1. Implementing the CCSS Standards for Mathematical Practice
Marlene M. Lovanio
CCLM Dinner Meeting
2012

2. A Picture of Bristol
DRG G 42% Free/reduced lunch 26% Minority 8613 Students 9 Elementary schools 3 Middle schools 2 high schools

3. Bristol’s Plan
Summer 2010
State Curriculum and
Sample Task Development
2011 – 2012
Introduce and Apply Mathematical Practice Standards
2010 – 2013
Curriculum Revision & Materials Alignment/Purchase
2011 – 2014 Implementation
New Assessment Smarter Balanced Assessment Consortium
Pose this question to the group…. Share answers.

5. A Focus on the Practice Standards
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 – 9 hours
HS – 6 hours
Elementary – 1 – 12 hours
MS PD Commitments
Utilize:
Strand 25 & Connected Math Project Activities
Word Walls
Writing in Math Journals
Next Steps:
Rubric Development
Technology Training
Strategies
Instructional support
HS PD Commitments
Focus on:
Problem solving
Modeling
Developing arguments
Next Steps:
Strategies
Instructional support

6. What does it look like?
The biggest challenge is to show what the standards mean and how that will change classroom practice.

7. Posing Meaningful problems

8. From this Identify each number as prime or composite to …

9. 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.
Which one is different? Explain your reasoning.
Find more than one
possible answer.

10. From this Find 20% of 350,000 to …

11. 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.
An international fast food chain reports 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.

12. From this Today we will use
Area = ½ (b1+b2) to solve area of trapezoid problems…
to …

13. 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.
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.

14. From this
A 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…

15. 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

16. Classroom Resources

19. Student’s Guide for Success

20. K-12 Resources

21. 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

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

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

24. 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.

25. 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
Principal
Ellen P. Hubbell School

26. New K, 2, 4 Materials
About 50,000

27. Interactive Learning

28. Visual Learning Bridge
Connects concrete work to pictorial models
Bridges from pictorial models to symbolic representation

29. Guided Practice

30. Problem-Solving Recording Sheet

31. Moving to Strategies 6-12

32. 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

33. 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

34. Word Walls

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

36. Next Steps

37. Next Steps: 2012 and Beyond Continued coaching at all levels
More PD sessions
Math Leadership Training
Dissemination of SBAC information and sample items