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+ Numbers and Operations in Base Ten Success Implementing CCSS for K-2 Math.

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Presentation on theme: "+ Numbers and Operations in Base Ten Success Implementing CCSS for K-2 Math."— Presentation transcript:

1 + Numbers and Operations in Base Ten Success Implementing CCSS for K-2 Math

2 + Introductions

3 + K – 2 Objectives Reflect on teaching practices that support the shifts (Focus, Coherence, & Rigor) in the Common Core State Standards for Mathematics. Deepen understanding of the progression of learning and coherence around the CCSS-M for Number and Operations in Base 10 Analyze tasks and classroom applications of the CCSS for Number and Operations in Base 10

4 + Success Implementing CCSS for K-2 Math Number and Operations in Base 10

5 + Why CCSS? Gretas Video Clip

6 + Common Core State Standards Define the knowledge and skills students need for college and career Developed voluntarily and cooperatively by states; more than 46 states have adopted Provide clear, consistent standards in English language arts/Literacy and mathematics Source: www.corestandards.org 6

7 + What We are Doing Doesnt Work Almost half of eighth-graders in Taiwan, Singapore and South Korea showed they could reach the advanced level in math, meaning they could relate fractions, decimals and percents to each other; understand algebra; and solve simple probability problems. In the U.S., 7 percent met that standard. Results from the 2011 TIMMS

8 + Theory of Practice for CCSS Implementation in WA 2-Prongs: 1. The What: Content Shifts (for students and educators) Belief that past standards implementation efforts have provided a strong foundation on which to build for CCSS; HOWEVER there are shifts that need to be attended to in the content. 2. The How: System Remodeling Belief that successful CCSS implementation will not take place top down or bottom up – it must be both, and… Belief that districts across the state have the conditions and commitment present to engage wholly in this work. Professional learning systems are critical

9 + WA CCSS Implementation Timeline 2010-112011-122012-132013-142014-15 Phase 1: CCSS Exploration Phase 2: Build Awareness & Begin Building Statewide Capacity Phase 3: Build State & District Capacity and Classroom Transitions Phase 4: Statewide Application and Assessment Ongoing: Statewide Coordination and Collaboration to Support Implementation

10 + Transition Plan for Washington State K-23-56-8High School Year 1- 2 2012-2013 School districts that can, should consider adopting the CCSS for K-2 in total. K – Counting and Cardinality (CC); Operations and Algebraic Thinking (OA); Measurement and Data (MD) 1 – Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT); 2 – Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT); and remaining 2008 WA Standards 3 – Number and Operations – Fractions (NF); Operations and Algebraic Thinking (OA) 4 – Number and Operations – Fractions (NF); Operations and Algebraic Thinking (OA) 5 – Number and Operations – Fractions (NF); Operations and Algebraic Thinking (OA) and remaining 2008 WA Standard 6 – Ratio and Proportion Relationships (RP); The Number System (NS); Expressions and Equations (EE) 7 – Ratio and Proportion Relationships (RP); The Number System (NS); Expressions and Equations (EE) 8 – Expressions and Equations (EE); The Number System (NS); Functions (F) and remaining 2008 WA Standards Algebra 1- Unit 2: Linear and Exponential Relationships; Unit 1: Relationship Between Quantities and Reasoning with Equations and Unit 4: Expressions and Equations Geometry- Unit 1: Congruence, Proof and Constructions and Unit 4: Connecting Algebra and Geometry through Coordinates; Unit 2: Similarity, Proof, and Trigonometry and Unit 3:Extending to Three Dimensions and remaining 2008 WA Standards

11 + Focus, Coherence & Rigor

12 + The Three Shifts in Mathematics Focus: Strongly where the standards focus Coherence: Think across grades and link to major topics within grades Rigor: Require conceptual understanding, fluency, and application

13 + Focus on the Major Work of the Grade Two levels of focus ~ Whats in/Whats out The shape of the content

14 + Shift #1: Focus Key Areas of Focus in Mathematics GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K-2Addition and subtraction - concepts, skills, and problem solving and place value 3-5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6Ratios and proportional reasoning; early expressions and equations 7Ratios and proportional reasoning; arithmetic of rational numbers 8Linear algebra and linear functions

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18 + Focus on Major Work In any single grade, students and teachers spend the majority of their time, approximately 75% on the major work of the grade. The major work should also predominate the first half of the year.

19 + Shift Two: Coherence Think across grades, and link to major topics within grades Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

20 + Coherence Across and Within Grades Its about math making sense. The power and elegance of math comes out through carefully laid progressions and connections within grades.

21 + Coherence Think across grades, and link to major topics within grades Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

22 + Coherence Across the Grades? Varied problem structures that build on the students work with whole numbers 5 = 1 + 1 + 1 + 1 +1 builds to 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 and 5/3 = 5 x 1/3 Conceptual development before procedural Use of rich tasks-applying mathematics to real world problems Effective use of group work Precision in the use of mathematical vocabulary

23 Coherence Within A Grade Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.5

24 + Rigor: Illustrations of Conceptual Understanding, Fluency, and Application Here rigor does not mean hard problems. Its a balance of three fundamental components that result in deep mathematical understanding. There must be variety in what students are asked to produce.

25 + Some Old Ways of Doing Business Lack of rigor Reliance on rote learning at expense of concepts Severe restriction to stereotyped problems lending themselves to mnemonics or tricks Aversion to (or overuse) of repetitious practice Lack of quality applied problems and real-world contexts Lack of variety in what students produce E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.

26 + Redefining what it means to begood at math Expect math to make sense – wonder about relationships between numbers, shapes, functions – check their answers for reasonableness – make connections – want to know why – try to extend and generalize their results Are persistent and resilient – are willing to try things out, experiment, take risks – contribute to group intelligence by asking good questions – Value mistakes as a learning tool (not something to be ashamed of)

27 + What research says about effective classrooms The activity centers on mathematical understanding, invention, and sense-making by all students. The culture is one in which inquiry, wrong answers, personal challenge, collaboration, and disequilibrium provide opportunities for mathematics learning by all students. The tasks in which students engage are mathematically worthwhile for all students. A teachers deep knowledge of the mathematics content she/he teaches and the trajectory of that content enables the teacher to support important, long-lasting student understanding

28 + What research says about effective classrooms The activity centers on mathematical understanding, invention, and sense-making by all students. The culture is one in which inquiry, wrong answers, personal challenge, collaboration, and disequilibrium provide opportunities for mathematics learning by all students. The tasks in which students engage are mathematically worthwhile for all students. A teachers deep knowledge of the mathematics content she/he teaches and the trajectory of that content enables the teacher to support important, long-lasting student understanding

29 + What research says about effective classrooms The activity centers on mathematical understanding, invention, and sense-making by all students. The culture is one in which inquiry, wrong answers, personal challenge, collaboration, and disequilibrium provide opportunities for mathematics learning by all students. The tasks in which students engage are mathematically worthwhile for all students. A teachers deep knowledge of the mathematics content she/he teaches and the trajectory of that content enables the teacher to support important, long-lasting student understanding

30 + What research says about effective classrooms The activity centers on mathematical understanding, invention, and sense-making by all students. The culture is one in which inquiry, wrong answers, personal challenge, collaboration, and disequilibrium provide opportunities for mathematics learning by all students. The tasks in which students engage are mathematically worthwhile for all students. A teachers deep knowledge of the mathematics content she/he teaches and the trajectory of that content enables the teacher to support important, long-lasting student understanding.

31 + Effective implies: Students are engaged with important mathematics. Lessons are very likely to enhance student understanding and to develop students capacity to do math successfully. Students are engaged in ways of knowing and ways of working consistent with the nature of mathematicians ways of knowing and working.

32 + Mathematical Progression: K-5 Number and Operations in Base Ten Everyone skim the OVERVIEW (p. 2-4) Divide your group so that everyone has at least one section: position, base-ten units, computations, strategies and algorithms, and mathematical practices Read your section carefully, share out 2 big ideas and give at least one example from your section

33 + Read through the progression document at your grade level. Discuss with your grade level team and record the following on your poster: Big ideas Progression within the grade level What is this preparing students for? Mathematical Progression: K-5 Number and Operations in Base Ten

34 Big Ideas Rather than learn traditional algorithms, childrens struggle with the invention of their own methods of computation will enhance their understanding of place value and provide a firm foundation for flexible methods of computation. Computation and place value development need not be entirely separated as they have been traditionally. Van de Walle 2006

35 Tens, Ones and Fingers Where does this activity fall in the progression and what clusters does this address? How can this activity be adapted?

36 36 Graphic Standards for Mathematical Practices

37 + The Standards for Mathematical Practice Skim The Standards for Mathematical Practice Read The Standards for Mathematical Practice assigned to you Reflect: What would this look like in my classroom? Review the SMP Matrix for your assigned practices Add to your recording sheet if necessary

38 + The Standards for Mathematical Practice Return to your home group and share out your practices.

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40 + Mathematical Practices in Action http://www.learner.org/r esources/series32.html? pop=yes&pid=873 http://www.learner.org/r esources/series32.html? pop=yes&pid=873 Using the matrix, what Mathematical Practices were included in these centers? What major and supporting clusters are addressed?

41 What makes a rich task? 1. Is the task interesting to students? 2. Does the task involve meaningful mathematics? 3. Does the task provide an opportunity for students to apply and extend mathematics? 4. Is the task challenging to all students? 5. Does the task support the use of multiple strategies and entry points? 6. Will students conversation and collaboration about the task reveal information about students mathematics understanding? Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al

42 + Environment for Rich Tasks Learners not passive recipients of mathematical knowledge Learners are active participants in creating understanding and challenge and reflect on their own and others understandings Instructors provide support and assistance through questioning and supports as needed

43 + Depth of Knowledge (DOK)

44 + Bring it all together Divide into triads Watch and reflect based on: What Makes a Rich Task? DOK Standards (which clusters and SMP were addressed?) As a group, using all three pieces of information, decide Is this a meaningful mathematical lesson?

45 + Bringing It All Together Counting Collections Video http://vimeo.com/45953002

46 + Estimating Groups of Tens and Ones Where does this activity fall in the progression and what clusters does this address? What mathematical practices are used? What makes this a good problem? What is the DOK? How can this activity be adapted?

47 Lets Analyze a Task

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49 Base-Ten Riddles Where does this activity fall in the progression and what clusters does this address? What mathematical practices are used? What makes this a good problem? What is the DOK? How can this activity be adapted?

50 https://www.teachingchannel.org/videos/second-grade- math-lesson

51 + Patterns on a 100 chart

52 + Adapting a Task In your group, think of ways to adapt this problem

53 More and Less on the Hundred Chart Where does this activity fall in the progression and what clusters does this address? What mathematical practices are used? What makes this a good problem? What is the DOK? How can this activity be adapted?

54 Big Ideas A good base-ten model for ones, tens and hundreds is proportional. That is, a ten model is physically ten times larger than the model for one, and a hundred model is ten times larger than the ten model. No model, including a group able model, will guarantee that children are reflecting on the ten-to-one relationship in the materials. With pre-grouped models, we need to make an extra effort to see that children understand that a ten piece really is the same as ten ones. Van de Walle 2006

55 + Homework Tasks At our next meeting we are going to analyze student work For your grade level task: Read through it at least twice Solve it Complete the Rich Task Pre-Planning Sheet

56 + Reflection What is your current reality around classroom culture? What can you do to enhance your current reality?

57 + Next Meeting… Questions? Contact? Next Meeting?

58 + Operations and Algebraic Thinking Success Implementing CCSS for K-2 Math

59 + Todays Objectives Develop a deeper understanding of how students progress in their understanding of the Common Core clusters related to operations and algebraic thinking in grades PreK-2. Learn engaging instructional strategies through hands on activities that connect content to the mathematical practices.

60 + Quiz What is your definition of Operations and Algebraic Thinking?

61 Collaboration Protocol-Looking at Student Work 1. Individual review of student work samples (10 min) All participants observe or read student work samples in silence, making brief notes on the form Looking at Student Work 2. Sharing observations (15 min) The facilitator asks the group What do students appear to understand based on evidence? Which mathematical practices are evident in their work? Each person takes a turn sharing their observations about student work without making interpretations, evaluations of the quality of the work, or statements of personal reference. 3. Discuss inferences -student understanding (15 min) Participants, drawing on their observation of the student work, make suggestions about the problems or issues of students content misunderstandings or use of the mathematical practices. Adapted from: Steps in the Collaborative Assessment Conference developed by Steve Seidel and Project Zero Colleagues 4. Discussing implications-teaching & learning (10 min) The facilitator invites all participants to share any thoughts they have about their own teaching, students learning, or ways to support the students in the future. How might this task be adapted to further elicit students use of Standards for Mathematical Practice or mathematical content. 5. Debrief collaborative process (5 min) The group reflects together on their experiences using this protocol. Select one group member to be todays facilitator to help move the group through the steps of the protocol. Teachers bring student work samples with student names removed.

62 + Read through your grade level progression document for your grade level. Discuss with your group and record on your poster. What fluencies are required for this domain? What conceptual understandings do students need? How can this be applied? Mathematical Progression: Operations and Algebraic Thinking Rigor

63 + Major and Supporting Clusters: A Quick Review One of the shifts from our current Math Standards to the Common Cores State Standards is the idea of focus. Students spend more time learning deeply with fewer topics. Grade level concepts have been divided into major, supporting and additional clusters.

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65 + Bring it all together… AGAIN! Divide into triads Watch and reflect based on: What Makes a Rich Task? DOK Standards (which clusters and SMP were addressed?) As a group, using all three pieces of information, decide Is this a meaningful mathematical lesson?

66 + Bringing It All Together Wheels Video http://www.learner.org/resources/series32.ht ml#

67 + Lunch

68 Eyes, Fingers, and Legs Where does this activity fall in the progression and what clusters does this address? What mathematical practices are used? What is the DOK? How might students solve these problems? What student misconceptions might arise? How can this activity be adapted?

69 + Homework: Adapting a Task

70 + Welcome Back Session 4

71 + Objectives for the day Develop a deeper understanding of how students progress in their understanding of the Common Core clusters related to operations and algebraic thinking in grades PreK-2. Learn engaging instructional strategies through hands on activities that connect content to the mathematical practices.

72 + HW - Analyzing and Adapting Tasks With a partner, go through the Deep Task Analysis Sheet on the task you adapted Consider: Do you achieve the outcome you expected? How well did your students engage in the task? Where their any surprises? What questions would ask students based on their work? How would you change this task for next time?

73 + Reviewing the SMP Reflect on the work we have done and your students have done and write the SMP assigned to your table in student friendly language. Record your thoughts on a poster.

74 + WA Kids

75 + Smarter-Balanced Assessment Consortium (SBAC) In your groups, work through the assessment task Consider – what standards are necessary for students to master in my grade level so they can be successful with this task?

76 + Consider WA Kids and SBAC… What are some implications of WA Kids and SBAC in mathematics? Look at your major and supporting clusters and the progression documents– what are the milestones students need to attain in order to prepare for the 3 rd grade assessment? Where should we focus instruction if students arent coming to us prepared? What can we do to ensure our students are prepared?

77 + Classroom Connections…. Students using Quick Images:As you watch this video Reflect on the following: Where does this fit on our progression? How can this be adapted to meet the needs ofyour students? What mathematical practices did you observe? What can be assessed from this activity? https://www.teachingchannel.org/videos/visualizing-number-combinations?fd=1 https://www.teachingchannel.org/videos/visualizing-number-combinations?fd=1

78 + Addition and Subtraction Situations There were 7 children at the park. Then 4 more showed up.How many children were at the park all together? There were 7 children at the park. Some more showed up.Then there were 11 children in all. How many more childrencame? There were some children at the park. Four more childrenshowed up. Then there were 11 children at the park. Howmany children were at the park to start with? Now consider different ways you can use these scenarios and what makes one more difficult than another. One might askstudents…..

79 + Which equation matches? + 4 = 10 6 + 4 = 6 + =10

80 + Teacher Questioning Strategies How can the questions you ask move students thinking forward? How should it differ forstruggling or high achieving students? Using the DOK, identify the level of some of thequestions on the matrix provided. What can students do to engage in themathematics more deeply? When you look at the website resources, whatmight work in your classroom? http://www.fcps.org/cms/lib02/MD01000577/Centricity/Domain/97/The%20art%20of%20questioning%20in%20math%20class.pdf http://www.fcps.org/cms/lib02/MD01000577/Centricity/Domain/97/The%20art%20of%20questioning%20in%20math%20class.pdf

81 + Connecting Literature with Math Concepts…. Other classroom connection ideas for OA? The hand game, Go Fish, Memory, Race to 10….

82 + Evaluation and Next Steps….


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