CCSS and Implication for Instruction October 11 HS

8/3/2019 CCSS and Implication for Instruction October 11 HS

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Common Core State StandardsImplication for Mathematics Instruction

Dale W. Vigil, Ed.D.Local District 4 Superintendent

October 12, 2011

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Why Common Core StateStandards?

o Internationally Competitiveo Continuity Across Stateso

New Emphasis on Math Reasoning

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Table Conversation

o What do you know about the CommonCore State Standards for Mathematics?

o What math instructional practices at yourschool would you like to see continued,refined, or eliminated?

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Objectives

o Gain a deeper knowledge of thestructure and content of the CommonCore State Standards for Mathematics

o Connect CCSS to our LD4 Goals

o Reflect on the implication ofinstructional practice

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Click to edit Master subtitle style

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MathCommon

CoreState

Standards

Standards forMathematical

Practice

Mathematical

Content

Standards

+ =


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Organization Overview

The CCSS for Mathematics are comprised of twocorresponding and connected sets of standards:

Standards for Mathematical Practiceq A set of 8 standards that describe the ways in

which the mathematics content standardsshould be approached

q Recurring through the grades

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The CCSS for Mathematics are comprised of twocorresponding and connected sets of standards:

Standards for Mathematical Contentq These standards define what students should

understand and be able to do in their study ofmathematics

q Different at each grade level

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Tab the following:

o LAUSD introduction I-VI (LAUSD Website)o Introduction P.2o

Standards for math Practice P.5

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Tab the following:

Levels:8th Grade/Alg. I:P.40 Geometry: P. 73

8th Grade:P.49 Stat/Prob.: P. 77

*HS Overview: P.54 Adv. Placement: P.83

HS Math Practice: P.55 Note on Courses: P.86

Number & Quantities: P.57 Glossary: P.87

Algebra: P.61Functions: P. 66

Modeling: 71

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Page 55

Standards for Mathematical Practice

Kindergarten through High School

______Standard title

[ ]Narrative description1010


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Standards for Mathematical Content

Kindergarten through High School

HS Number and Quantity Example:o Introduction P.57-58

o Domain P.59

o Clusters/cluster heading P.59

o

Standards P.59 1111


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Format of K-12 Standards P.63

1212

Seeing Structure in Expressions A-SSE

Interpret the structure of expressions1. Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For

example,

2. Use the structure of an expression to identify ways to rewrite it. For examplea. Use the distributive property to express a sum of terms with a common factor as a

multiple of asum of terms with no common factor. For example, express xy2 + x2y

as xy (y + x). (CommonCore Standard A-SSE-2a)b. Use the properties of operations to express a product of a sum of terms as a sum of

products. For example

2.1 Apply basic factoring techniques to second- and simple third-degree polynomials.

Thesetechniques include finding a common factor for all terms in a polynomial,recognizing the differenceof two squares, and recognizing perfect squares of binomials.

(CA Standard Algebra I - 11.0)

Domain

ClusterStandards


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Standards for Mathematical ContentKindergarten through High School

o

Introduction (P.57-58; HS Sample)Provides important contextual information and callsout and describes critical areas of focus.

Note: Math Practice Standards are also onintroduction page for each grade level/conceptual

catagories

o DomainLarge groups of related standards; connects topics

and content between and among grade levels.1313


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Standards for Mathematical ContentKindergarten through High School

o Clusters/cluster headingSmaller set of related standards within the domain;

identifies the primary idea.

o Standards

Describes what students should know and be ableto do for that cluster heading, domain, and gradelevel.

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CCSS Domain Progression

K 1 2 3 4 5 6 7 8 HS

Counting &Cardinality

Number and Operations in Base TenRatios and Proportional

Relationships Number &QuantityNumber and Operations

FractionsThe Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics &Probability

CA

Algebra

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Common Core State Standards:Components

Standards for Mathematical Practice P. 55

o Similar to Reasoning Standards

o Front of document and beginning of each topic

o Describe habits of mind of a mathematically expert studentacross all grade levels

o Fosters 21st century skills

o Consistent with Local District 4 goals with an emphasis inreasoning and students voice

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Why are 21st Century Skills andHabits of Mind Important?

o Work in pairs

o One person be the expert in 21st Century Skills

o The other be the expert in Habits of Mind

o After reading, share your insights and thendiscuss similarity to Local District 4 goals

o Share out

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Diving Deeper into 8 Standards forMath Practices

o Divide into 2 groups at your table

o

Each group becomes expert at one ofthese two Standards for Math Practice(Standard 1 or Standard 3)

o Discuss and clarify the meaning of thestandards

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Implication for Practice -

Making Conjectures1. What does this look like? 2. What does this sound like?

3. What will EL and SEL students

need in order to do this?

4. What will teachers need in order

to do this?

5. Implications for assessments? 6. Implications for grading?

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Contextualizing the Eight Math

Practice Standards-

o Analyze Possible Assessment Task

o How are Math Practice Standardsapparent in the Task & Questions fromLesson Plan?

o Revisit your conjecture poster. Anyrevision or additions?

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Reflection

o What insight did you gain about theMath CCSS?

o

What is the implication for mathinstructional practice?o Reflect on your opening conversation

during the Table Talk. Any revision for

math practice youd want to seecontinued, refined or eliminated atyour school?

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Our two cents - Implication for

practice

o Working and solving challenging non-routineproblems;

o Explaining methods and justifying conclusions;o Predicting and conjecturing about:

n Unknown numbersn Measurementsn Quantitative relationsn Behavior of functionsn How well a model fits reality

o Looking for patterns and structure in places likediagrams, equations, number systems, proofs,problems, tables, graphs, and real-world objects.

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CCSS and Implication for Instruction October 11 HS