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

+

Numbers and Operations in Base Ten

Success Implementing

CCSS for K-2 Math

+Introductions

+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

+Why CCSS?

Greta’s Video Clip

+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

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+What We are Doing Doesn’t 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

+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

+ WA CCSS Implementation Timeline

2010-11 2011-12 2012-13 2013-14 2014-15

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

+Transition Plan for Washington State

K-2 3-5 6-8 High School

Year 1- 22012-2013

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 andUnit 4: Connecting Algebra and Geometry through Coordinates; Unit 2: Similarity, Proof, and Trigonometry andUnit 3:Extending to Three Dimensions and remaining 2008 WA Standards

+Focus, Coherence & Rigor

+The Three Shifts in MathematicsFocus: Strongly where the standards focus

Coherence: Think across grades and link to major topics within grades

Rigor: Require conceptual understanding, fluency, and application

+Focus on the Major Work of the Grade

Two levels of focus ~• What’s in/What’s out• The shape of the content

+Shift #1: Focus Key Areas of Focus in MathematicsGrade

Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K-2 Addition and subtraction - concepts, skills, and problem solving and place value

3-5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6 Ratios and proportional reasoning; early expressions and equations

7 Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra and linear functions

+

+

+

+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.

+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.

+Coherence Across and Within Grades

It’s about math making sense.

The power and elegance of math comes out through carefully laid progressions and connections within grades.

+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.

+Coherence Across the Grades?

Varied problem structures that build on the student’s work with whole numbers5 = 1 + 1 + 1 + 1 +1 builds to

5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 and

5/3 = 5 x 1/3Conceptual development before proceduralUse of rich tasks-applying mathematics to real world problemsEffective use of group workPrecision in the use of mathematical vocabulary

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

+Rigor: Illustrations of Conceptual Understanding, Fluency, and Application Here rigor does not mean “hard problems.”

It’s a balance of three fundamental components that result in deep mathematical understanding.

There must be variety in what students are asked to produce.

+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.

+Redefining what it means to be “good 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)

+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 teacher’s 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















A teacher’s 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.

+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.

+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

+

Read through the progression document at your grade level.

Discuss with your grade level team and record the following on your poster: Big ideasProgression within the grade levelWhat is this preparing students for?

Mathematical Progression:K-5 Number and Operations in Base Ten

Big Ideas

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

Graphic

Standards for Mathematical Practices

+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

+The Standards for

Mathematical Practice Return to your home group and share out your

practices.

+

Mathematical Practices in Action

http://www.learner.org/resources/series32.html?pop=yes&pid=873

Using the matrix, what Mathematical Practices were included in these centers?

What major and supporting clusters are addressed?

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

+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

+Depth of Knowledge (DOK)

+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?

+

Bringing It All Together

Counting Collections Video

http://vimeo.com/45953002

Let’s Analyze a Task

+Patterns on a 100 chart

+Adapting a Task

In your group, think of ways to adapt this problem

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?


Big Ideas

+Homework TasksAt 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

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+

Next Meeting…Questions?

Contact?

Next Meeting?

+

Operations and Algebraic Thinking

Success Implementing

CCSS for K-2 Math

+Today’s 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.

+Quiz

What is your definition of Operations and Algebraic Thinking?

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 student’s 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 student’s 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 today’s facilitator to help move the group through the steps of the protocol.

Teachers bring student work samples with student names removed.

+

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

+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.

+

+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?

+

Bringing It All Together

Wheels Video

http://www.learner.org/resources/series32.html#

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?


+Homework: Adapting a Task

+

Welcome BackSession 4

+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.

+WA Kids

+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?

+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 3rd grade assessment?

Where should we focus instruction if students aren’t coming to us prepared?

What can we do to ensure our students are prepared?

+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 of your students?

What mathematical practices did you observe?

What can be assessed from this activity?

https://www.teachingchannel.org/videos/visualizing-number-combinations?fd=1

+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 children came?

There were some children at the park. Four more children showed up. Then there were 11 children at the park. How many 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 ask students…..

+Which equation matches?

+ 4 = 10

6 + 4 =

6 + =10

+Teacher Questioning Strategies

How can the questions you ask move students’ thinking forward? How should it differ for struggling or high achieving students?

Using the DOK, identify the level of some of the questions on the matrix provided.

What can students do to engage in the mathematics more deeply?

When you look at the website resources, what might work in your classroom?

http://www.fcps.org/cms/lib02/MD01000577/Centricity/Domain/97/The%20art%20of%20questioning%20in%20math%20class.pdf

+Connecting Literature with Math Concepts….

Other classroom connection ideas for OA?The “hand game”, Go Fish, Memory, Race to 10….

+Evaluation and Next Steps….

Documents

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