huntsville city 6-8 math
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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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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
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