2 Outcomes:Participants will review the Standards of Mathematical PracticeParticipants will analyze K-5 number talks.Participants will form a global perspective for the school community.Participants will identify one change they plan to make in their classroom practice related to number talks.
3 Standards for Mathematical Practice Carry across all grade levelsDescribe habits of mind of a mathematically expert studentMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments & critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoning33
4 Make sense of problems and persevere in solving them. #1When presented with a problem, I can make a plan, carry out my plan, and evaluate its success.AFTER…CHECKIs my answer correct?How do my representations connect to my algorithms?EVALUATEWhat worked?What didn’t work?What other strategies were used?How was my solution similar to or different from my classmates?BEFORE…EXPLAIN the problem to myself.Have I solved a problem like this before?ORGANIZE information.What is the question I needto answer?What is given?What is not given?What tools will I use?What prior knowledge do Ihave to help me?DURING…PERSEVEREMONITOR my work.CHANGE my plan ifit isn’t working out.ASK myself, “Does thismake sense?”
5 Reason abstractly and quantitatively I can use reasoning habits to help me contextualize and decontextualize problems.#2CONTEXTUALIZEI can take numbers and put them in a real-world context.For example, if given3 x 2.5 = 7.5,I can create a context:I walked 2.5 miles per day for 3 days. I walked a total of 7.5 miles.DECONTEXTUALIZEI can take numbers out of context and work mathematically with them.For example, if givenI walked 2.5 miles per day for 3 days, How far did I walk?I can write and solve3 x 2.5 = 7.5.
6 Construct viable arguments and critique the reasoning of others #3I can make conjectures andcritique the mathematicalthinking of others.I can critique the reasoningof others by…listening.comparing arguments.identifying flawed logic.asking questions toclarify or improvearguments.I can construct, justify, andcommunicate arguments by…considering context.using examples and non-examples.using objects, drawings,diagrams and actions.
7 Model with mathematics #4I can recognize math in everyday life and use math I know to solve everyday problems.concretemodelsI can…make assumptions andestimate to makecomplex problemseasier.identify importantquantities and use toolsto show their relation-ships.evaluate my answer andmake changes if needed.picturessymbolsRepresentMathorallanguagereal-world situations
8 Use appropriate tools strategically #5I know when to use certain tools to help me explore and deepen my math understanding.I have a math toolbox.I know HOW to use mathtools.I know WHEN to use mathI can reason: “Did the tool Iused give me an answerthat makes sense?”
9 I can use precision when solving problems and communicating my ideas. #6Attend to precisionI can use precision when solving problems and communicating my ideas.Problem SolvingI can calculate accurately.I can calculate efficiently.My answer matches what the problem asked me to do–estimate or find an exact answer.CommunicatingI can SPEAK, READ, WRITE, and LISTEN mathematically.I can correctly use…math symbolsmath vocabularyunits of measure
10 Look for and make use of structure I can see and understand how numbers and spaces are organized and put together as parts and wholes.#7SHAPESFor example:DimensionLocationAttributesTransformationNUMBERSFor example:Base 10 structureOperations and propertiesTerms, coefficients, exponents
11 Look for and express regularity in repeated reasoning I can notice when calculations are repeated. Then, I can find more efficient methods and short cuts.#8Patterns:1/9 = ….2/9 = …3/9 = …4/9 = ….5/9 = ….I notice the pattern which leads to an efficient shortcut!!!
12 Number Talks Helping Children Build Mental Math and Computation Strategies Grades K-5 By Sherry Parrish
13 Number talks help students develop efficient, flexible, and accurate computational strategies that build upon key foundational ideas of mathematics.
14 Classroom conversations and discussions centered around purposefully crafted computation problems are the at very core of number talks.
15 By sharing and defending their solutions and strategies, students are provided with the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics.
17 Key Components of Number Talks Students Teacher Environment
18 Classroom Environment and Community Safe and risk freeStudents are comfortable offering responses for discussion, questioning themselves and others, and investigating new strategiesCulture of acceptance is based on a common quest for learning and understanding
19 Sharing and Discussing Computation Strategies Clarify their own thinkingConsider and test other strategiesInvestigate and apply mathematical relationshipsBuild a repertoire of efficient strategiesMake decisions about choosing effective strategies
20 Mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures.
21 When students approach problems without paper and pencils, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated. Mental computation causes them to be efficient with the numbers and avoid holding numerous quantities in their heads.
22 Teacher’s Role Moves into the role of facilitator Keeps discussion focused on the important mathematicsHelps students learn to structure their comments and wonderingsGuides students to ponder and discuss examples that build upon their purposes
23 16 x 35 Work mentally two ways Video 5.3 – Fifth Grade16 x 35Work mentally two waysLook for Standards for Mathematical Practice
24 Questions to be thinking about: What are the similarities and differences between the grades?Classroom community?Teacher’s role?Student’s role?Communication?How do the content skills build from grade to grade?
25 Standards for Mathematical Practice Carry across all grade levelsDescribe habits of mind of a mathematically expert studentMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments & critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoning2525
26 Standards for Mathematical Practice SMP1: Explain and make conjectures…SMP2: Make sense of…SMP3: Understand and use…SMP4: Apply and interpret…SMP5: Consider and detect…SMP6: Communicate precisely to others…SMP7: Discern and recognize…SMP8: Note and pay attention to…
27 Purposeful Computation Problems Problems are crafted to guide students to focus on mathematical understanding and knowledge. The goals and purposes for the number talk should determine the numbers and operations chosen.
28 Grade Level Groups-Charts Write an addition number talk problem.Solve each problem using at least two strategies students might commonly use.
29 Gallery WalkHow do the strategies build from grade level to grade level?What math concepts need to be developed at each grade level to allow students to be mathematically powerful?How does this affect student understanding in future grade levels?
30 Your Practice: A Closer Look How are the student and teacher roles in your classroom similar to or different from the classroom clips?Think about a recent math lesson you have taught. What role does a learning community play in your lesson? What opportunities exist for students to learn through inquiry-based tasks? How does your lesson build number sense?
31 What is one change you plan to make? What instructional strategies can you incorporate into future math lessons to help support student thinking and mathematical understanding?Remember to start small in making shifts in your classroom practice related to number talks.What is one change you plan to make?
32 Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5. Sausalito: Math Solutions.