August 2012

Common Core State Standards in Mathematics:

ECE-5

Agenda

•Instructional Shifts in Mathematics•Activating the Instructional Shifts•Learning Trajectory•Standards for Mathematical Practice•Using classroom video to make connections•DPS Tools/Resources

1.Focus: Narrow and deep emphasis based on standards.

2.Coherence: Across grades and to major topics within grades.

3.Rigor: Equal intensity of conceptual understanding, procedural skills and fluency, and application.

Instructional Shifts in Mathematics

Turn and Talk: What do these shifts mean?

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Application

CCSS Domain Progression

Instructional Shift: Focus

• K: Counting and Cardinality, Joining (addition) and Separating (subtraction); Place Value

• 1: Addition and Subtraction, Place Value, Measurement

• 2: Addition and Subtraction (with application to measurement), Place Value

• 3: Multiplication and Division, Fractions as Number; Area and Measurement

• 4: Four Operations, Place Value, Fraction Equivalence (including decimals) and Operations

• 5: Place Value (including decimals), Operations with Fractions, Volume

Development of Fluency

Mathematics Inequalities

Turn and Talk:

• Fluency with Basic Facts ≠ Memorized Basic Facts

• Knowing from Memory ≠ Memorization

Activate Knowledge about Shifts

Tomas and Sarah collect baseball cards.  Sarah has 18 more cards than Tomas.  She has 200 cards.  How many cards does Tomas have?

A pencil costs 59¢ and a sticker costs 20¢ less. How much do a pencil and a sticker cost together?

Connecting: Practice Standards with Content Standards

• Standards for Mathematical Practice: Ways students should engage with content as they grow in mathematical maturity and expertise

• Standards for Mathematical Content: Balanced combination of procedure and understanding

• Content standards which set an expectation of understanding are “points of intersection” between the Standards for Mathematical Content AND the Standards for Mathematical Practice

Rationale for Trajectory: Addition and Subtraction

• Important starting point for professional development in the new standards

• Major area of emphasis at multiple grade levels

• Provides a framework for analyzing• Development of representational models/tools• Key contexts such as joining, separating, and

comparing• Multiple strategies (e.g., place-value strategies

and properties of operations)

Organization of Math Standards

Studying the Learning Trajectory

• Read the standards for each grade level (begin with K) and discuss what students need to know and be able to do in that grade.

• As you shift to the next grade level, analyze how the demands of the standards change. Consider changes in:• Content (e.g., number system and magnitude of

numbers)• Representations (e.g., use of number sentence,

manipulatives, graphs, diagrams, charts, tables)• Processes (e.g., problem solving, reasoning, mental

math, communication)• Document your findings in the table provided.

Learning Trajectory Discussion

• What are the key learnings from this kind of analysis?

• What evidence of the instructional shifts can you identify from your study of the learning trajectory?

• What are the key ideas that support the Big Idea from the Learning Trajectory?

Implications of Learning Trajectory

• Therefore, it’s about . . .• Understanding alignment and its

implications • Collaborative processes • K-12 perspective on alignment• Collegial conversations

Activate Knowledge about Shifts

• Luke wrote a note to his mother. It took him 68 seconds to find a pen, 42 seconds to find paper, and 41 seconds to write it. Did it take Luke more than 3 minutes to complete the note? Explain.

• What content has to be understood to solve this problem?

• Where on our learning trajectories do you see the content necessary to solve this problem?

Standards for Mathematical Practice

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.

SMP: 1 and 7

• Carefully read these Standards for Mathematical Practice• Share the verbs. We will chart these.• How do these verbs show evidence of

the instructional shifts in math?

Learning from Video

The videos are not used to critique the teaching we will see. Teaching is far too complex for a thoughtful judgment to be made from a video segment that allows us no more than a brief glimpse into the classroom.

Common Core Classrooms in Action

• How might second grade students solve the following problems?

46 233

+37 +158

Common Core Classrooms in Action: Take 1

As you watch the video, consider:• How is conceptual understanding of addition

demonstrated by the students in the video?• How do the students use place value to solve the

addition problems? How does this represent the Instructional Shifts?

• How are students developing their expertise in the Standards for Mathematical Practice?

Common Core Classrooms in Action: Take 2

As you watch the video a second time, consider:• How does the teacher’s questioning reveal student

understanding?• How are these teacher moves reflected in the

Framework for Effective Teaching? Focus on I-2 to I-4 (pp 9-13) both teacher and student behaviors.

Instructional Tasks

•Provide students with necessary skills to engage successfully in complex tasks or non-routine situations

•Provide students with opportunities that prepare them for the rigor of the new standards

•Provide teachers with strategies to support students’ engagement and perseverance in complex tasks

Instructional Tasks

• Incorporated in a current unit of study (will replace a lesson, an activity, or an assessment)

• Provide opportunity to apply the Standards to specific tasks with explicit reference to the CCSS for Mathematics

• Explicit connection to the Framework for Effective Teaching—New this year!

• Includes content/language objective--New this year!

Instructional Task: Do the Math!

• Individually, do the math.• Individually, consider:

• What mathematical content and practices can be learned from the task?

• What are all the ways the task can be solved?• What misconceptions might students have?• What errors might students make?• What resources/tools might you want to have

available?• Share at table.

Instructional Tasks: Connections

• How will the Instructional Task support the Instructional Shifts?

• What opportunities does the Task provide for students to develop expertise in the Standards for Mathematical Practice? Which Standard(s)? How?

• In looking at the Expectations and Indicators in the Framework for Effective Teaching, how are these enacted in the Task?

Components of DPS Content/Language Objective

• Content: What will students learn based on the lesson?

• Targeted Domain: What domain (speaking, listening, reading, writing) will be targeted in lesson?

• Language Function: How will students use the language in the lesson?

• Language Form: What grammatical structures and what academic vocabulary will be used?

• Differentiated Language Supports: What supports will my students need to understand the content?

Content/Language Objective

Students will add fractions to make the sum of one whole and explain their thinking, orally and in writing, using academic language (e.g., equal, equation, equivalent fractions) and supports such as

a. fraction bars,

b. drawings, or

c. other classroom manipulatives.

DPS Tools/Resources to Support Instructional Shifts

• Instructional Tasks with PCK Modules • Time Frame documents

• Provide a guide to ensure that sufficient time is devoted to the topics of major emphasis

• Essential Learning Goal (ELG) documents• Describe the key learnings for students

based on the topics of major emphasis in the CCSS

Reflection on Session

Quick Write: How will this learning impact your work this year?

Turn and Talk: Share your responses with a partner at your table.

Keep in mind: 2012-13 is a transition and learning year to prepare us for full implementation of CCSS in 2014-15.