feb16 2pm math8th
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Common Core Georgia Performance g
Standards8th Grade
Brooke Kline and James PrattBrooke Kline and James PrattSecondary Mathematics Specialists
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Thank you for being here today.
You will need the following materials g
during today’s broadcast:
• 8th Grade handouts
• Note-taking materialsg
Activate your brain
Understand and apply theapply the Pythagorean Theorem.
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Why Common Core Standards?• Preparation: The standards are college- and career-
ready. They will help prepare students with the y y p p pknowledge and skills they need to succeed in education and training after high school.
• Competition: The standards are internationally benchmarked. Common standards will help ensure our students are globally competitiveour students are globally competitive.
• Equity: Expectations are consistent for all – and not dependent on a student’s zip code.
Why Common Core Standards?• Clarity: The standards are focused, coherent, and
clear Clearer standards help students (andclear. Clearer standards help students (and parents and teachers) understand what is expected of them.
• Collaboration: The standards create a foundation to work collaboratively across states and districts,
li d ti t tpooling resources and expertise, to create curricular tools, professional development, common assessments and other materials.
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Common Core State Standards
Building on the strength of current state standards, the CCSS are designed to be:
• Focused, coherent, clear and rigorous• Internationally benchmarked
A h d i ll d di• Anchored in college and career readiness • Evidence and research based
Common Core State Standards in Mathematics
K 1 2 3 4 5 6 7 8 9 - 12
Measurement and Data Statistics and Probability
The Number SystemNumber and Operations in Base Ten
Number and Operations Fractions
Expressions andAl b
Number and Quantity
FunctionsRatios &
Proportional Relationships
CC
Modeling
Geometry
Operations and Algebraic ThinkingExpressions and
EquationsAlgebra
© Copyright 2011 Institute for Mathematics and Education
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Standards for Mathematical Practicem
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2. Reason abstractly and quantitatively.3. Construct viable arguments and
iti th i f th
Reasoning and explaining
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critique the reasoning of others
4. Model with mathematics.5. Use appropriate tools strategically.
7. Look for and make use of
Modeling and using tools
Seeing
(McCallum, 2011)
1.M
ake
pers
e6.
A
tten
structure.8. Look for and express regularity in repeated reasoning.
Seeing structure and generalizing
Functions 8.F
Define, evaluate, and compare functions.
MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions) For example given a linear function represented by a tabledescriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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While the standards focus on what is most essential, they do not describe all that can or should be taught. A great deal is left to the g gdiscretion of teachers and curriculum developers. The aim of the standards is to articulate the fundamentals, not to set out an exhaustive list or a set of restrictions that limits
h t b t ht b d h t i ifi dwhat can be taught beyond what is specified. corestandards.org
What’s an 8th Grade Teacher to do?
• Read your grade level standards• Use the CCGPS Teaching Guide found on
Georgia Standards.org and Learning Village
• Discuss the standards with your• Discuss the standards with your colleagues
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8th Grade OverviewUnit 1: Transformations, Congruence and Similarity
The Number Systemy
◦ Understand congruence and similarity using physical models, transparencies, or geometry software.
New Content
◦ Transformation – came from 7th grade
S f th◦ Similarity – came from 7th grade
◦ Congruence – not addressed in this manner
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8th Grade OverviewUnit 2: Exponents
Expressions and EquationsExpressions and Equations
◦ Work with radicals and integer exponents.
◦ Analyze and solve linear equations and pairs of simultaneous linear equations.
The Number System
◦ Know that there are numbers that are not rational, and approximate them by rational numbers.
New Content
◦ Cube Root – came from high school
8th Grade OverviewUnit 3: Geometric Applications of Exponents
GeometryGeometry◦ Understand and apply the Pythagorean Theorem.◦ Solve real-world and mathematical problems involving volume of cylinders, cones,
and spheres.Expressions and Equations◦ Work with radicals and integer exponents.
New ContentNew Content
◦ Distance Using Pythagorean Theorem – came from high school
◦ Volumes of cones, cylinders, & spheres – cones and cylinders from 6th grade / spheres from high school
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8th Grade OverviewUnit 4: Functions
FunctionsFunctions◦ Define, evaluate, and compare functions.
8th Grade OverviewUnit 5: Linear Functions
Expressions and EquationsExpressions and Equations
◦ Understand the connections between proportional relationships, lines, and linear equations.
Functions
◦ Define, evaluate, and compare functions.
New ContentNew Content
◦ Similar triangles → slope – Not addressed in this manner
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8th Grade OverviewUnit 6: Linear Models and Tables
FunctionsFunctions
◦ Use functions to model relationships between quantities.
Statistics and Probability
◦ Investigate patterns of association in bivariate data.
New Content
I i f i i i bi i d◦ Investigate patterns of association in bivariate data
◦ Increasing/Decreasing Functions – came from high school
8th Grade OverviewUnit 7: Solving Systems of Equations
Expressions and EquationsExpressions and Equations
◦ Analyze and solve linear equations and pairs of simultaneous linear equations.
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FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
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Focus
The student… • spends more time thinking and working on priority
concepts.
• is able to understand concepts and their connections to processes (algorithms).
Focus
The teacher…• builds knowledge, fluency and understanding of why
and how certain mathematics concepts are done.
• thinks about how the concepts connect to one another.
• pays more attention to priority content and invests the y yappropriate time for all students to learn before moving onto the next topic.
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GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2 Addition and subtraction, measurement using whole number quantities
3-5 Multiplication and division of whole numbers and fractions
6 Ratios and proportional reasoning; early expressions and equations
7 Ratios and proportional reasoning; arithmetic of rational numbers
8 Linear algebra
9-12 Modeling
Critical AreasIn 8th Grade, instructional time should focus on three critical areas:
(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance,
l i il it d d d t di d l i thangle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
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Priorities in 8th Grade
• Linear Equationsq
Focus taskUnderstand the connections b i lbetween proportional relationships, lines, and linear equations.
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What is no longer in 8th grade?
• Absolute Value
• Inequalities
• Set Theory
• Number of Outcomes
• Probability
FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
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Coherence
The student...• builds on knowledge from year to year, in a coherent
learning progression.
Coherence
The teacher...• connects mathematical ideas across grade levels.
• thinks deeply about what is being focused on.
• thinks how those ideas connect to how it was taught the years before and the years afterthe years before and the years after.
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FAL Structure
• Pre-Assessment / openingp g
• Collaborative activity
• Whole-class discussion
• Return to the pre-assessment / openingp p g
What do 8th Grade students bring?
What are they connecting to later?U d t d dUnderstand congruence and similarity using physical models, transparencies, or geometry software.
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Transformation Overview
4th Grade• Work with angles and lines of symmetry
5th Grade• Graph on coordinate plane
Transformation Overview
6th Grade6 Grade• Draw geometric figures in coordinate plane
7th Grade • Draw geometric figures based upon conditions
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Transformation Overview
Coordinate AlgebraCoordinate Algebra• Describe transformations as functions
Analytic Geometry • Connect congruence criteria to transformations
FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
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Fluency
The student...• spends time practicing skills with intensity and
frequency.
Fluency
The teacher...• pushes students to know skills at a greater level of
fluency based on understanding.
• focuses on the listed fluencies by grade level.
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Grade Required Fluency
K Add/subtract within 51 Add/subtract within 102 Add/subtract within 20 & Add/subtract within 100 (pencil and paper)3 Multiply/divide within 100 & Add/subtract within 10003 u p y/d de 00 & dd/sub ac 0004 Add/subtract within 1,000,0005 Multi-digit multiplication6 Multi-digit division & Multi-digit decimal operations7 Solve px + q = r, p(x + q) = r8 Solve simple 22 systems by inspection
Algebraic manipulation in which to understand structure.W iti l t t l ti hi b t t titi
9-12Writing a rule to represent a relationship between two quantities.Seeing mathematics as a tool to model real-world situations.Understanding quantities and their relationships.
What does Fluency Look Like in 8th Grade?
• FLEXIBLY
• ACCURATELY
• EFFICIENTLY
• APPROPRIATELY
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FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
Deep Understanding
The student...• shows mastery of material at a deep level in numerous
ways.
• uses mathematical practices to demonstrate understanding of different material and concepts.
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Deep Understanding
The teacher...• asks what mastery/proficiency really looks like and
means.• plans for progression of levels of understanding. • spends the time to gain the depth of the
understanding.g• becomes flexible and comfortable in own depth of
content knowledge.
What does depth mean in 8th Grade?
Understand congruence and similarity using physical models, transparencies, or geometry software.
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FocusFocusCoherenceFluencyDeep UnderstandingApplicationsppBalanced Approach
Application
The student...• applies mathematics in other content areas and
situations.
• chooses the right mathematics concept to solve a problem when not necessarily prompted to do so.
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Application
The teacher...• contextualizes mathematics.
• creates real world experiences in which students use what they know, and in which they are not necessarily prompted to use mathematics.
Mathematizing 8th GradeInvestigate patterns of association in bivariate data.
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FocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
Balanced Approach
The student...• practices mathematics skills to achieve fluency.
• practices mathematics concepts to ensure application in novel situations.
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Balanced Approach
The teacher...• finds the balance between understanding and practice.
• normalizes the productive struggle.
• ritualizes skills practice.
Balanced Approach
Use functionsUse functions to model relationships between quantities.
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FocusFocusCoherenceFluencyDeep UnderstandingApplicationsApplicationsBalanced Approach
What’s in 7B – 8• Inferences
◦ Use random sampling to draw inferences about a population.Use random sampling to draw inferences about a population.◦ Draw informal comparative inferences about two populations.
• Geometry◦ Draw, construct, and describe geometrical figures and describe the
relationships between them.◦ Solve real-life and mathematical problems involving angle measure,
area, surface area, and volume.P b bilit• Probability◦ Investigate chance processes and develop, use, and evaluate
probability models.
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CCGPS Suggestions:1.Review the CCGPS. The teaching guide, curriculum map,
and standards can all be found in Learning Village on theand standards can all be found in Learning Village, on the Mathematics Program Page and on Georgia Standards.org
2.View the Fall 2011 Grade Level Webinar if you haven’t already seen it.already seen it.
3.Review this broadcast with your team to identify key areas of focus.
CCGPS Suggestions:4.Participate in the unit-by-unit webinars beginning in May.
8th G d U it 1 M 8 2012 4 308th Grade Unit 1: May 8, 2012, 4:30pm
5.Structure time for grade level/content areas to use framework units as a guide for planning.
6.Plan to get together with your colleagues at the end of each CCGPS unit to analyze student work samples and compare how student learning and performance look.
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8th Grade Support:Now-• Fall 2011 Grade Level Webinar• Fall 2011 Grade Level Webinar• Standards Document• Teaching Guide• Curriculum MapComing soon-• Framework Units (posting April 2012)Framework Units (posting April 2012)• Unit-by-unit webinars:
8th grade Unit 1 May 8, 2012, 4:30pm
Takeaways
3 Things-3 gs
1. What’s new?
2. What’s different?
3 Wh t d t3. What resources and support are available for CCGPS mathematics?
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“The resources we need in order to grow as t h b d t ithi th itteachers are abundant within the community of colleagues. Good talk about good teaching is what we need…”
Parker PalmerCourage to Teach
Brooke Kline James Pratt
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Thank you for participating in this CCGPS Professional Learning Session. We value your feedback. Please go to the following website, take the anonymous feedback survey, and complete the participation log to
receive a certificate of participation:
http://survey.sedl.org/efm/wsb.dll/s/1g10aIf you have questions, feel free to contact any of the English/Language Arts or
Mathematics staff at the following email addresses:Sandi Woodall, Georgia Mathematics Coordinator Kim Jeffcoat, Georgia ELA [email protected] [email protected]
James Pratt, Secondary Mathematics Susan Jacobs, Secondary ELA [email protected] [email protected]
Brooke Kline, Secondary Mathematics Sallie Mills, Elementary [email protected] [email protected]
Turtle Gunn Toms, Elementary Mathematics Andria Bunner, Elementary ELA