Numbers and Operations in Base Ten

+

Numbers and Operations in Base Ten

Success Implementing

CCSS for K-2 Math

Day 1

+Introductions

+Overall Outcomes

Recognize the interconnectedness of the Standards for Mathematical Practice and content standards in developing student understanding and reasoning.

Illuminate practices that establish a culture where mistakes are a springboard for learning, risk-taking is the norm, and there is a belief that all students can learn.

+We need to Support the

Whole Child (ASCD)

Healthy

Safe

Engaged

Supported

Challenged

Sustainability

+ Whole Child Tenet 1:

Healthy

Each student enters school healthy and learns about and practices a healthy lifestyle.

ASCD

+ Whole Child Tenet 2:

Safe

Each student learns in an environment that is physically and emotionally safe for students and adults.

ASCD

+ Whole Child Tenet 3:

Engaged

Each student is actively engaged in learning and is connected to the school and broader community.

ASCD

+ Whole Child Tenet 4:

Supported

Each student has access to personalized learning and is supported by qualified, caring adults.

ASCD

+ Whole Child Tenet 5:

Challenged

Each student is challenged academically and prepared for success in college or further study and for employment and participation in a global environment.

ASCD

+ Whole Child Tenet 6:

Sustainability

Schools implementing a whole child approach use collaboration, coordination, and integration to ensure the approach’s long-term success.

ASCD

+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

14

+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

+ 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

The materials should devote at least 65% and up to approximately 85% of the class time to the major work of the grade with Grades K–2 nearer the upper end of that range, i.e., 85%.

K-8 Publishers Criteria for CCSS-M

+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 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

+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

+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

+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.

+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.

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+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?

45

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

Video……

Using the matrix, identify one Mathematical Practice that was included in these centers?

What math skills/concept(s)are the students working on.

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)

+

Bringing It All Together

+Bring it all together

Divide into triads

Watch video 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?

VIDEO- Counting Collections

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?

How can this activity be adapted?

Big Ideas

+Homework and Reflections

+Preparing for Homework TasksAt our next meeting we are going to analyze student work

For your grade level task:

Read through the task at least twice

Solve it

Complete the Rich Task Pre-Planning Sheet

+Homework

Bring back copies of student work from grade level homework task (6-8 different students showing a variety of understanding, no names please or teacher marks).

Create/Modify/Find a Rich Task (Claim 2/3) to include in the Intel CCSS-M Item bank.

Bring back all handouts to our next session.

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+Wrap up Activity

Feedback

Stars – something new I learned today that earns a star

Wish – a question I wish to have answered

Hope – what I still hope to learn

Thank You!

See you next session…………..June 4th