math common core standards

4251 3

0011 0010 1010 1101 0001 0100 1011

Math Common Core Standards

Jennie WintersLake County ROE

jwinters@lake.k12.il.us

4251 3

0011 0010 1010 1101 0001 0100 1011

Focus for Today

1. 3 types of change2. Standards for Mathematical Practice3. Focus, Coherence & Rigor4. Assessment5. Curriculum: Quality Units/Lessons6. Q & A

4251 3

0011 0010 1010 1101 0001 0100 1011

Common Core Implementation

Curricular Change

Instructional Change

Assessment Change

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

1. Make sense of problems and persevere in solving them.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

2. Reason abstractly and quantitatively.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

3. Construct viable arguments and critique the reasoning of others.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

4. Model with mathematics.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

5. Use appropriate tools strategically.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

6. Attend to precision.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

7. Look for and make use of structure.

4251 3

0011 0010 1010 1101 0001 0100 1011

Practice Standards

8. Look for and express regularity in repeated reasoning.

4251 3

0011 0010 1010 1101 0001 0100 1011

Modes of Representation(Lesh, Post, & Behr, 1987)

Pictures

Manipulative Models

Written Symbols

Real-world Situations

Oral/WrittenLanguage

4251 3

0011 0010 1010 1101 0001 0100 1011

Modes of Representation

Manipulative/ Tools

Picture/Graph

Table/Chart

Symbols (Equations,

etc.)

Oral & Written Language

Real-Life Situations

4251 3

0011 0010 1010 1101 0001 0100 1011

14

The CCSS Requires Three Shifts in Mathematics

1. Focus: Focus strongly where the standards focus.

2. Coherence: Think across grades, and link to major topics

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

4251 3

0011 0010 1010 1101 0001 0100 1011

Rigor

15

• The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving

situations

• Pursuit of all threes requires equal intensity in time, activities, and resources.

4251 3

0011 0010 1010 1101 0001 0100 1011

Solid Conceptual Understanding

• Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives

• Students are able to see math as more than a set of mnemonics or discrete procedures

• Conceptual understanding supports the other aspects of rigor (fluency and application)

16

4251 3

0011 0010 1010 1101 0001 0100 1011

Fluency• The standards require speed and accuracy

in calculation.

• Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts

17

4251 3

0011 0010 1010 1101 0001 0100 1011

18

Required Fluencies in K-6Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations

4251 3

0011 0010 1010 1101 0001 0100 1011

Application• Students can use appropriate concepts and

procedures for application even when not prompted to do so.

• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

19

4251 3

0011 0010 1010 1101 0001 0100 1011

Assessment

• Conceptual Assessment– Includes Observational Tools

4251 3

0011 0010 1010 1101 0001 0100 1011

2nd Grade Example

Students each create their own paper airplane and take turns flying them. They use a tape measure to find the distance each has flown to the nearest foot.

What concepts are being assessed?

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

Assessment

• Conceptual Assessment– Includes Observational Tools

• Procedural Skill & Fluency Assessment– Includes Extended Response

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

Assessment

• Conceptual Assessment– Includes Observational Tools

• Procedural Skill & Fluency Assessment– Includes Extended Response

• Application– Includes Rich Tasks

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

Curriculum

• Sequence of units (Coherence)• Prioritization• Sequence within units:

– Conceptual before procedural– Application throughout

4251 3

0011 0010 1010 1101 0001 0100 1011

The Tri-State Quality Review Rubric Criteria

4251 3

0011 0010 1010 1101 0001 0100 1011

4 Dimensions

• Alignment to the Rigor of the CCSS• Key Areas of Focus in the CCSS• Instructional Supports• Assessment

4251 3

0011 0010 1010 1101 0001 0100 1011

1 – Alignment to the Rigor of the CCSS

The unit aligns with the letter and spirit of the CCSS:

• Targets a set of grade level mathematics standard(s) at the level of rigor in the CCSS for teaching & learning

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

1 – Alignment to the Rigor of the CCSS

The unit aligns with the letter and spirit of the CCSS:

• Standards for Mathematical Practice that are central to the unit are identified, handled in a grade-appropriate way, and well connected to the content being addressed.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

1 – Alignment to the Rigor of the CCSS

The unit aligns with the letter and spirit of the CCSS:

• Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts that

are reflected in the CCSS.• Focus Centers on the concepts,

foundational knowledge and level of rigor that are prioritized in the standards.

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts that

are reflected in the CCSS.• Coherence Makes connections and

provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts

that are reflected in the CCSS.• Rigor Requires students to engage

with an demonstrate challenging mathematics in the following ways:

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSS• Conceptual Understanding Requires

students to demonstrate conceptual understanding through complex problem solving, in addition to writing and speaking about their understanding.

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSS• Procedural Skill & Fluency Expects,

supports and provides guidelines for procedural skill and fluency with core calculations, mathematical procedures and strategies (when called for in the standards for the grade) to be performed quickly and accurately.

4251 3

0011 0010 1010 1101 0001 0100 1011

2-Key Areas of Focus in the CCSS• Application Provides opportunities for

students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsThe unit is responsive to varied student

needs:• Includes clear and sufficient guidance

to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsThe unit is responsive to varied student

needs:• Uses and encourages precise and

accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g. pictures, symbols, expressions, equations, graphics, models) in the discipline.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsThe unit is responsive to varied student

needs:• Engages students in productive

struggle through relevant, thought-provoking questions, problems, and tasks that stimulate interest and elicit mathematical thinking.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsThe unit is responsive to varied student

needs:• Addresses instructional expectations

and is easy to understand and use.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsProvides appropriate level and type of

scaffolding, differentiation, intervention, and support for a broad range of learners:

• Supports diverse cultural and linguistic backgrounds, interests and styles.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsProvides appropriate level and type of

scaffolding, differentiation, intervention, and support for a broad range of learners:

• Provides extra supports for students working below grade level.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional SupportsProvides appropriate level and type of

scaffolding, differentiation, intervention, and support for a broad range of learners:

• Provides extensions for students with high interest or working above grade level.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional Supports• Recommend and facilitate a mix of

instructional approaches for a variety of learners such as using multiple representations, (including models) using a range of questions, checking for understanding, flexible grouping, pair-share, etc.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional Supports• Gradually remove supports, requiring

students to demonstrate their mathematical understanding independently.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional Supports• Demonstrate an effective sequence

and a progression of learning where the concepts or skills advance and deepen over time.

4251 3

0011 0010 1010 1101 0001 0100 1011

3 – Instructional Supports• Expects, supports, and provides

guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

4251 3

0011 0010 1010 1101 0001 0100 1011

4 – Assessment

The lesson/unit regularly assesses whether students are mastering standards-based content and skills:

• Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.**

4251 3

0011 0010 1010 1101 0001 0100 1011

4 – Assessment

The lesson/unit regularly assesses whether students are mastering standards-based content and skills:

• Assesses student proficiency using methods that are accessible and unbiased, including the use of grade level language in student prompts.**

4251 3

0011 0010 1010 1101 0001 0100 1011

4 – Assessment The lesson/unit regularly assesses

whether students are mastering standards-based content and skills:

• Includes aligned rubrics, answer keys, and scoring guidelines that provide sufficient guidance for interpreting student performance.

4251 3

0011 0010 1010 1101 0001 0100 1011

4 – Assessment The lesson/unit regularly assesses

whether students are mastering standards-based content and skills:

• Use varied modes of curriculum embedded assessments that may include pre-, formative, summative and self-assessment measures.

4251 3

0011 0010 1010 1101 0001 0100 1011

4251 3

0011 0010 1010 1101 0001 0100 1011

Questions and (Hopefully) Answers