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Common Core State Standards for Mathematics

- Christine Downing, CCSS Consultant NH DOE
- Patty Ewen, Office of Early Childhood Education,

NH DOE

Whos in the room?

- Name, position, school/district
- Tell me something you already know about the CCSS

for Mathematics? - Now tell me something you hope to learn more

about in terms of CCSS for Mathematics?

Goals of Presentation

- Dig into the Common Core State Standards for

Mathematics - 2. Get down and dirty with SBAC
- Content Specifications, Assessment Claims, Item

Specifications - Throughout we will sift through and mix the

resources!

Instructional Shifts

- Focus
- Coherence
- Fluency
- Deep Understanding
- Application
- Dual Intensity

Dig Into CCSS Mathematics

1

Context for Treasure Hunt

- As you complete the treasure hunt, consider the

following Common Core Message. - CCSS Solve Three Specific Problems
- Increased Skills Demand and Competition
- Students Not College/Career Ready
- Variance Across the Country in Standards/Expectati

ons - Is there evidence in CCSS for Mathematics to

support this?

Treasure Hunt

- Form Small Groups that represent the grade ranges

from K through 12 - As a group complete the Treasurer Hunt for

Mathematics - As you complete the Treasurer Hunt, keep track of

what intrigues you? What do you want to

investigate deeper? Also, what surprised you?

Lets Do a Quick Overview of Mathematics

- Here are some common, key messages that can be

used to begin the discussion - Hang onits going to be quite a ride!

Criteria for New Standards

- Fewer, clearer, and higher (Consistent, rigorous,

and shared aligned with college and work

expectations) - Aligned with college and work expectations
- Include rigorous content and application of

knowledge through high-order skills - Build upon strengths and lessons of current state

standards (think DNA of education) - Internationally benchmarked, so that all students

are prepared to succeed in our global economy and

society - Based on evidence and research

Mathematics

- Focus and coherence
- Focus on key topics at each grade level.
- Coherent progressions across grade levels.
- Balance of concepts and skills
- Content standards require both conceptual

understanding and procedural fluency. - Mathematical practices (8 practices)
- Foster reasoning and sense making in mathematics.
- College and career readiness
- Level is ambitious but achievable.

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Topic Placement in Top Achieving Countries

Topic Placement in the U.S.

International Comparison

CCSS Distribution of Emphasis

CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression

Domains K 1 2 3 4 5 6 7 8

Counting and Cardinality

Operations and Algebraic Thinking

Number and Operations in Base Ten

Number and Operations Fraction

Ratios and Proportional Reasoning

The Number System

Expressions and Equations

Functions

Measurement and Data

Geometry

Statistics and Probability

CCSS versus GLE/GSE emphasis In NECAP

CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression

Domains K 1 2 3 4 5 6 7 8

Counting and Cardinality

Operations and Algebraic Thinking

Number and Operations in Base Ten

Number and Operations Fraction

Ratios and Proportional Reasoning

The Number System

Expressions and Equations

Functions

Measurement and Data

Geometry

Statistics and Probability

NECAP Assessment Changes in Mathematics

Test Grade GLEs NOT Assessed in Fall 2013

NECAP Mathematics 3 DSP 2-4 Combinations

NECAP Mathematics 4 DSP 3-5 Probability

NECAP Mathematics 5 DSP 4-4, DSP 4-5, and GM 4-5 Combinations/Permutations Theoretical Probability Similarity

NECAP Mathematics 6 DSP 5-5 Experimental Theoretical Probability

NECAP Mathematics 7 DSP 6-4, DSP 6-5, FA 6-2, and GM 6-5 Combinations/Permutations Experimental Theoretical Probability Slope Similarity

NECAP Mathematics 8 FA 7-2 Slope Constant/Varying Rates of Change

CCSS Mathematics-High School

The high school standards are listed in

conceptual categories Number and Quantity

Algebra Functions Modeling Geometry

Statistics and Probability

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Lets Pause for a Bit

- Lets Jigsaw the strands of mathematical

proficiency. - Please form groups of 5.
- All read pages 115 to 118 and 133 to 135
- Person 1 reads conceptual understanding
- Person 2 reads procedural fluency
- Person 3 reads strategic competence
- Person 4 reads adaptive reasoning
- Person 5 reads productive disposition

- How do the strands of mathematical proficiency

relate to the 8 mathematical habits of mind?

National Council of Teachers of Mathematics NCTM

- Mathematical Process Standards
- Communication
- Connections
- Representations
- Problem Solving
- Reasoning
- Proof
- www.nctm.org

New Hampshire Connection to 8 Mathematical

Practices

PreK-16 Numeracy Action Plan for the 21st

Century http//www.education.nh.gov/innovations/pr

e_k_num/index.htm

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Lets Dig a Little Deeper

- The new standards support improved curriculum and

instruction due to increased - FOCUS, via critical areas at each grade level
- COHERENCE, through carefully developed

connections within and across grades - CLARITY, with precisely worded standards that

cannot be treated as a checklist - RIGOR, including a focus on College and Career

Readiness and Standards for Mathematical Practice

throughout Pre-K-12

Structure of Knowledge

Structure of Knowledge in CCSS

- Critical Areas
- Domains
- Clusters
- Standards

Top Level

Similar to STRANDS from GLEs and GSEs

Middle Level

Similar to STEMS from GLEs and GSEs

Bottom Level

Critical Areas

- There are typically two to four Critical Areas

for instruction in the introduction for each

grade level or course. - They bring focus to the standards at each grade

by grouping and summarizing the big ideas that

educators can use to build their curriculum and

to guide instruction.

Example of a Critical Area

- __________________________________________________

_____________________________________ - Kindergarten
- __________________________________________________

_____________________________________ - In Kindergarten, instructional time should focus

on two critical areas (1) representing,

relating, and operating on - whole numbers, initially with sets of objects

and (2) describing shapes and space. More

learning time in - Kindergarten should be devoted to number than to

other topics. - (1) Students use numbers, including written

numerals, to represent quantities and to solve

quantitative problems, such as counting objects

in a set counting out a given number of objects

comparing sets or numerals and modeling simple

joining and separating situations with sets of

objects, or eventually with equations such as 5

2 7 and 7 2 5. (Kindergarten students

should see addition and subtraction equations,

and student writing of equations in Kindergarten

is encouraged, but it is not required.) Students

choose, combine, and apply effective strategies

for answering quantitative questions, including

quickly recognizing the cardinalities of small

sets of objects, counting and producing sets of

given sizes, counting the number of objects in

combined sets, or counting the number of objects

that remain in a set after some are taken away. - (2) Students describe their physical world using

geometric ideas (e.g., shape, orientation,

spatial relations) and vocabulary. They identify,

name, and describe basic two-dimensional shapes,

such as squares, triangles, circles, rectangles,

and hexagons, presented in a variety of ways

(e.g., with different sizes and orientations), as

well as three-dimensional shapes such as cubes,

cones, cylinders, and spheres. They use basic

shapes and spatial reasoning to model objects in

their environment and to construct more complex

shapes. - The Standards for Mathematical Practice

complement the content standards at each grade

level so that students - increasingly engage with the subject matter as

they grow in mathematical maturity and expertise.

How do critical areas promote focus?

- What is the number of critical areas per grade

level/course? - How will/could it improve teaching and learning

in our school/district when each grade focuses on

a few Critical Areas?

Grade level K 1 2 3 4 5 6 7 8

of Critical Areas 2 4 4 4 3 3 4 4 3

Course Alg I Geo Alg II Math I Math II Math III

of Critical Areas 5 6 4 6 6 4

Main Activity Focusing on the Critical Areas

- In small groups, read the Critical Areas for a

grade level including the description. - Read each content standard, marking the recording

sheet with a - v when a standard strongly matches or supports

your Critical Area and - ? when you are not sure
- Leave blank if the standard does not match or

support the Critical Area

- Did every standard fall within a Critical Area?
- Are there standards that fall within more than

one Critical Area? - Do all the standards within a cluster fall within

the same Critical Area?

- How do the Critical Areas help organize and bring

focus to your grade level standards? - How should we as a school (or district) use what

we have learned today about Critical Areas in

planning for the implementation of the new

standards? - How could this work be linked to existing

curriculum built on GLEs/GSEs?

Down and Dirty with SBAC

2

- Content Specifications
- Assessment Claims
- Item Specifications

SMARTER Balanced

- Computer Adaptive
- Multiple Choice, Constructed Response, Technology

Enhanced - Performance Tasks
- Writing, listening and speaking
- Emphasis of mathematical practices

Components of SBAC System

- Summative Assessments
- Grades 3-8 and 11 in ELA and Mathematics
- Computer Adaptive Testing
- Performance Tasks
- Interim Assessments
- Optional
- Progress of Students
- Linked to content clusters in CCSS
- Formative Tools and Processes
- Evidence of progress toward learning goals

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Mathematics Content Specs

- Claim 1 Conceptual Understanding and Procedural

Fluency Students can explain and apply

mathematical concepts and interpret and carry out

mathematical procedures with precision and

fluency. - Claim 2 Problem Solving Students can solve a

range of complex well-posed problems in pure and

applied mathematics, making productive use of

knowledge and problem solving strategies.

Mathematics Content Specs

- Claim 3 Communicating Reasoning Students can

clearly and precisely construct viable arguments

to support their own reasoning and to critique

the reasoning of others. - Claim 4 Modeling and Data Analysis Students can

analyze complex, real-world scenarios and can

construct and use mathematical models to

interpret and solve problems.

Lets look at SBAC Resources

- Assessment Claims and Target Standards
- Claim 1 of the Content Specifications
- Design of Performance Tasks
- Sample Items from Showcase 2 and 3

Where do you find all this for SBAC?

- www.smarterbalanced.org
- Now explore on your own!

Share

- So what ahas did you have as you explored the

wealth of information on SBAC? - What concerns do you have?
- What will you do next?

Other Math Resources

- MASS DOE presentation materials
- NCSM Alignment Tool for CCSS resources
- NCTM Reasoning and Sense Making Tools
- Indiana Resources new??
- North Carolina Unpacking

Questions/Comments

- Thank you!
- Christine Downing
- Christine.downing_at_nh.gov
- Patty Ewen
- Patricia.ewen_at_doe.nh.gov