Transcript 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.
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

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 halfmast or close lid

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
Assessment
A More
Smartly
Balanced
Assessment
System
Interim
Assessments
Tab2:
Understanding
CCSS-M Grade 8
Tab 3: SBAC
Claims and
Item
Specifications
Tab 4:
Curriculum
Guide
Tab 1: CCSS-M
Grades 5-9
Agenda
RSD Documents
Math 8
Binder
Tab 5:
Supplemental
Lessons and
Common
Assessment
Washington
State
Transition Plan
Department
Heads
DMLT
RSD Transition
Plan to
Common Core
Principals
District
Leadership
 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

2012-2013 (WA 2008/CCSS-M)
MSP/EOC
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2013-2014 (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 CCSSM aligned unit
District Math Leaders

Deepen understanding of the CCSSM and apply the Standards for
Mathematical Practice
In Fall 2013 and Winter 2014,
implement with fidelity next CCSSM aligned units along with
remaining 2008 WA standards
Track and report feedback on CCSSM aligned units


Math Course Work Teams
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

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
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Professional Development
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
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.
2013-2014
2012-2013
CCSSM
Units
2008 Standards
CCSSM
Linear Functions
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
Units
Linear Functions
Thinking/Math Models
8.1.A, 8.1.C, 8.1.D, 8.SP.1, 8.SP.2, 8.SP.3, Thinking/Math Models
8.1.E, 8.1.F, 8.1.G 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
8.EE.1
Exponents/Square Roots
8.2.E, 8.4.C
8.EE.3, 8.EE.4
Scientific Notation
8.NS.1, 8.EE.2, 8.G.6,
8.G.7, 8.G.8
8.G.5
Inequalities (must teach until
June 2014)
Units
CCSSM
Proportional Relatioships and Linear
8.EE.5, 8.EE.6, 8.EE.7a,
Equations using CMP2 Supplement Inv 2 8.EE.7b, 8.F1
Functions to Model Relationships
8.SP.1, 8.SP.2, 8.SP.3,
between Quantities using Thinking with 8.EE.5, 8.EE8, 8.F.2,
Mathematical Models Inv 1, 2
8.F.3, 8.F.4, 8.F.5
Patterns of bivariate data using CMP2
Supplement Inv 5
8.SP.4
8.NS.1, 8.NS.2, 8.EE.2, Pythagorean Theorem using
8.2.F, 8.2.G
8.G.6, 8.G.7, 8.G.8
Looking For Pythagoras Inv 1-4
and CMP2 supplemetn Inv 1
Define, Evaluate, and Compare
Functions
8.F.2, 8.F.3, 8.F.4,
8.F.5
8.4.A, 8.4.B
8.EE.1
Exponents/Square Roots
8.2.E, 8.4.C
Pythagorean Theorem using Looking For 8.NS.1, 8.NS.2, 8.EE.2,
Pythagoras Inv 1-4 and 8 CC Inv 1
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
8.EE.1, 8.EE.3, 8.EE.4
Exponents and Scientific Notation unit
Properties of Geometric Figures
8.2.A, 8.2.B, 8.2.C, 8.G.5
8.2.D
8.1.B
Properties of Geometric Figures8.2.A, 8.2.B,
8.2.C, 8.2.D
Properties of Geometric Figures and
Three Dimensional Geometry
8.G.5, 8.G 9
Congruence and Similarity
8.2.A, 8.2.B,
through Transformations using: 8.2.C, 8.2.D
KHM Inv. 2,3, and 5 (KHM) and
CMP2 supplements Inv 3
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
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 8.3.F
2014)
Probability (must teach until
June 2014)
8.3.F
Algebra Prep
Algebra Prep
8.G.1, 8.G.2, 8.G.3, 8.G.4 Congruence and Similarity
8.2.D
through Transformations using:
Kaleidoscopes, Hubcaps, and
Mirrors Inv. 2,3, and 5 (KHM) and
CMP2 supplements Inv 3
8.SP.1, 8.SP.2, 8.SP.3
2014-2015
2008 Standards
Samples and Populations
8.G.1, 8.G.2, 8.G.3,
8.G.4
8.3.A, 8.3.B, 8.3.C, 8.SP.1, 8.SP.2, 8.SP.3
8.3.D
 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
Focus
CCSSM
Rigor
Coherence
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
 From
your binder, take out the yellow packet
of standards that spans grades 5-8
 Turn to page 54
Domain
Cluster
Standards
Current WA State Learning Standards for Grade 8 Transformational Geometry
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
What key differences do you see between the writing of the
current WA State Learning Standards and the Common Core State
Standards for Mathematics?
 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
1.
2.
3.
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
Grasping the concept of a function and using
functions to describe quantitative relationships
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)
 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?
 Stand
up
 Stretch
 See you in 10 minutes
“The Standards for
Mathematical Practice
describe varieties of
expertise that mathematics
educators at all levels
should seek to develop in
their students. These
practices rest on important
“processes and
proficiencies” with
longstanding importance in
mathematics education.”
(CCSS, 2010)
http://www.youtube.com/watch?v=m1rxkW8u
cAI&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.
 Take
out the “Student Look-Fors” within the
second tab of your binder
 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 video

Look 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?
Content
Standards
Standards for
Mathematical Practice
 Please
sit by school when you return from
lunch
 If you are the only one from your school, join
any school you want
 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 halfmast or close lid

 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 strategies
Student misconceptions
 Find
the Flip Book under Tab 2 (blue packet)
and turn to page 33
Key Mathematical
Concepts Developed in
Understanding
Congruence and Similarity
Cluster (8.G.1-8.G.4)
Write key concepts
students must
learn within this
cluster of
standards
Instructional Strategies
Collect descriptions
of how students
should engage with
the content
Common Misconceptions
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
Claim #1 - Concepts &
Procedures
Claim #2 - Problem
Solving
“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.”
Claim #3 - Communicating
Reasoning
“Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique
the reasoning of others.”
Claim #4 - Modeling and
Data Analysis
“Students can analyze complex, real-world scenarios and
can construct and use mathematical models to interpret
and solve problems.”
 Process:



Read SBAC Claim 1 item specifications (more on this
next)
Looked at prior and recently developed assessments
Drafted test and scoring guide
 Next



Steps:
Pilot
Provide Feedback
Adjust
 Currently
based on current WA state
standards and CCSS-M 8.G.1-8.G.4
 Pilot assessment items during unit
 Feedback




on:
Clarity of directions
Timing
Alignment to CCSS-M 8.G.1-8.G.4
Length of grading time
 The

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


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


supplemental lessons will include:
Mathematical Practices
Content and Language Objectives
Connections to Prior Knowledge
Questions to Develop Mathematical Thinking
Common Misconceptions/Challenges
Launch
Explore with Teacher Moves to Promote the
Mathematical Practices
Summarize
Solutions
Feedback
 In
your PLC, you many want to look at and
discuss:



Kaleidoscopes, Hubcaps, and Mirrors Investigations
Modified Problems
CMP2 Supplemental Lessons
 Email
 PLC
meetings
 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
 Title

and Number of In-service Program
Math 8 Common Core Training #4283
 Instructor

Deborah Sekreta
 Clock

6.5
 Clock



Hours
Hour Fee
$13.00
Checks made out to Renton School District
Must have check in order to submit paperwork
A student made this conjecture about reflections on an
x-y coordinate plane.
“When a polygon is reflected over the y-axis, the xcoordinates of the corresponding vertices of the
polygon and its image are opposite, but the ycoordinates 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 ycoordinates 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 ycoordinates are the same. This means the conjecture
is correct.
 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