1. Common Core Summer Institute: Delving In and Making a Difference
Dionne Mathews Nelloms
Elementary Mathematics Program Specialist
Education Transformation Office, Gadsden County Schools

2. Welcome Today, you have a two-fold morning mission:
Using the materials on you table, please make a table tent that includes your name, school, and anticipated grade level that you will be teaching for the school year.
Take a notecard and write at least one of the following:
Success—Briefly describe something that you have done in terms of implementing the Common Core State Standards that has worked for you and your students.
Goal(s)—Describe your goals for this year in terms of implementing the Common Core State Standards.

3. Unpacking the Standards (How & Why)
Day One: Agenda
Morning Session
Afternoon Session
College and Career Readiness
Exploring the Standards (Content and Practice)
Break
Examining the Critical Areas for grades 3-5
A peek inside the Common Core model classroom
Break
Unpacking the Standards (How & Why)

4. Objectives for the next few days…
Enhance our knowledge base of the Common Core State Standards for Mathematics.
Become more familiar with the structure of the Common Core State Standards for Mathematics.
Deepen our understanding of the Common Core Standards for Mathematics Practice.
Broaden our repertoires of instructional methods and techniques that support the standards.

5. Mission Statement
The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.
National CC website..sets the tone and grants us a purpose for this movement.

6. Integrating Initiatives
College & Career Ready Students
Standards-based and Data Driven Instruction
Common Core State Standards
Teacher/ Leader Effectiveness
Primary goal of the CC movement is to develop students that are College and Career Ready
Supporting this overarching goal are three main initiatives…

7. Florida’s CCSS Implementation Plan
Full Implementation Grade K
Begin Implementation of Literacy Standards in ALL Content Areas for Grades 6-12
Begin Implementation of Rich and Complex Text and Informational Text for Grades K-12
Full Implementation Grades K-1
Full Implementation of Literacy Standards in ALL Content Areas for Grades 6-12
Continue Implementation of Rich and Complex Text and Informational Text for Grades K-12
Full Implementation Grades K-2
Implementation of a Blended Curriculum (CCSS and Supplemental NGSSS Aligned to FCAT 2.0 and EOCs) for Grades 3-12
Full Implementation Grades K-12
PARCC Assessments Aligned to CCSS
Phase 1 ( )
Phase 2 ( )
Phase 3 ( )
Phase 4 ( )
Phase 3 of Florida’s implementation plan provides for full implementation of the Common Core State Standards for grades K-12 across all content areas.
The final implementation phase in will include assessments aligned to the Common Core State Standards for English Language Arts and Mathematics.

8. What does it mean to be college and career ready? BeyondTestPrep
With your tablemates, please share attributes of a career and college ready person.

9. Let’s See What Research Tells Us…
Read the article included in your handouts.
As we read, we will employ a close reading strategy of text marking.

10. Marking Up the Text
Check ideas that you are familiar with or are already doing in your classroom.
Mark anything that is new or interesting with an exclamation mark.
If there are confusing ideas or points that warrant clarification, please note them with a question mark.

11. Article Reflection Exercise
Share your notes with your tablemates, using the pass the microphone method.
Once everyone has shared, come to a consensus regarding the attributes of a career and college ready learner.
Now…creatively, cleverly, and clearly develop a chart that expresses your group’s ideas.
-Gallery Walk

12. Florida Transitions to Common Core State Standards
NGSSS
CCSS
Standards-based instruction
Test item specifications guide development of curriculum maps
Focus mini-assessments aligned to individual benchmarks and used to monitor student progress
Teaching benchmarks in isolation results in long lists of tasks to master
Standards-based instruction facilitated by learning goals
Big ideas and learning goals guide the development of curriculum maps
Learning progressions or scales describe expectations for student progress in attaining the learning goals
Assessments used to monitor student progress are aligned directly to the learning progressions or scales
Teaching big ideas narrows the focus and allows students to delve deeper for a greater depth of understanding

13. Priorities in Math
Grade
Priorities Support Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2
Addition and subtraction, measurement using whole number quantities
3–5
Multiplication and division of whole numbers and fractions 6
Ratios and proportional reasoning; early expressions and equations 7
Ratios and proportional reasoning; arithmetic of rational numbers 8
Linear algebra

14. Mathematics Shift 1: Focus
What the Student Does…
What the Teacher Does…
Spend more time on fewer concepts.
Gleam content from the curriculum
Focus instructional time on priority concepts
Give students the gift of time

15. Mathematics Shift 2: Coherence
What the Student Does…
What the Teacher Does…
Build on knowledge from year to year, in a coherent learning progression
Connect the threads of math focus areas across grade levels
Connect to the way content was taught the year before and the years after
Focus on priority progressions

16. Mathematics Shift 3: Fluency
What the Student Does…
What the Teacher Does…
Spend time practicing, with intensity, skills (in high volume)
Push students to know basic skills at a greater level of fluency
Focus on the listed fluencies by grade level
Uses high quality problem sets, in high volume

17. Key Fluencies K Add/subtract within 5 1 Add/subtract within 10 2
Grade
Required Fluency K
Add/subtract within 5 1
Add/subtract within 10 2
Add/subtract within 20
Add/subtract within 100 (pencil and paper) 3
Multiply/divide within 100
Add/subtract within 1000 4
Add/subtract within 1,000,000 5
Multi-digit multiplication 6
Multi-digit division
Multi-digit decimal operations 7
Solve px + q = r, p(x + q) = r 8
Solve simple 22 systems by inspection
Activity—fluency game

18. Mathematics Shift 4: Deep Understanding
What the Student Does…
What the Teacher Does…
Show mastery of material at a deep level
Articulate mathematical reasoning
Demonstrate deep conceptual understanding of priority concepts
Create opportunities for students to understand the “answer” from a variety of access points
Ensure that EVERY student GETS IT before moving on

19. Mathematics Shift 5: Application
What the Student Does…
What the Teacher Does…
Apply math in other content areas and situations, as relevant
Choose the right math concept to solve a problem when not necessarily prompted to do so
Apply math including areas where its not directly required (i.e. in science)
Provide students with real world experiences and opportunities to apply what they have learned

20. Mathematics Shift 6: Dual Intensity
What the Student Does…
What the Teacher Does…
Practice math skills with an intensity that results in fluency
Practice math concepts with an intensity that forces application in novel situations
Find the dual intensity between understanding and practice within different periods or different units
Be ambitious in demands for fluency and practice, as well as the range of application

21. Domains for K-12 Number and Operations in Base Ten (NBT)3 4 5 6 7 8 HS
Counting and Cardinality (CC)
Number and Quantity
Number and Operations in Base Ten (NBT)
The Number System
Number and Operations-Fractions (NF)
Ratios and Proportional Relationships (RP)
Operations and Algebraic Thinking (OA)
Functions (F)
Expressions and Equations (EE)
Algebra
Geometry (G)
Measurement and Data (MD)
Statistics and Probability (SP)

22. Florida’s Numbering of the Common Core State Standards
MACC.K.CC.2.5
Subject Grade Domain Cluster Standard
Subject
Mathematics Common Core
Grade K
Domain
Counting and Cardinality
Cluster
Count to tell the number of objects
Standard
Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
A-Z

23. Domain
Standards
Cluster Headings

24. Cluster Headings Cluster Headings Cluster Headings Cluster Headings
Domain
Cluster Headings
Domain
Cluster Headings
Domain
Cluster Headings
Domain
Cluster Headings 24

25. K-5 Domains and Critical Areas
Kindergarten Domains
Kindergarten Critical Areas
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Measurement and Data
Geometry
Representing and comparing whole numbers, initially with sets of objects.
Describing shapes and space.
More learning time in Kindergarten should be devoted to number than to other topics
1st Grade Domains
1st Grade Critical Areas
Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20.
Developing understanding of whole number relationships and place value, including grouping in tens and ones.
Developing understanding of linear measurement and measuring lengths as iterating length units.
Reasoning about attributes of, and composing and decomposing geometric shapes.
2nd Grade Domains
2nd Grade Critical Areas
Extending understand of base-ten notation.
Building fluency with addition and subtraction.
Using standard units of measure.
Describing and analyzing shapes.
3rd Grade Domains
3rd Grade Critical Areas
Number and Operation in Base Ten
Number and Operation: Fractions
Developing understanding of multiplication and division strategies for multiplication within 100.
Developing understanding of fractions, especially unit fractions (fractions with numerator 1).
Developing understanding of the structure of rectangular arrays and of area.
Describing and analyzing two-dimensional shapes.
4th Grade Domains
4th Grade Critical Areas
Number and Operations: Fractions
Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends.
Developing understanding of fractions equivalence, addition and subtraction of fractions with like denominators, multiplication of fractions by whole numbers.
Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
5th Grade Domains
5th Grade Critical Areas
Developing fluency with addition and subtraction of fractions, developing understanding of the multiplication of fractions and of division of fractions in limited case (unit fractions divided by whole numbers and whole numbers divided by unit fractions).
Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.
Developing understanding volume.

26. Two critical areas in Kindergarten
In Kindergarten, instructional time should focus on two critical areas:
Representing, relating, and operating on whole numbers, initially with sets of objects 1.
Describing shapes and space 2.
Presenter Directions
Say: Let’s begin by examining the Critical Areas in Kindergarten.
Say: Please locate the Kindergarten section of the Common Core State Standards for Mathematics. The Kindergarten section begins on page 9.
Say: Please take a few minutes to read the two critical areas.
Say: When you finish reading the Critical areas, glance over the Kindergarten Clusters.
Time for Reading the Critical Areas and Clusters: 3-4 minutes 26

27. Four critical areas in 1st Grade
In Grade 1, instructional time should focus on four critical areas:
developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 1.
developing understanding of whole number relationships and place value, including grouping in tens and ones 2.
developing understanding of linear measurement and measuring lengths as iterating length units 3.
Presenter Directions
Say: Let’s now look at the 1st grade critical areas.
Say: Please locate the First Grade section of the Common Core State Standards for Mathematics. This section begins on page 14 in your Common Core document.
Say: Take a few minutes to read the four critical areas and the clusters.
Time for Reading the Critical Areas and Clusters: 3-4 minutes
reasoning about attributes of, and composing and decomposing geometric shapes 4.

28. Four critical areas in 2nd Grade
In Grade 2, instructional time should focus on four critical areas:
extending understanding of base-ten notation 1.
building fluency with addition and subtraction 2.
using standard units of measure 3.
Presenter Directions
Say: Please locate the 2nd Grade section of the Common Core State Standards for Mathematics. The critical areas for 2nd Grade are found on page 17.
Read the 4 Critical Areas shown on the Slide.
Say: Take a few minutes to read the four critical areas and the clusters.
Say: As you read the critical areas what are some of the learning progressions that you noticed from 1st grade to 2nd grade?
Possible Answers:
Extension of the Base-Ten system
Develop fluency with addition and subtraction within 100.
Mentally calculate sums and differences with only tens or hundreds.
Recognize the need for standard units of measure.
Use rules or other measurement tools with an understanding of iteration of units.
Describes shapes examining their sides and angles.
Decompose and combine shapes to make other shapes.
Begin to develop an understanding of area, volume, congruence, similarity and symmetry.
Time for Reading the Critical Areas and Clusters: 3-4 minutes
describing and analyzing shapes 4. 28

29. Four critical areas in 3rd Grade
In Grade 3, instructional time should focus on four critical areas:
developing understanding of multiplication and division and strategies for multiplication and division within 100 1.
developing understanding of fractions, especially unit fractions (fractions with numerator 1) 2.
developing understanding of the structure of rectangular arrays and of area 3.
describing and analyzing two-dimensional shapes 4. 29

30. Three critical areas in 4th Grade
In Grade 4, instructional time should focus on three critical areas:
developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends 1.
developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers 2.
understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. 3.

31. Three critical areas in 5th Grade
In Grade 5, instructional time should focus on three critical areas:
developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) 1.
extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations 2.
Presenter Directions
Say: Please locate the 5th Grade section of the Common Core State Standards for Mathematics. The critical areas for 5th Grade are found on page 33.
Read the 3 Critical Areas shown on the Slide.
Ask: What are some of the learning progressions that you noticed from Kindergarten to 5th grade?
Possible answers include:
A more in depth understanding of the place values system
Performing operations from single digits to multi-digit wholes numbers and with decimals to hundredths.
Applying previous understanding of whole operations to multiply and divide fractions.
Converting like measurements units within a given measurement system.
Representing and interpreting data.
Understanding concepts of volume.
Graphing points on the coordinate plane.
Classifying 2-dimensional figures into categories based on their properties.
Time for Reading the Critical Areas and Clusters: 3-4 minutes
developing understanding of volume 3.

32. Learning Pyramid Passive Learning Active Learning
adapted from Ntl Institute for Applied Behavioral Science (n.d.)
California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

33. Standards for Mathematical Practice
“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.”
- Bill McCallum

34. Standards for Mathematical Practice
Reasoning and Explaining
Seeing Structure and Generalizing
Overarching Habits of Mind of a
Productive Mathematical Thinker
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
Modeling
and
Using Tools
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
1. Make sense of problems and persevere in solving them
6. Attend to precision 34

35. Why Unpack the Standards
Unpacking the Standards
Clarity
Alignment
Continuity
Integration

36. Kindergarten Mathematics Grade: Course: Standard(s):
Skills – Students should be able to do
Concepts – Student should know
Critical Area of Focus:
Learning Goal:
Essential Question:
Target Learning Progression:
Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. MACC.K.CC.2.5
20 things
10 things
Arranged in a line
Scattered configuration
Arranged in a rectangular array
1-20
Arranged in a circle
objects
Count
Count objects
Count to answer how many
#1. Representing and comparing whole numbers, initially with sets of objects.
Given a number from 1-20, students will count out that many objects.
How can you arrange things or objects to count how many things you have?
Given a number from 1-20, count out that many objects.

37. Unpacking the Standards Review
Identify the concepts, skills, and context
MACC.5.OA.1.1
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

38. Let’s Practice Unpacking the Content Area Standards!
Begin by unpacking the critical areas for your grade level.
Move into unpacking your assigned standard(s).
Remember, you should read your standard(s) carefully and fully.
Identify the verbs (skills), nouns (content or concepts), and any special context
Use the graphic unpacking graphic organizer as your guide through this process.

39. Unpacking Share Out
Discuss your standards and the elements noted on your graphic organizer.
Then, discuss activities, formative assessments, or performance tasks you might include in your classroom to support this standard.

40. Unpacking the Mathematics Practice Standards
With your group, unwrap your assigned mathematics practice standard.
Develop a visual that represents your group’s unwrapped standard
Develop an physical activity that makes the standard memorable for students and teachers
Be prepared to share your ideas with the group!