Huntsville City 6-8 Math

March 18, 2013Jeanne SimpsonAMSTI Math Specialist

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•Name•School•Classes you teach•Your favorite math topic to teach

Welcome

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4

He who dares to teach

must never cease to

learn.John Cotton Dana

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Intervention

Assessment

Collaboration

Five Fundamental Areas Required for Successful Implementation of CCSS

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Instruction•Deep conceptual understanding•Collaborative lesson design•Standards for Mathematical

Practice

Content• Fewer standards with greater

depth• Understanding, focus, and

coherence• Common and high-demand tasks

Intervention• Common required response to

intervention framework response

• Differentiated, targeted, and intensive response to student needs

• Student equity, access, and support

Assessment•PLC teaching-assessing-learning

cycle•In-class formative assessment

processes•Common assessment instruments

as formative learning opportunities

Collaboration

How do we teach?

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A Shared Vision•Does each of us have a shared vision of what teaching and learning a mathematics lesson looks like?

• Taking about 5 minutes, think of 3 or more components of a mathematics lesson you feel are important and should be found in a mathematics lesson.

• Please do not share with your group, yet.

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• Draw a circle in the center of your chart paper.

• Write your ideas anywhere on the chart paper provided to your group, just not in the circle.

• Take about 5-7 minutes to discuss your ideas with your group.

• Do your ideas reflect current research in mathematical education?

• Do your ideas reflect the vision of the College- and Career-Ready standards?

A Shared Vision

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A Shared Vision• Now, in your groups,

write in the circle using 15 words or less, what your group decided are the components of a good mathematics lesson.

• After 10 minutes, each group will share their thoughts.

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Instruction•Deep conceptual understanding•Collaborative lesson design•Standards for Mathematical

Practice

Content• Fewer standards with greater

depth• Understanding, focus, and

coherence• Common and high-demand tasks

Intervention• Common required response to

intervention framework response

• Differentiated, targeted, and intensive response to student needs

• Student equity, access, and support

Assessment•PLC teaching-assessing-learning

cycle•In-class formative assessment

processes•Common assessment instruments

as formative learning opportunities

Collaboration

How do we teach?

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SMP1 - Make sense of problems and persevere in solving them

SMP2 - Reason abstractly and quantitativelySMP3 - Construct viable arguments and critique the

reasoning of othersSMP4 - Model with mathematicsSMP5 - Use appropriate tools strategicallySMP6 - Attend to precisionSMP7 - Look for and make use of structureSMP8 - Look for and express regularity in repeated

reasoning

Standards for Mathematical Practice

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•Capture the processes and proficiencies that we want our students to possess

•Not just the knowledge and skills but how our students use the knowledge and skills

•Describe habits of mind of the mathematically proficient student

•Carry across all grade levels, K-12

What Are The Practice Standards?

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•√ I already do this.

• ! This sounds exciting!• ? I have questions.

Standards of Mathematical Practice

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•Problem solving•Demanding tasks•Student understanding•Discussion of alternative

strategies•Extensive mathematics

discussion•Effective questioning•Student conjectures•Multiple representations

High-Leverage Strategies

Name

Strategy or SMP

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Instruction• D

eep conceptual understanding

• Collaborative lesson design

• Standards for Mathematical Practice

Content• F

ewer standards with greater depth

• Understanding, focus, and coherence

• Common and high-demand tasks

Intervention• C

ommon required response to intervention framework response

• Differentiated, targeted, and intensive response to student needs

• Student equity, access, and support

Assessment• P

LC teaching-assessing-learning cycle

• In-class formative assessment processes

• Common assessment instruments as formative learning opportunities

Collaboration

What are we teaching?

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Unpacking the StandardsStep 1: Target a standardStep 2: Chunk the Main

CategoriesStep 3: Identify all standard

componentsStep 4: Identify the

Developmental Progression

Step 5: Identify Key Vocabulary

Step 6: Add Clarifying Information

“To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand, and be able to do. (Unpacking) may also be used to facilitate discussion among teachers and curriculum staff and to encourage coherence…(Unpacking), along with on-going professional development is one of many resources used to understand and teach the CCSS.”

-North Carolina Dept of Public Instruction

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Why are we Unpacking Standards?

To understand what the standards are asking students to know, understand, and be able to do

To make time for professional discussion about the standards

To build upon and use common terminology when discussing the implementation of the standards

Unpacking is standards is not a substitute document for the Common Core Standards, it is a

record of the conversation of those who are involved in the process of digging into the

standards.

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Step 1 – Target a Standard

•What are you teaching this spring?

•Find a group of 2-4 teachers who will explore that topic with you.

•What standards are involved?

192.G.3Partition circles and

rectangles into two, three, or four

equal shares

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

Partition

Builds on 1.G.3 Needed for 3.G.2

partition

Equal shares

rectangle HalvesHalf of

circlePartition a shape into fourths in different ways

Pattern Blocks Fraction

Bars/Circles

Describe

ThirdsThird of

FourthsFourth of

whole

Identicalwhole

2/2 = one whole

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four fourths

2.G.3

Recognize that equal shares of identical

wholes need not have the same shape

2.G.3

Recognize

The final product….

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Example2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Step 2: Chunk the Main Categories

1.All Standard(s) in the cluster(s)

2.Identify Key Verbs

2.G.3Partition

circles and rectangles into two,

three, or four equal shares

Describe RecognizePartition

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Step 3: Identify all standard components

Components from CCSS:Analyze nouns and verbs

What do students need to do?Include bullets, examples, footnotes, etc.

Take standard apart according to the verbs to separate skills within the standard

What do the students need to know?

lt blue

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Example 2.G.3

Partition circles and rectangles into two, three, or four equal

shares

Partition RecognizeDescribe

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four

fourths2.G.3

Recognize that equal shares of identical wholes need not have

the same shape2.G.3

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

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Step 4: Identify the Developmental Progression

Questions to consider when looking at the developmental progression of the standards…

•How would you utilize these chunks (blue) for scaffolding toward mastery of the entire standard?

• Where would you start when teaching this standard?

• What is the chunk that demonstrates the highest level of thinking?

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Vertical AlignmentUsing the progression document(s) from Ohio Department of Education and CCSS Writing Team:Look to the grade level(s) below to see if the standard is introduced.

Look to the grade level(s) above to see if the standard is continued.

Code each standard on the poster with: builds on introduced needed for or mastered

and the grade level to which the standard aligns.

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Introduced?Mastered?

Needed for?Builds on?

2.G.3Partition circles and rectangles into two, three, or four equal

shares

Partition RecognizeDescribe

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four

fourths2.G.3

Recognize that equal shares of identical wholes need not have

the same shape2.G.3

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

Builds on 1.G.3

Needed for 3.G.2

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Step 5: Identify Key Vocabulary

Identify content vocabulary directly from the standard. Identify additional vocabulary students will need to know to meet the standard.

green

272.G.3Partition circles and

rectangles into two, three, or four

equal shares

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

Partition

Builds on 1.G.3 Needed for 3.G.2

partition

Equal shares

rectangle HalvesHalf of

circle

Describe

ThirdsThird of

FourthsFourth of

whole

Identicalwhole

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four fourths

2.G.3

Recognize that equal shares of identical

wholes need not have the same shape

2.G.3

RecognizePartition circles and rectangles into two equal

shares, using the word halves,

half of2.G.3

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Step 6: Add Clarifying Information

Kid-friendly language to add clarity Clarifying pictures, words, or phrasesDefinitions, examplesSymbols, formulas, pictures, etc.

CAUTION: do not replace important vocabulary that is included in the standard.

yellow

292.G.3Partition circles and

rectangles into two, three, or four

equal shares

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

Partition

Builds on 1.G.3 Needed for 3.G.2

partition

Equal shares

rectangle HalvesHalf of

circlePartition a shape into fourths in different ways

Pattern Blocks Fraction

Bars/Circles

Describe

ThirdsThird of

FourthsFourth of

whole

Identicalwhole

2/2 = one whole

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four fourths

2.G.3

Recognize that equal shares of identical

wholes need not have the same shape

2.G.3

Recognize

Partition circles and rectangles into two equal

shares, using the word halves,

half of2.G.3

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Transfer Unwrapping to Chart

312.G.3Partition circles and

rectangles into two, three, or four

equal shares

Partition circles and rectangles into two equal shares, using

the word halves, half of2.G.3

Partition

Builds on 1.G.3 Needed for 3.G.2

partition

Equal shares

rectangle HalvesHalf of

circlePartition a shape into fourths in different ways

Pattern Blocks Fraction

Bars/Circles

Describe

ThirdsThird of

FourthsFourth of

whole

Identicalwhole

2/2 = one whole

Partition circles and rectangles into three equal shares, using

the word thirds, third of2.G.3

Partition circles and rectangles into four equal shares, using

the word fourths, fourth of

2.G.3

Describe the whole as two halves, three thirds, four fourths

2.G.3

Recognize that equal shares of identical

wholes need not have the same shape

2.G.3

Recognize

Partition circles and rectangles into two equal

shares, using the word halves,

half of2.G.3

Main Idea of Standard

Key Verbs

Take standard apart according to the verbs to separate skills within the standard.

Use all components of standard. Put in a logical sequence

Vertical alignment

Vocabulary

Clarifying information, student-friendly

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Effective Instructional Tasks

•Engage students with challenging tasks that involve active meaning making

•Help students connect new learning with prior knowledge and address preconceptions and misconceptions

•Engage students in socially constructing knowledge through talk, activity, and interaction around meaningful problems

•Provide students timely feedback so they can revise their work, thinking, and understandings

Common Core Mathematics in a PLC at Work: Grades 6-8, p. 58

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Lesson/Unit Planning•What tasks can help your students learn

this standard?▫acos2010.wikispaces.com

Huntsville City 6-8 Websites

▫CMP Units

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Criti

cal A

reas

of

Foc

us

“These (Mathematical) practices are intended to underlie all

instruction in mathematics, but if one focuses only on the standard

statements very little direct evidence of them can be found.

Also, the first page at each grade (K-8) identifies a series of

‘Critical Areas’ that are to be used as the broad ideas on which to plan all instruction around at

that grade…A focus on the standards statements will find no reference to these and will miss a

large part of the instructional impact intended with the new

Standards.”-Kansas Department of Education

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6th Grade Focus AreasRatios and Proportional

RelationshipsConnect to whole number multiplication and division

Applying to problems

Standards 1-3

Number Systems

Dividing fractionsNegative numbersCoordinate plane

Standards 4-11

Expressions and Equations

Variables and expressionsSolve one-step equations

Standards 12-20

Statistics

Understanding different measures of center

Standards 25-29

Geometry – Standards 21-24

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7th Grade Focus AreasRatios and Proportional

Reasoning

Applying to problemsGraphing and slope

Standards 1-3

Number Systems, Expressions and

Equations

Standards 4-10

Geometry

Scale drawings, constructions, area,

surface area, and volume

Standards 11-16

Statistics

Drawing inferences about populations based on samples

Standards 17-20

Probability – Standards 21-24

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8th Grade Focus AreasExpressions and

EquationsRepresent, analyze, and solve

a variety of problemsLinear equations, systems of equations, linear functions,

slope, bivariate dataStandards 7-10, 25-28

Functions

Define, evaluate, compareUse to model relationships

Standards 11-15

Geometry

Transformations, similar triangles, angles formed by parallel lines, Pythagorean

theorem, volumeStandards 16-24

Other

Irrational numbers, radical, integer

exponents

Standards 1-6

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Power Standards•ENDURANCE – something a student will

need to know for a longer period of time

•LEVERAGE – something that is taught and used in more than one curricular area

•READINESS – something that is a prerequisite skill for future learning

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Instruction• D

eep conceptual understanding

• Collaborative lesson design

• Standards for Mathematical Practice

Content• F

ewer standards with greater depth

• Understanding, focus, and coherence

• Common and high-demand tasks

Intervention• C

ommon required response to intervention framework response

• Differentiated, targeted, and intensive response to student needs

• Student equity, access, and support

Assessment• P

LC teaching-assessing-learning cycle

• In-class formative assessment processes

• Common assessment instruments as formative learning opportunities

Collaboration

How do we know if they learned?

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Step OneCollaborative teams

identify learning targets and design common unit

tasks and assessment instruments.

Step TwoTeachers implement

formative assessment

classroom strategies.

Step ThreeStudents take action on in-class formative

assessment feedback.

Step FourStudents use assessment

instruments from step one for motivation,

reflection, and action.

Step FiveCollaborative teams

use ongoing assessment feedback

to improve instruction.The PLC

Teaching-Assessing-Learning Cycle

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Step OneCollaborative teams

identify learning targets and design

common unit tasks and assessment instruments.

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Step TwoTeachers implement formative

assessment classroom strategies.

Questioning Whiteboards

Traffic LightsClickers

Diagnostic Interviews

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Step ThreeStudents take

action on in-class formative

assessment feedback.

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Step FourStudents use assessment

instruments from step one for motivation,

reflection, and action.

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Step FiveCollaborative teams use

ongoing assessment feedback to improve

instruction.

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Common Formative Assessments

Are… Are not…

•Created by collaborative teams of teachers

•Unit-by-unit•Given in time to adjust instruction

•District benchmark tests

•Summative•Always graded

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Common Formative Assessments1. Decide what to assess2. Decide how to assess3. Develop the assessment plan4. Determine the timeline5. Write the assessment6. Review the assessment before

administration7. Set proficiency criteria and decide how

to gather the data

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1. Decide what to assess•Which learning targets are most likely to

cause certain students difficulty?•Which targets are prerequisite skills for

information to come later in this unit?•Which targets are absolutely necessary

for students to know?•What level of thinking do we expect from

our students for each learning target?

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2. Decide how to assess• Selected-response

▫Multiple-choice, fill-in-the-blank, matching, true/false

▫Easy to grade, quick results▫Not best for assessing high-level thinking

• Constructed or written extended-response▫Graded with rubric▫Helps teachers see misconceptions

• Performance assessments▫Most accurate▫Time-consuming

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3. Develop the assessment plan•Are the important learning targets

included in the assessment?•Are the items assessing student learning

at the cognitive level you desire?

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4. Determine the timeline

•Every one to three weeks

•Three learning targets or less

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5. Write the assessment

6. Review the assessment before administration

7. Set proficiency criteria and decide how to gather the data

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With your group

•Follow the Sample Protocol for Developing an Assessment

•Get your group’s contact information for follow-up on your plan

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What’s Next?•I think we need to…

•I would like to help by…

•I would like to learn more about…

•I would like someone to help me with…

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Jeanne SimpsonUAHuntsville AMSTI

jeanne.simpson@uah.edu

acos2010@wikispaces.com

Contact Information