Implementing the CCSS Standards for

Mathematical Practice

Marlene M. Lovanio CCLM Dinner Meeting

2012

A Picture of Bristol

DRG G42% Free/reduced lunch

26% Minority8613 Students

9 Elementary schools3 Middle schools

2 high schools

Bristol’s Plan

Summer 2010State Curriculum and Sample Task Development

2011 – 2012 Introduce and Apply Mathematical Practice Standards

2010 – 2013 Curriculum Revision & Materials Alignment/Purchase

2011 – 2014 Implementation

2014 -2015 New Assessment Smarter Balanced Assessment Consortium

A Focus on the Practice Standards

• MS – 9 hours• HS – 6 hours • Elementary – 1 – 12 hours

Elementary PD Comments

What is clear?

“Change is coming, modeling math w/real world situations is important, discussion is essential.”

“We need to push them further & use more discussion during lessons (critique & reason).”

What are your next steps?

“Infusing the practices learned today to help students become better mathematicians.”

MS PD Commitments

Utilize:• Strand 25 & Connected Math

Project Activities• Word Walls• Writing in Math Journals

Next Steps:Rubric DevelopmentTechnology TrainingStrategies Instructional support

HS PD Commitments

Focus on:Problem solvingModelingDeveloping arguments

Next Steps:StrategiesInstructional support

What does it look like?

The biggest challenge is to show what the standards mean and how that will change classroom practice.

POSING MEANINGFUL PROBLEMS

From this

Identify each number as prime or composite

to …

Which one is different? Explain your reasoning.

25 51 53 52 135

Find more than one possible answer.

Mathematical Practices

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.

From this

Find 20% of 350,000

to …

An international fast food chainreports that 8% of the people in the United States eat at its restaurants each day. The fast food chain currently has 12,800 stores in the United States. The most recent Census Bureau report states that approximately 310 million people live in the United States.

Make a conjecture as to whether or not you believe the report from the fast food chain to be accurate. Create a mathematical argument that validates your conclusion.

Mathematical Practices

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.

From this Today we will use Area = ½ (b1+b2) to solve area of

trapezoid problems…

to …

The area of a trapezoid can be determined from the what you know about the area of rectangles and parallelograms. Determine how the areas of these figures are related using your manipulatives. Explain your reasoning.

Mathematical Practices

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.

From thisA rectangle has side lengths of 7 m and 9 m. A

square with side length 5 m is cut out of the rectangle. Find the area of that rectangle after the square is cut out.

to…

Below is a satellite photo of Geoff’s yard. He is interested in re-sodding his entire yard. Help him out by providing a cost estimate.

• Develop a list of questions you would need answered before you can solve the problem.

Contributed by Bristol Central Geometry Teachers

CLASSROOM RESOURCES

Student’s Guide for Success

K-12 Resources

Elementary Schools

• Curriculum Development and Implementation K, 2, 4• Introduction of enVision Math Common Core • Professional Development

– Job embedded coaching– PD Days– Wednesday afternoons

• Principals Guide and PD

Lesson Components

What the teacher is doing…

What the students are doing…

Assessment of learning

Instructional Delivery

(15-20 min.)

•Observing individual and group work

•Listening and probing further

•Using quick-checks to gauge student understanding

•Engaging students in self-assess

A Principal’s Guide to Elementary Mathematics Instruction K-5

• Working independently or cooperatively in small groups

• Asking questions to clarify and deepen understanding

• Participating and actively listening to discussions

• Sharing strategies and solutions

• Making connections to the real world, among math concepts and other disciplines

• Recording work/important concepts

• Launching investigation of a concept or real-world problem

• Modeling new concepts

• Posing a variety of levels of questions

• Providing opportunities to move between diff. representations

• Introducing new vocabulary and utilizing the word wall

• Facilitating discussions, noting key ideas and uncovering misconceptions

Lesson Components

What the teacher is doing…

What the students are doing…

Assessment of learning

Active Learning

(20–30 min.)

•Facilitating small group learning and independent practice

•Using a workshop model to differentiate instruction

•Providing students with a variety of problems, centers, games or rich tasks for practice and extension

•Working independently or cooperatively in small groups

•Asking questions to clarify and deepen understanding

•Making connections to the real world, among math concepts and other disciplines

•Developing proficiency

•Observing individual and group work

•Listening and probing further

•Collecting and analyzing written work

A Principal’s Guide to Elementary Mathematics Instruction K-5

Throughout the lesson students should be: (CT Common Core Mathematical Practice Standards)

Problem Solving – Rich problems are part of the lessons. Students make sense of problems, know how they relate to similar problems, plan and persevere in solving problems using a variety of methods and recognize when an answer makes sense or doesn’t.Reasoning Mathematically – Situations are presented that require students to make sense of the numbers involved, the relationship between them and be able to use numbers and symbols to match the situations. Students interpret and write story problems. Justifying and Explaining – Opportunities are created for students to communicate about their strategies and solutions orally and in writing. They listen to other strategies, point out when a solution is mathematically valid or not, explain why and adopt more efficient ones.Modeling with Mathematics – Real-world scenarios are discussed and presented. Students use appropriate mathematical representations (number sentences, geometric shapes) to represent problems and solve them. Students interpret a solution in context. Using Appropriate Tools – Tools, manipulatives and technology are used. Students know what tools to use to solve a problem (e.g. base- ten blocks, calculator, ruler, pen and paper) and explain why. They estimate solutions prior to computing. Using Precise Vocabulary, Symbols and Labels – Everyone is accountable for mathematical language. Students use mathematical terms and know their definitions. They understand what symbols mean and correctly label and assign units when appropriate. Looking For and Make Use of Structure and Regularity – Patterns and the structure of math is highlighted. Students recognize and describe patterns in their problem solving. They apply mathematical properties and find shortcuts to solve similar problems.

A Principal’s Guide to Elementary Mathematics Instruction K-5

Principal’s Guide

“ I Love it.  (It) focuses on just the lesson design and delivery and is great for teachers that have management and rapport, climate down. ”

Rochelle Schwartz PrincipalEllen P. Hubbell School

New K, 2, 4 Materials

Interactive Learning

Visual Learning Bridge

• Connects concrete work to pictorial models

• Bridges from pictorial models to symbolic representation

Guided Practice

Problem-Solving Recording Sheet

MOVING TO STRATEGIES 6-12

Strategies to Promote the MPS• Pose meaningful problems• Plan and use higher order questions• Develop perseverance

Examples include:• Ask 3 then me• Group diplomats• Fermi problems • Poster method • Explorations

Strategies to Promote the MPS• Encourage communication & listening• Create an environment for questions• Develop thinkers

Examples include:

• Ask Why? Do you agree? Why? Why not?• Four Corners• Philosophical Chairs • Turn and talk• Think(Jot)-Pair-Share• Quick Draw• Summarization• Multiple Methods

Word Walls

Exit Tickets

Explain how to break apart 7 6 into two smaller facts in order to solve the problem.

Next Steps

Next Steps: 2012 and Beyond

• Continued coaching at all levels• More PD sessions• Math Leadership Training• Dissemination of SBAC information and

sample items