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COMMON CORE STANDARDS
FOR MATHEMATICS
Grade 8
Please sign in and try to sit next to someone from a different school this morning.
This is an opportunity that we do not often get to have.
MORNING OBJECTIVES
Create common understanding around Common Core State Standards and Smarter Balanced Assessment Consortium
Build an awareness of the Secondary plan for transition to the Common Core State Standards for Mathematics
Develop a common understanding of the Common Core State Standards for Mathematics
Develop a common understanding of the Standards for Mathematical Practice (embedded within the CCSS-M)
Examine connections between instructional practice and the Standards for Mathematical Practice
COLLABORATIVE NORMS Honor your responsibilities Participate fully and actively Honor each person’s place of being Assume positive intent Learn from and encourage each other Share airtime Avoid judgmental comments Honor confidentiality Communicate your needs If you need to attend to something else, step
out of the room Laptops: When instructed to do so go to half-
mast or close lid
MORNING OBJECTIVES
Create common understanding around Common Core State Standards and Smarter Balanced Assessment Consortium
Build an awareness of the Secondary plan for transition to the Common Core State Standards for Mathematics
Develop a common understanding of the Common Core State Standards for Mathematics
Develop a common understanding of the Standards for Mathematical Practice (embedded within the CCSS-M)
Examine connections between instructional practice and the Standards for Mathematical Practice
Summative
Assessments
Teacher Resources for use in Formative Assessmen
t
A More Smartly
Balanced Assessment System
Interim Assessmen
ts
WHAT’S IN THE BINDER?
Math 8
Binder
AgendaRSD
Documents
Tab 1: CCSS-M Grades 5-9
Tab2: Understandin
g CCSS-M Grade 8
Tab 3: SBAC Claims and
Item Specifications
Tab 4: Curriculum
Guide
Tab 5: Supplemental Lessons and
Common Assessment
EVOLUTION OF DISTRICT TRANSITION PLAN
Washington State
Transition Plan
DMLT
District LeadershipPrincipals
Department Heads RSD
Transition Plan to
Common Core
RSD TRANSITION PLAN Big Picture Focus for 2012-2013:
Build common awareness of the CCSS-M, the Standards for Mathematical Practice, and the transition plan at the secondary level for teachers and leaders
Create and implement one unit at each course Math 6 though Algebra 2
2012-2013 unit to be aligned and implemented:8th Grade: Congruence and Similarity
through Transformational Geometry using Kaleidoscopes, Hubcaps, and Mirrors and aligned gap lessons
Grades 6-12 Math Teachers District Math Leaders Math Course Work Teams Professional Development
2012-2013 (WA 2008/CCSS-M)MSP/EOC
Create an awareness of the CCSS-M and begin to think about instructional implications
In Spring 2013, implement with fidelity first CCSS-M aligned unit along with remaining 2008 WA standards
Track and report feedback on CCSS-M aligned unit
Define effective mathematics instruction for the RSD
Analyze alignment of existing curriculum guides and materials with the CCSS-M
Select CCSS-M unit to implement in 2012-2013
Draft curriculum map, scope and sequences, and pacing guides for Math 6 through Algebra 2
Establish Course Work Teams Plan for and implement
professional development by course
Establish system for feedback and adjustment as units are being taught
Develop understanding of mathematical progressions within each domain
Refine the scope and sequence and pacing guide for course and units to be implemented
Develop CCSS-M aligned secondary units
Participate in the planning and presentation of professional development
Collect feedback on CCSS-M aligned unit and modify unit as needed
In Winter 2013 and Spring 2013: Develop awareness of CCSS-M,
district transition plan, and changes from 2008 WA Standards
Build awareness of the key instructional shifts to the Standards of Mathematical Practice and of the connections between the CCSS-M, RSD VOI, and Definition of Effective Mathematics Instruction
Develop content understanding of first unit mathematical progression
Introduce curriculum materials for unit(s) to be implemented
2013-2014 (WA 2008/CCSS-M)MSP/EOC
Deepen understanding of the CCSS-M and apply the Standards for Mathematical Practice
In Fall 2013 and Winter 2014, implement with fidelity next CCSS-M aligned units along with remaining 2008 WA standards
Track and report feedback on CCSS-M aligned units
Continue 2012-2013 process with next unit identified by DMLT
Refine professional development plan in response to establishment of a definition of effective mathematics instruction
Plan for upcoming course professional development
Refine the scope and sequence and pacing guide for course and units to be implemented based on teacher feedback
Continue to develop CCSS-M aligned secondary units
Participate in the planning and presentation of professional development
Collect feedback on CCSS-M aligned units and modify units as needed
In Fall 2013 and Winter 2014 : Develop content
understanding of next unit mathematical progression
Introduce curriculum materials for next units to be implemented
Deepen understanding of the key instructional shifts to the Standards of Mathematical Practice
Continue connecting Standards of Mathematical Practice to RSD Vision of Instruction and Definition of Effective Mathematics Instruction
Questions to think about while you read:• What is my role in the transition plan?• What is the role at the district level?• I wonder why…is not in the plan?
We will share out after you have had some time to look at the plan.
TRANSITIONING BY UNIT DRAFT
2012-2013 2013-2014 2014-2015
CCSSM Units 2008 Standards CCSSM Units 2008 Standards
Units CCSSM
Linear Functions Linear Functions Proportional Relatioships and Linear Equations using CMP2 Supplement Inv 2
8.EE.5, 8.EE.6, 8.EE.7a, 8.EE.7b, 8.F1
8.SP.1, 8.SP.2, 8.SP.3, 8.EE.5, 8.EE8, 8.F.2, 8.F.3, 8.F.4, 8.F.5
Thinking/Math Models 8.1.A, 8.1.C, 8.1.D, 8.1.E, 8.1.F, 8.1.G
8.SP.1, 8.SP.2, 8.SP.3, 8.EE.5, 8.EE8, 8.F.2, 8.F.3, 8.F.4, 8.F.5
Thinking/Math Models Functions to Model Relationships between Quantities using Thinking with Mathematical Models Inv 1, 2
8.SP.1, 8.SP.2, 8.SP.3, 8.EE.5, 8.EE8, 8.F.2, 8.F.3, 8.F.4, 8.F.5
Inequalities (must teach until June 2014)
8.1.B Inequalities (must teach until June 2014)
8.1.B Patterns of bivariate data using CMP2 Supplement Inv 5
8.SP.4
8.EE.1 Exponents/Square Roots 8.2.E, 8.4.C 8.NS.1, 8.NS.2, 8.EE.2, 8.G.6, 8.G.7, 8.G.8
Pythagorean Theorem using Looking For Pythagoras Inv 1-4 and CMP2 supplemetn Inv 1
8.2.F, 8.2.G Define, Evaluate, and Compare Functions
8.F.2, 8.F.3, 8.F.4, 8.F.5
8.EE.3, 8.EE.4 Scientific Notation 8.4.A, 8.4.B 8.EE.1 Exponents/Square Roots 8.2.E, 8.4.C Pythagorean Theorem using Looking For Pythagoras Inv 1-4 and 8 CC Inv 1
8.NS.1, 8.NS.2, 8.EE.2, 8.G.6, 8.G.7, 8.G.8
8.NS.1, 8.EE.2, 8.G.6, 8.G.7, 8.G.8
Looking for Pythagoras 8.2.F, 8.2.G 8.EE.3, 8.EE.4 Scientific Notation 8.4.A, 8.4.B Radical and Integer Exponents using Exponents and Scientific Notation unit
8.EE.1, 8.EE.3, 8.EE.4
8.G.5 Properties of Geometric Figures
8.2.A, 8.2.B, 8.2.C, 8.2.D
8.G.5 Properties of Geometric Figures
8.2.A, 8.2.B, 8.2.C, 8.2.D
Properties of Geometric Figures and Three Dimensional Geometry
8.G.5, 8.G 9
8.G.1, 8.G.2, 8.G.3, 8.G.4
Congruence and Similarity through Transformations using: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2,3, and 5 (KHM) and CMP2 supplements Inv 3
8.2.D 8.G.1, 8.G.2, 8.G.3, 8.G.4
Congruence and Similarity through Transformations using: KHM Inv. 2,3, and 5 (KHM) and CMP2 supplements Inv 3
8.2.A, 8.2.B, 8.2.C, 8.2.D
Congruence and Similarity through Transformations using: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2,3, and 5 (KHM) and CMP2 supplements Inv 3
8.G.1, 8.G.2, 8.G.3, 8.G.4
8.SP.1, 8.SP.2, 8.SP.3 Samples and Populations 8.3.A, 8.3.B, 8.3.C, 8.3.D
8.SP.1, 8.SP.2, 8.SP.3 Samples and Populations 8.3.A, 8.3.B, 8.3.C, 8.3.D
Analyze and Solve Linear Equations using Shapes of Algebra Inv 2-4
8.EE.8a, 8.EE.8b, 8.EE.8c
Probability (must teach until June 2014)
8.3.F Probability (must teach until June 2014)
8.3.F
Algebra Prep Algebra Prep
WHAT DO YOU KNOW ABOUT COMMON CORE STATE STANDARDS
FOR MATHEMATICS (CCSS-M)?
With your elbow partner, find 1-2 common understandings you currently have around the CCSS-M The actual math standards
Identify 1-2 questions you both hope to have answered today
THREE MAJOR SHIFTS OF CCSS-M
CCSS-M
Focus
CoherenceRigor
Grade 6 through 8 standards
Domains - larger groups that progress across grades
Clusters - groups of related standards
Content standards - what students should understand and be able to do
VOCABULARY OF CCSS
DOMAINS ACROSS MIDDLE SCHOOL
DESIGN AND ORGANIZATION OF THE STANDARDS From your binder, take out the yellow
packet of standards that spans grades 5-8
Turn to page 54
Cluster
Standards
Domain
COMPARING STANDARDSCurrent WA State Learning Standards for Grade 8 Transformational Geometry
What key differences do you see between the writing of the current WA State Learning Standards and the Common Core State Standards for Mathematics?
Grade 8 Common Core Math Standards related to Transformational Geometry
• Common Core Math Standards are more easily read on pages 55-56
• Read 8.G.1 up to 8.G.4
LET’S READ A BIT In the yellow standards packet, please
read the Grade 8 synopsis on page 52 Highlight details that jump out at you
while you read about the four critical areas
We will share out what is new, similar, or deeper than our current standards
GRADE 8 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, angle, similarity and congruence, and understanding and applying the Pythagorean Theorem
What’s Going? What’s Staying? What’s Coming?
One- and two-step linear inequalities and graph solution (8.1.B)
Solve one-variable linear equations (8.1.A)
Know and apply properties of integers with negative exponents
Complementary, supplementary, adjacent, or vertical angles, and missing angle measures (8.2.A)
Linear functions, slope, and y-intercept with verbal description, table, graph, and expressions (8.1.C -8.1.G)
Use and evaluate cube roots of small perfect cubes
Summarize and compare data sets using variability and measures of center (8.3.A)
Missing angle measures using parallel lines & transversals (8.2.B)
Operations with scientific notation when exponents are negative
Box-and-whisker plots (8.3.B) Sum of the angle measures of polygons and unknown angle measures (8.2.C)
Graph proportional relationships and interpret unit rate as slope of graph
Describe different methods of selecting statistical samples and analyze methods (8.3.D)
Effects of transformations of a geometric figure on coordinate plane (8.2.D)
Use similar triangles to explain slope
Determine whether conclusions of statistical studies reported in the media are reasonable (8.3.E)
Square roots of the perfect squares from 1 through 225 and estimate the square roots of other positive numbers (8.2.E)
Analyze and solve pairs of simultaneous linear equations (systems of equations)
All probability topics (8.3.F) Pythagorean Theorem, its converse and apply to solve problems (8.2.F and 8.2.G)
Transformations to verify congruency and similarity between figures
Solve problems using counting techniques and Venn diagrams (8.3.G)
Create a scatterplot, sketch and use a trend line to make predictions (8.3.C)
Know and apply formulas for volume of cone, cylinder, and spheres
Scientific notation and solving problems with scientific notation (8.4.A and 8.4.B)
Understand patterns and relationships of bivariate categorical data
Evaluate expressions involving integer exponents using the laws of exponents and the order of operations (8.4.C)
Identify rational and irrational numbers (8.4.D)
THINK TIME
Take a few minutes to think about the following questions and write your response on your notes page. You may want to browse through the standards on 54-56.
What connections are you making between the 2008 and Common Core Standards for Grade 8?
How might instruction look different with these new standards?
DIG DEEPER
BREAK Stand up Stretch See you in 10 minutes
STANDARDS FOR MATHEMATICAL PRACTICE
“The Standards forMathematical Practicedescribe varieties ofexpertise that mathematicseducators at all levelsshould seek to develop intheir students. Thesepractices rest on important“processes andproficiencies” withlongstanding importance inmathematics education.”(CCSS, 2010)
STANDARDS FOR MATHEMATICAL PRACTICE
THE IMPORTANCE OF THE MATHEMATICAL PRACTICEShttp://www.youtube.com/watch?v=m1rxkW8ucAI&list=PLD7F4C7DE7CB3D2E6
As you watch the video, think about the following two questions:How do the math practices support student
learning?How will the math practices support
students as they move beyond middle school and high school?
Standards for Mathematical Practice As a mathematician,
Make sense and persevere in solving problems.
I can try many times to understand and solve problems even when they are challenging.
Reason abstractly and quantitatively. I can show what a math problem means using numbers and symbols.
Construct viable arguments and critique the reasoning of others.
I can explain how I solved a problem and discuss other student’s strategies too.
Model with mathematics. I can use what I know to solve real-world math problems.
Use appropriate tools strategically. I can choose math tools and objects to help me solve a problem.
Attend to precision. I can solve problems accurately and efficiently. I can use correct math vocabulary, symbols, and labels when I explain how I solved a problem.
Look for and make use of structures. I can look for and use patterns to help me solve math problems.
Look for and express regularity in repeated reasoning.
I can look for and use shortcuts in my work to solve similar types of problems.
STUDENT LOOK-FORS
Take out the “Student Look-Fors” within the second tab of your binder
MATH PRACTICES IN ACTION While you watch the video:
Script the student actions What are they saying? What are they doing?
Look at the Student Look-Fors page Choose a specific math practice to focus on
during the videoLook for evidence of students engaging in
your specific mathematical practice Let’s watch the video again
What evidence showed students engaging in a math practice?
What did the teacher do to promote student engagement in the content and math practices?
Take a few minutes to think about the following questions and write your response on the notes page:
Which math practice(s) are your students already engaged in during a math lesson or unit?
How do we get students to engage in these practices if they are not already?
THINK TIME
Content Standards
Standards for Mathematical Practice
LUNCH
Please sit by school when you return from lunch
If you are the only one from your school, join any school you want
AFTERNOON OBJECTIVES
Develop understanding of the progression of the Geometry domain and the cluster of standards being aligned for the first unit to be implemented
Connect the Geometry progression to the first CCSS-M aligned unit that will be taught after the training
Discuss the implementation and feedback plan for the first unit to be aligned with the CCSS-M
Honor your responsibilities Participate fully and actively Honor each person’s place of being Assume positive intent Learn from and encourage each other Share airtime Avoid judgmental comments Honor confidentiality Communicate your needs If you need to attend to something else, step
out of the room Laptops: When instructed to do so go to half-
mast or close lid
COLLABORATIVE NORMS
KSU 8TH GRADE COMMON CORE STATE STANDARDS FLIP BOOK
Compiled current learning from CCSS website, Arizona DOE, Ohio DOE, and North Carolina DOE
Intended use is to show connections to the Standards for Mathematical Practice and content standards
Flip Book includes:Explanation and examples Instructional strategiesStudent misconceptions
Find the Flip Book under Tab 2 (blue packet) and turn to page 33
AS YOU READ…Key Mathematical
Concepts Developed in Understanding Congruence and Similarity Cluster
(8.G.1-8.G.4)
Instructional Strategies
Common Misconceptions
Write key concepts students must learn within this cluster of standards
Collect descriptions of how students should engage with the content
Identify any student misconceptions or challenges
• Read independently pages 33-39• When finished, discuss as a group key concepts,
instructional strategies and common misconceptions
• Then, create a poster based on the bolded standard on your graphic organizer
• Poster should include essential learning for students during unit and possible misconceptions
“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”
“Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”
“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”
Claim #1 - Concepts & Procedures
Claim #2 - Problem Solving
Claim #3 - Communicating Reasoning
Claim #4 - Modeling and Data Analysis
CLAIMS FOR SBAC ASSESSMENT
RE-WRITING DISTRICT COMMON ASSESSMENTS
Process:Read SBAC Claim 1 item specifications (more
on this next)Looked at prior and recently developed
assessmentsDrafted test and scoring guide
Next Steps:PilotProvide FeedbackAdjust
Currently based on current WA state standards and CCSS-M 8.G.1-8.G.4
Pilot assessment items during unit
FEEDBACK ON DISTRICT COMMON ASSESSMENTS
Feedback on:Clarity of directionsTimingAlignment to CCSS-M 8.G.1-
8.G.4Length of grading time
LESSON STRUCTURE:SUPPORTING MATH PRACTICES
The supplemental lessons will include:Mathematical PracticesContent and Language ObjectivesConnections to Prior KnowledgeQuestions to Develop Mathematical ThinkingCommon Misconceptions/ChallengesLaunchExplore with Teacher Moves to Promote the
Mathematical PracticesSummarizeSolutionsFeedback
TIME TO LOOK AT THE STUFF
In your PLC, you many want to look at and discuss:Kaleidoscopes, Hubcaps, and Mirrors
InvestigationsModified ProblemsCMP2 Supplemental Lessons
FEEDBACK SYSTEM Email PLC meetings
EXIT TICKET Please take a few minutes to fill out the
exit ticket. Your feedback will be used to help plan
the next Math 8 training Clock hour information next
CLOCK HOURS AND EVALUATION FORM
Title and Number of In-service ProgramMath 8 Common Core Training #4283
InstructorDeborah Sekreta
Clock Hours6.5
Clock Hour Fee$13.00Checks made out to Renton School DistrictMust have check in order to submit
paperwork
8.G.3 SAMPLE SBAC ASSESSMENT ITEM
A student made this conjecture about reflections on an x-y coordinate plane.
“When a polygon is reflected over the y-axis, the x-coordinates of the corresponding vertices of the polygon and its image are opposite, but the y-coordinates are the same.”
Develop a chain of reasoning to justify or refute the conjecture. You must demonstrate that the conjecture is always true or that there is at least one example in which the conjecture is not true. You may include one or more graphs in your response.
When a polygon is reflected over the y-axis, each vertex of the reflected polygon will end up on the opposite side of the y-axis but the same distance from the y-axis.
So, the x-coordinates of the vertices will change from positive to negative or negative to positive, but the absolute value of the number will stay the same, so the x-coordinates of the corresponding vertices of the polygon and its image are opposites.
Since the polygon is being reflected over the y-axis, the image is in a different place horizontally but it does not move up or down, which means the y-coordinates of the vertices of the image will be the same as the y-coordinates of the corresponding vertices of the original polygon.
As an example, look at the graph below, and notice that the x-coordinates of the corresponding vertices of the polygon and its image are opposites but the y-coordinates are the same. This means the conjecture is correct.
8.G.3 SAMPLE SBAC ASSESSMENT ITEM
AFTERNOON OBJECTIVES
Develop understanding of the progression of the Geometry domain and the cluster of standards being aligned for the first unit to be implemented
Connect the Geometry progression to the first CCSS-M aligned unit that will be taught after the training
Discuss the implementation and feedback plan for the first unit to be aligned with the CCSS-M
