Implementing the Common Core State Standards

1st and 2nd Grade Math Series

January 17, 2011Barb Diliegghio

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GOALS OF MATH SERIES • Investigating the Common Core State Standards and the Standards for Mathematical Practice. (Critical Areas – Focal Points)

• Explore tasks that incorporate instructional strategies that deepen student understanding across the curriculum?

• Explore resources to support your Implementation efforts.

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FOCUS OF SERIES -CRITICAL AREAS (FOCAL POINTS)

Day 1: Developing understanding of whole number relationships and place value, including grouping in tens and ones (1st Grade) Extending understanding of base-ten notation (2nd grade)

Day 2: Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 (1st Grade) Building fluency with addition and subtraction (2nd Grade)

Day 3: Reason about attributes of, and composing and decomposing geometric shapes. (1st Grade)Describing and analyzing shapes (2nd Grade)

Developing understanding of linear measurement and measuring lengths as iterating length units (1st Grade) Using standard units of measure (2nd Grade) 3

AGENDA- DAY 1 Activities PART 1: INTRODUCTION Goals and Overview of the Core Content State Standards What’s New in Content? What’s New to Instruction?

Visit to a classroom video - Thinking Through a Lesson Protocol

PART 2: Day 1 Looking at ONE of the CRITICAL AREAS (Rich Tasks) Making Meaning of Number 1 – 20 Magnitude, comparing and ordering to 1000

LunchPART 2 continued: Magnitude of Number (Comparing and Ordering) PART 3: ASSESSMENT What’s New with the MEAP – Assessment PART 4: RESOURCESHearing From the Authors – Progression Document Using Today’s Information in your classroom – Homework

COMMON CORE STATE STANDARDS• Prepare students with

knowledge and skills needed for success in college and work

• Ensure consistent expectations regardless of student’s zip code

• Provide educators, parents and students with clear, focused guideposts (fewer, clearer) 5

http://www.corestandards.org

COMMON CORE STATE STANDARDS

Forty-five states have officially adopted the standards as of July 25, 2011. Michigan adopted as state curriculum, June, 2010. 6

COMMON CORE STATE CONTENT STANDARDS

The Content Standards focus on learning expectations for students,

• Include rigorous content and application of knowledge through high-order skills

• Includes both conceptual and procedural knowledge

• Build upon strengths and lessons learned from current state standards

• Internationally benchmarked• Based on evidence and research

7http://www.corestandards.org/

DESIGN AND ORGANIZATION Content standards define what students should understand

and be able to do Clusters are groups of related standards Domains are larger groups that progress across grades

REGROUP INTO GRADE LEVEL GROUPS

CCSS (CONTENT) – CROSSWALK DOCUMENT

Organized by Critical Areas:

• Common Content?• Content Moving into Level? • Content Moving Out?

The CCSS are intended to be clearer, more focused, learning trajectories across grade levels.

COMMON CORE STATE MATHEMATICAL PRACTICE STANDARDS

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning

of others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

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GROUPING THE PRACTICES

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William McCallum

Standards for Mathematical Practice Tucson, April 2011

Reasoning andexplaining

Modeling andUsing tools

Seeing structureand generalizing

PUMPKIN SEEDS

• http://www.learner.org/vod/vod_window.html?pid=874

While you watch the video:

• Teacher Moves• Teacher Questions• Evidence of Mathematical

Practices.

THINKING THROUGH THE LESSON PROTOCOL

Part of the Lesson Actions and Questions Part 1: LAUNCH

(Engage) What did you notice about the LAUNCH?

How did the teacher start the Task? How did the Teacher Organize the Task?

How did the teachers engage the students?How did the teacher introduce the math?

Teacher Questions? Part 2: EXPLORE How did the teacher have the students

investigate the mathematics? What were some of their strategies?

Teacher Questions? Part 3: DISCUSSION How did the teacher use the strategies to

help the students understand the mathematics? Teacher Questions?

MAKING MEANING OF NUMBER RELATIONSHIP

“ Three pictures hang in front of a six month-old child. The first shows two dots, the others one dot and three dots. The infant hears three drumbeats. Her eyes move to the picture with three dots.”

Learning and Teaching Early Mathematics, Clements and Surama, 2009 Taylor and Francis.

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NUMBER RELATIONSHIPS

Early Number Relationships• Spatial relationships

• One - Two More

• One - Two Less

• Benchmarking 5 and 10

HOW MANY ?

BUILDING NUMBER

1.) Five Frame2.) Ten Frame3) Double 10 frame

Games: Snap ShotWhat’s My Number?

USING PATTERNS AND STRUCTURELESSON: MAKING SENSE OF TEEN NUMBERS

• Making Numbers to 20

Word: ElevenSubitizing: 10 + 1 Place Value Notation:1 ten, 1 one

Patterns and Structure:16 = 10 + 5 + 1 19 = 20 – 1 Bundles: Generalizing: Fuel the Brain Applet.htm

http://www.fuelthebrain.com/Interactives/app.php?ID=29

GENERALIZING

1 more than 6 is 7

10 more than 6 tens is 7 tens.

100 more than 6 hundreds is 7 hundreds.

6 and 2 make 860 and 20 make 80600 and 200 make 800

4 and 4 make 8 5 and 3 make 8 40 and 40 make 8050 and 30 make 80

USING PATTERNS AND STRUCTURE

1st Grade: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. 1.) Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); 2.) decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); 3.) using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); 4.) creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

• Grade 2: 1.) Fluently add and subtract within 20 using mental strategies. 2 ) By end of Grade 2, know from memory all sums of two one-digit numbers.

COMPOSING AND DECOMPOSING

• Putting Together – 5 frame and 10 frame

7 +3

What do you notice?Can you take a fact you know and use a pattern to find the sum of another?

BEAN ACTIVITY MOVING FROM COUNTING TO PLACE VALUE • Count the number of Beans in your Bag• How would your students count the beans?

Is there an easier way to count these beans?

How can we be more accurate?

Multiple Representations: Place Value: 3 tens, 2 ones Symbolic: 32 Expanded Notation: 30 + 2 Manipulative : Bundles

Tens Ones

3 2

NUMBER LINE

• Spatial – Linear Model (Distance) Empty Number Line Activity How many Numbers? What Numbers? Patterns?

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157 159 160

http://www.fuelthebrain.com/Game/play.php?ID=15

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Balanced Assessment Consortium

What we think we know… What we don’t know yet…

• The SMARTER Balanced proposal suggests that there will be a constellation of assessments for grades 3-11 including: a) Adaptive comprehensive summative assessment that includes:

• 22% selected-response• 41% technology-enhanced constructed-response• 14% traditional constructed response• 23% performance

b) Adaptive interim/benchmarks based on learning progressions and or CCSS content clusters that calls for performance event bank and non-secure pool of items

c) Formative assessment tools, processes and practices that call for a variety of lesson embedded tools for different purposes.

We don’t know how much grade level content will be tested each year. “..full range of CCS with emphasis on problem solving, analysis, synthesis, and critical thinking.”

Assessing the Common Core Across States

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HOW DO I KNOW THEY UNDERSTAND ?

Unifix cubes10 frames

2 sided countersBean sticks

Number LineNumber Cards

Bundles

Ten framesDot patterns100 chart

Number LinePlace Value Charts

NumbersWords

Expanded FormPlace Value Notation

GeneralizeUnderstand

John A. Van de Walle

NUMBER RELATIONSHIP MAT Number Relationship Mat

1.) Work with a friend. You will need a mat, sleeve, dry erase marker.

2.) Choose a number between 11 – 19 that you will both write inside the star on your mat.

3) By yourself, fill in all the sections on your mat.

4.) Compare your mats. Do you agree? What is the same about your mats? What is different?

HTTP://WWW.INSIDEMATHEMATICS.ORG/INDEX.PHP/TOOLS-FOR-TEACHERS/NUMBER-OPERATIONS/389-2ND-GRADE

INSIDEMATHEMATICS.ORG

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Carol’s Numbers

1. Work through this activity. 2. Rubric3. Student Responses. 4. Information about student thinking.

RESOURCES • Progression Document - Number and Operation in Base 10, pages 1 – 11

• Arizona Department of Education http://www.azed.gov/standards-practices/mathematics-standards/Unpacking the Common Core State Standards

• MAISD Wikki site http://maisdccssm.wikispaces.com/

From the Common Core State Standards Introduction

• Page 5

These Standards are not intended to be new names for old ways of doing business.They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.

END-OF-DAY REFLECTIONS

1. Pick an idea that came up today and that you found particularly interesting.

2. What questions do you still have?

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HOMEWORK

Task: • Choose at least one

task. (10 frames, beans, counting, patterns in facts, number line, Carol’s Numbers.)

• Collect student work. • Be prepared to share

student samples.

Readings: Articles

1.) Fluency and the License to Think

2.) Preparing For Problem Solving