1. Common Core Mathematics Updates
Convocation 2013
Common Core Mathematics Updates

2. The digits of a four-digit number are 1,3,6 and 9, but not necessarily in that order.
- The thousands digit is prime.
- The hundreds digit is 3 more than the tens digit.
- What is the number?
2. A zoo has several ostriches and several giraffes. They have 30 eyes and 44 legs. How many ostriches and how many giraffes are in the zoo?

3. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable Arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning

4. Universal Design for Learning (UDL)
A set of principles for
curriculum development that applies
to the general education curriculum to promote learning environments that meet the needs of all learners

5. Actions and Expressions
Representation
Engagement
Actions and Expressions
“WHAT”
“WHY”
UDL
“HOW”
After reviewing Wall Wisher results;
These are the 3 Principles of UDL.
After setting goals and considering barriers for a lesson, you can eliminate most of the barriers by incorporating the 3 principles of UDL.
UDL Principles 5

6. UDL Principle 1: Representation 6
Recognition learning: identify and interpret patterns of sound, light, taste, smell and touch
Make connections with math instruction.
Provide multiple examples in every lesson (try to include examples and non-examples if possible)
Highlight critical features students need to know (through speaking, text, or digitally; use highlighters, circle key words, add post-it notes, etc.)
Present information in multiple media formats (such as being able to see, hear, or manipulate it)
Support and build on background knowledge (remembering that all students come to your classroom with very different experiences, tie background knowledge to new patterns) 6

7. Multiple Means of Representation Improves Learning for All
Act/ Express
Engage
Multiple Means of Representation Improves Learning for All
Non-verbal
Modeling
Pictures/videos
Realia/Concrete objects
Gestures
Movement
Manipulatives
Demonstrations
Hands-on
Picture dictionaries
Language Support
Word banks
Word walls
Labels
Graphic organizers
Sentence starters
Sentence frames
UDL Principle I: Provide Multiple Means of Representation (the “what” of learning).
Examples supportive of English Language Learners:
Non-verbal representation is important for English language learners as, by definition, their English language skills are weak.
Make use of the five senses: sight, touch, smell, hearing, and taste in representation.
Model content and academic language so students can see and hear;
Bring in real objects (also referred to as concrete objects or realia) so students can see, touch, smell, and perhaps taste the object
Use math manipulatives so students can see and touch math concepts, etc.
Representation that provides language support is critical.
Word banks, work walls, labels provide vocabulary.
Sentence starters and sentence frames which provide explicit language forms should be used to move students along the language continuum from the entering level to that of proficiency.
FIST to FIVE: On scale of 1-5 where are you? 7

8. Principle II: Multiple Means of Action and Expression
Represent
Represent
Action Expression
Engage
The “how” of learning: there is not one means of action and expression that will be optimal for all learners; providing options for action and expression is essential.
Judy Augatti 8

9. Principle 2: Action and Expression
UDL
Principle 2: Action and Expression

10. Multiple Means of Action and Expression
Represent
Role-play
Illustrations/ Drawings / Visuals
Gestures
First language use
Online tools (journaling, blogging, interactive math problem solving, assessments)
Action Expression
Engage
UDL Principle II:(the “how” of learning).]
Learners differ in the ways they navigate a learning environment and express what they know. There is not one means of action and expression that will be optimal for all learners; providing options for action and expression is essential for ELLs.
English language learners have limited knowledge of social and academic English. They may understand a concept, but not be able to express comprehension in English.
Differentiating instruction to include role-play, illustrations, gestures and focused use of their first language allows greater access to academic content<FOR ALL STUDENTS>
Online Instruction and Assessment tools include Socrative, Poll Everywhere, Student Response Systems
First language (L1) development is important in the acquisition of the second language. The stronger a student is in his first language, the easier it is to learn a second language. Math is often referred to as the universal language. (Miriam Leiva) The L1 can be used to clarify concepts and/or directions for classroom activities/procedures. ELLs may use their first language to help each other, tutor, ask and answer questions, use a bilingual dictionary, or clarify information. 
Teachers may use the student’s first language to check comprehension, explain an activity, provide books in languages other than English, and build relationships with students and families. 10

11. Principle III: Multiple Means of Engagement
Represent
Act/ Express
Engage
(The “why” of learning). 11

12. Principal 3: Engagement
Affect represents a crucial element to learning, and learners differ markedly in the ways in which they can be engaged or motivated to learn. There are a variety of sources that can influence individual variation in affect including neurology, culture, personal relevance, subjectivity, and background knowledge, along with a variety of other factors presented in these guidelines.
Some learners are highly engaged by spontaneity and novelty while other are disengaged, even frightened, by those aspects, preferring strict routine. Some learners might like to work alone, while others prefer to work with their peers.
There is not one means of engagement that will be optimal for all learners in all contexts; providing multiple options for engagement is essential. 12

13. Multiple Means of Engagement
UDL Requires
Multiple Means of
Engagement
Graphics
Group Writing
Problem Solving Teams
Role Plays
Interest Projects
Response Cards
Student Presentations
Real Life Simulations
Online tools
Manipulatives
Stimulate interest and motivation for learning 13

14. Content Emphasis
After reading sample CCSSM topics for their grade, ~80% say CCSSM is “pretty much the same” as their former standards
If CCSSM places a topic they currently teach in a different grade only about ¼ would drop it
From Bill Schmidt with Achieve
cc: Microsoft.com
- Bill Schmidt, Achieve 14

15. Focus - Coherence - Rigor -
The Three Shifts
Focus -
What do we want students to know and be able to do?
Coherence -
How will we know when they know it?
What will we do when they don’t know it?
Animate RIGOR
Rigor -
What will we do when they know it? 15

16. FOCUS = Major Work Major Work of the grade - Content Emphases
Do’s & Don’ts

17. Major Work Look at the major work for your grade level.
List ways that you can see the major work being applicable to the supplemental standards.

18. COHERENCE = Relationships
Always recognize vertical alignment.
Use support standards for reinforcement and application of major work standards.
Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole.

19. RIGOR
Conceptual
Understanding
Application
Skills and Procedures

20. RIGOR Conceptual understanding Teach more than “how to get the answer”
Ability so see math as more than a set of procedures or steps
Demonstrated by applying math concepts in new situations and speaking about their understanding

21. RIGOR Skills and Procedures
Expectation for speed and accuracy in calculation
Core function practice is necessary for fluency
Allows for understanding and manipulation of more complex concepts

22. RIGOR
Application
Requires rich brain base of conceptual and procedural understanding and fluency
Ability to choose the appropriate concept for application even when not prompted to do so
“real world”

23. Does a textbook offer rigor?
85% of teachers say the textbook is main resource- rather than the standards.
cc: Microsoft.com

24. Hong Kong / US Data US students ranked near the bottom.
Hong Kong had the highest scores in the most recent TIMSS.
Hong Kong students were taught 45% of objectives tested.
Hong Kong students outperformed US students on US content that they were not taught.
Hong Kong had the highest scores in the most recent TIMSS.
Hong Kong students were taught 45% of objectives tested.
Hong Kong students outperformed US students on US content that they were not taught.
US students ranked near the bottom.
US students ‘covered’ 80% of TIMSS content.
US students were outperformed by students not taught the same objectives.

25. What do you consider to be your greatest resource?

26. EACH OTHER 26

27. Resources
See the WIKI