Implementing the Common Core State Standards

1st and 2nd Grade Math Series

February 6, 2012Barb Diliegghio

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WELCOME

Welcome Back!!!

Table Share: What Activity? Adaptations? Thoughts? Observations?

What did you learn about Student Thinking?

FOCUS OF SERIES -CRITICAL AREAS (FOCAL POINTS)

Day 1: Number Relations: 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: Operations and Algebraic Thinking: 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: Geometry and Measurement: 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 2 Activities PART 1: Sharing out over Day 1 tasks.

PART 2 Developing understanding of Meaning of addition, subtraction, Investigate the CCSS. Look at modeling – Table 1 PART 3 Investigate the CCSS Initiative – Oakland Schools LunchPART 4 Building fluency with addition and subtraction (2nd Grade) Using the number line and base 10 blocksPart 5: Rich Task: Bean Sprouts, The Apple Farm, Illuminations

Hearing From the Authors – Progression Document Using Today’s Information in your classroom – Homework

CCSS ACROSS THE GRADE LEVEL

Domains: Operations and Algebraic Thinking

Number and Operation in Base 10

Addition and Subtraction Progressions Across the Grade Levels:

Study your grade Level, be ready to share: 1st? 2nd?

PART 1: MAKING MEANING OF ADDITION AND SUBTRACTION

Math is a human activity. The operations are a verb. Children have been “doing math” all their lives. • First breath : What operation? Why? • Look into a child’s life a.) Getting Ready for School b.) In your classroom c.) On the playground d.) At Home, family chores

MAKING MEANING OF ADDITION AND SUBTRACTIONPROBLEM TYPES (TABLE 1 – CCSS )

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COMMON CORE STATE STANDARDS INITIATIVE

The Common Core State Standards Initiative (CCSSI) provide support and direction for educators as they move toward full implementation:

CCSS aligned curriculum and coherent units of study to highlight needed shifts in content related and pedagogical practices

• Highlight Lesson• Formative Assessment• Resources (video, sample student work, rubrics, instructional websites, etc.)

KEY FEATURES OF CCSS UNIT

• Use of student thinking

• Incorporation of mathematical talk, multiple representations, multiple strategies

• Learning opportunities that include student inquiry and exploration

Adapted from Van de Walle, J.A. (2004) Elementary and Middle Schools Mathematics: Teaching Developmentally.

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Pictures

Oral Language

ManipulativeModels

Real-World Situations

WrittenSymbols

2012 - 2014 IMPLEMENTATION

Year 1 August 2011 1 unit per grade level

Year 2 August 2012 4 units per grade level

Year 3 August 2013 3 units per grade level

ORIENTATION TO THE UNIT

Use the annotated template and your grade level unit to orient

yourself with the format of a Unit.

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GRADE LEVEL UNIT COMPONENTS 1. Unit Themes

• Graphic• Focus Questions• Intellectual Processes• Key Concepts

2. Content Standards• Abstract• CCSS Standards

3. Instructional Resources• Illuminations• Texas Instruments• TI-nSpire• References• Applets

4. Professional Resources• NCTM Articles• Books 12

CONCEPT MAP, KEY CONCEPTS, FOCUS QUESTIONS, PRACTICES

Locate your unit of study within the sequence of unit titles for the year. Then, looking at only the sections on the first page of your grade level unit consider the following questions:

How does this unit compare to your current practice around the concept of place value

What is the same? What seems to be different?

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UNIT ABSTRACT AND CCSS STANDARDSLooking at the Abstract and CCSS Standards sections of your grade level unit consider the following questions:

How does the information in these two sections add to teachers’ understanding of what students need to know and be able to do at the end of unit?

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INSTRUCTIONAL AND PROFESSIONAL RESOURCES

In your table groups cooperatively explore the Instructional and Professional Resource sections of your grade level unit and consider the following questions:

How might you use the resources in these two sections to deepen your understanding of the mathematics and how might you support your student’s learning?

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TAKE A BREAK

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ORIENTATION TO THE LESSON

Orient yourself with the format of a Highlight Lesson.

Compare a Unit and the corresponding Highlight Lesson,

how are they related and how are they unique?

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HIGHLIGHT LESSON COMPONENTS 1. Model Lesson Themes

• Graphic• Focus Questions• Intellectual Processes• Key Concepts

2. Model Lesson Content Standards• Abstract• CCSS Standards• Lesson Instructional

Resources

3. Sequence of Lesson Activities• Selecting and Setting up a

Mathematical Task• Launch• Supporting Students’

Exploration of the Task• Sharing and Discussing the

Task

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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?

METHODS USED FRO SOLVING SINGLE-DIGIT ADDITION AND SUBTRACTION PROBLEMS

GROUPING THE PRACTICES

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William McCallum

Standards for Mathematical Practice Tucson, April 2011

Reasoning andexplaining

Modeling andUsing tools

Seeing structureand generalizing

http://oaklandk12-public.rubiconatlas.org/c/maps/search.php

1.) Search Tab 2.) School : Common Core

3.) Choose Grade Level 4.) Subject: Mathematics

LUNCH11:30-12:00

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DEMONSTRATING THE MATHEMATICAL PRACTICES

Standard 2.Oa.1, Solve Addition And Subtraction Word Problems Within 100Teaching Children Mathematics, “CCSSM: The Big Picture”, Feb. 2012

1.) Make sense and persevere in solving problems

Students make sense of the context and find a way to explore the problem using objects or drawings.

2.) Reason abstractly andquantitatively

Students can decontextualize the problem and match quantities to the numbers of dogs. Further, students can contextualize the quantities and explain what each quantity represents.

3.) Construct viable arguments and critique the reasoning of others

Students clearly and accurately make an argument to defend their strategy. Likewise, students accurately evaluate their classmates’ strategies.

4.) Model with mathematics Students create an equation to match their strategy and work. In our example, this could be 74 +__ = 131 or 131 – 74 = __.

5.) Use appropriate tools strategically

Students successfully use objects (e.g., base-ten blocks) or pictures to support their work.

6.) Attends to precision Students clearly and accurately communicate their process using visual models and written explanations. Their answers are accurate

7.) Look for and make use of structure

Students apply structure of our base-ten number system to support their work. In this example, students may start at 74 and recognize that if they skip count by tens, they eventually get to 124 and then can count on by ones to reach 131.

8.) Look for and express regularity in repeated reasoning

While solving future problems, students use known information to help them. For example, a student may reason, “I know that when I have a missing addend, I can start with my first number and count up. So I am going to start at 34 and then count up until I get to 131

HOW DO I KNOW THEY UNDERSTAND ADDITION AND SUBTRACTION?

GeneralizeUnderstand

John A. Van de Walle

Number linesBase 10 blocksPlace Value Chart

Quick Draw

Building and Drawing

Math Sentence

Talk Aloud

MODELING:NUMBER LINE

• Counting All, Counting On• Counting Back

• Skip Counting - DecomposeJump, Jump, Game

There are 56 frogs on the walk, 27 hopped away. How many are left?

Strategies on the Number Line?

MODELS

Building and Drawing: 1.) Place Value Chart 2.) Base 10 Blocks3.) Quick Draw (Handout) = 100

I = 10 = 1

LET’S DO THE MATH

Real World Connection: There are 26 first grade students at the farm, 39 second grade teachers joined them. How many students are at the farm?

RE-GROUPING: PLACE VALUE CHART

Hundreds

Tens Ones

I I I I I

Addend

Addend

Decision ?

SUM

I

I I I I I I

I I I I I

SUBTRACTION : PLACE VALUE CHART

The students in our class are earning money for a trip to the zoo.

They need $43 for the trip. This month they earned $18 for the trip.

How much more money do they need to earn? (Compare)

BUILD ON THE PLACE VALUE CHARTHundreds Tens Ones

I I I I I

Minuend

Subtrahend

TAKE A BREAK

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BEAN SPROUTS

http://www.learner.org/resources/series32.html?pop=yes&pid=877#

YOUR TURN

2nd Grade: Apple Farm

1st Grade: Illuminations Tasks

1.) Work through the task2.) Use the TTLP to frame the activity3.) Focus on questioning strategies.

RESOURCES

• Progression Document : Algebraic Thinking

• Illuminations.nctm.org http://illuminations.nctm.org/LessonDetail.aspx?ID=U41

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

NATIONAL & STATE ONLINE RESOURCES

• Common Core Standards http://www.corestandards.org/

• Crosswalk Document www.mi.gov/mathematics

• Progression Documents http://math.arizona.edu/~ime/progressions/

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: • CCSSI Highlight

Lesson • Bean Sprouts • Apple Farm • Illuminations Tasks

Readings: Articles

1.) Progression Document: Cardinality and Algebraic Thinking, K-2

2.) Thinking About Place Value