in fishbowl – each take a turn explaining your strategy, then others inside the fishbowl ask questions of the person explaining.

COOPERATIVE GROUP LEARNING “Let’s face it: The best educators are those who plan. Of course, excellent teachers must know their content, and of course, they must be compassionate and caring. But just as important, the best teachers think about what it is they expect of their students, and they teach their students to meet those expectations. And when students don’t meet the expectations, the best teachers ask, ‘What got in the way of those students being successful with that particular skill?’ ”  Chris Opitz, Anchorage School District, Alaska

THE 6 SHIFTS IN MATHEMATICS REVISITED  Focus  Coherence  Fluency  Deep Understanding  Application  Dual Intensity Rigor

ASSESSMENT AND THE COMMON CORE CONTENT & PRACTICE STANDARDS What types of evidence will students have to demonstrate to show they’ve mastered both the content and practice standards? What types of test questions will be developed to gather this evidence? There are two big questions when thinking about the new assessment system for CCSSM

If we look at proposed assessment items, it will help us understand the expectations in the Practice Standards. SMARTER Balanced released a draft document outlining the content specifications that are intended to ensure that the assessment system accurately assesses the full range of the standards (including the Practice Standards). Assessments are scheduled for full implementation in Include a variety of question types: selected response, short constructed response, extended constructed response, technology enhanced, and performance tasks

CLAIMS & EVIDENCE FOR CCSS MATHEMATICS ASSESSMENTS Claim #1—Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Claim #2—Students can frame and solve a range of complex problems in pure and applied mathematics. Claim #3—Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Claim #4—Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

ASSESSING LEVELS OF EXPERTISE Level 1: Demonstrating basic procedural skills AND conceptual understanding. Level 2: Assessing knowledge in a context where their work on complex tasks is scaffolded. Level 3: Unscaffolded situations that call on substantial chains of reasoning.

SAMPLE SELECTED RESPONSE TASKS (LEVEL 1) CLAIM #1—CONCEPTUAL UNDERSTANDING AND PROCEDURAL FLUENCY  Fraction example: The task is a Level 1 task, but is somewhat different from typical multiple choice items in that it requires the student to make a choice about each example, which makes it a more complex task.

SAMPLE SELECTED RESPONSE TASKS (LEVEL 1) CLAIM #1—CONCEPTUAL UNDERSTANDING AND PROCEDURAL FLUENCY  Base 10 example:

SAMPLE SELECTED RESPONSE TASKS (LEVEL 1) CLAIM #1—CONCEPTUAL UNDERSTANDING AND PROCEDURAL FLUENCY  Integer example:

SAMPLE SELECTED RESPONSE TASKS (LEVEL 1) CLAIM #1—CONCEPTUAL UNDERSTANDING AND PROCEDURAL FLUENCY  HS Geometry example:

Grade 8 example: Each day, Maria walks from home to school and then from school to home. The graphs that follow show the distance that Maria is from home at different times during the walk. Match the graphs to the descriptions of Maria’s walk shown to the right of the graphs. Next to each graph, enter the letter (A, B, C, D) of the description that best matches the graph. CONSTRUCTED RESPONSE

WEB SITE FOR SMARTER BALANCED   Under Assessments choose Sample Items and Performance Tasks  Scroll to the paragraph illustrated  Experience the mathematics test items for your particular grade level by clicking on:.  Finish by attempting the Practice Pilot Test.  Large Group Discussion – What are the connections of questions to CCSS and SMP?

PERFORMANCE TASK DESCRIPTION Performance Tasks (PT)—integrate knowledge and skills across multiple learning targets; measure capacities such as depth of understanding, research skills and/or complex analysis with relevant evidence; require student-initiated planning, management of information/data and ideas; reflect a real-world task and/or scenario-based problem; allow for multiple approaches, and so on. Performance Tasks assess Claim #4—Modeling and Data Analysis. Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems. Performance Tasks (PT) can be a combination of Extended Response (ER) items that contribute to the performance task component and that are administered during the performance task component of the assessment, but are graded as separate components. You will see examples of ER tasks at the beginning of the PT on which you will be working; the ER tasks lead up to the more rigorous portion of the PT.

SAMPLE PERFORMANCE TASKS—ELEMENTARY, MS, HS Choose your grade-level task and work on the problem. Read suggested solutions. Elementary: Planting Tulips MS: Taking a Field Trip HS: Thermometer Crickets Move to the Task Specifications and discuss the targets in relation to the content standards and standards for mathematical practice.

SAMPLE PERFORMANCE TASKS (CONTINUED) Smarter Balanced assessment tasks are designed to assess both the Content Standards AND the Practice Standards. What actions will you need to take to prepare your students to be proficient knowing that they will be faced with similar assessment tasks? Discussion – whole group

 What are 3 Big Ideas that you want to focus on?  What are 2 questions you still have?  What is 1 aspect of this training you will use in the classroom tomorrow? 3-2-1