Transcript Assessment Literacy on Steroids

Common Core Lite
Mathematics
Brought to
you by….
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Provide an overview of the Common Core
State Standards for Mathematics.
Conduct this workshop with a process that
you can replicate with large or small groups
of teachers.
Provide you with the materials necessary to
get all K-12 teachers ‘dipped’ into the
standards.
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1.
Our focus today is to learn HOW to investigate the Common
Core State Standards for math.
2.
You will not investigate all of the standards today. You will
be given a process and materials to duplicate today’s
process in your school.
3.
WI has Early Learning Standards that address expectations
for children birth to the beginning of first grade. When
developing curriculum and assessment practices for 4K
and 5K, the WMELS need to be considered along side the
CCSS
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1. An open and willing mind
2. The materials at your table
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Practices
Understandings
Connections
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The CCSS mandates the student learning outcomes
for every grade level/grade band.
Students will be tested and instructional effectiveness
will be measured based on CCSS (beginning 2015).
Federal funding is tied to CCSS adoption,
implementation, and accountability.
ELA and Mathematics CCSS are just the beginning.
Science and Social Studies are in the draft
stage…more subject area standards are being
developed.
CCSS create an opportunity for educators to talk and
share knowledge across state lines.
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…the acquisition of the knowledge and skills a
student needs to enroll and succeed in creditbearing, first-year courses at a postsecondary
institution (such as a two- or four-year college,
trade school, or technical school) without the
need for remediation. (ACT)
The standards were built on this vision for every
single student who graduates from high school.
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Activity
1
◦ Foundation in whole numbers, addition,
subtraction, multiplication, division,
fractions and decimals
◦ Procedural as well as conceptual
◦ Hands-on
◦ Apply mathematical ways of thinking to
real world issues and challenges
◦ Rigorous definition of college and career
readiness
◦ Emphasize mathematical modeling
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Standards for Mathematical Practice
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Carry across all grade levels
Standards
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Describe habits of mind of a
Document –
mathematically expert student
page 6
1.
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3.
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6.
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Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments & critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
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Refer to the
Standards
Documents
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K-8 standards presented by grade level
Organized into domains that progress over
several grades
Grades K-8 introductions give 2 to 4 domains
at each grade level
High school standards presented by
conceptual theme (Number & Quantity,
Algebra, Functions, Modeling, Geometry,
Statistics & Probability)
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Provide a sense of …
◦ the sophistication for mathematical
understanding at the grade level.
◦ the learning progressions for the grade.
◦ extensions from prior standards.
◦ what’s important at the grade level.
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Grade 1
Narrative
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The Math Structure is Like a File Cabinet
Intent - File Cabinet
Cluster- Hanging Files
Domain- Drawer
File Folders –
Grade Level Standards
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Activity
2
Task:
 Note the descriptions of domains described.
 Divide the grade level focus areas among table
partners and read the descriptions.
 Use the organizers provided to note what you
discover and think about the standard’s intent.
 Discuss your thinking with your table partners
about all of the critical focus areas.
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Standards for
Mathematical
Practice are
provided in detail.
The Practices are
also listed at the
beginning of each
grade level
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Domains are larger groups that progress across grades
Grade Level Standards define what students should
understand and be able to do
Clusters are groups of related standards
Domain
Operations and Algebraic Thinking
Grade
Level
Standards
1.0A
Cluster
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Simple…Like a File Cabinet
Intent - File Cabinet
Cluster- Hanging Files
Domain- Drawer
File Folders –
Grade Level Standards
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Activity
3
Task:
 Find the Grade 8 Mathematics Standards.
 Examine the standards provided in the
activity.
 Find all the elements Grade/Domain/Cluster),
and note them in the chart.
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Activity
3
Investigating the Content Standards’ Structure
Task:
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Grade
Go to the Mathematics Standards to review the components of the content standards structure.
See the standards provided in the table below.
Scavenger Hunt for each standard, find all the elements (Cluster, Domain and Grade/Conceptual
Category), and note them in the table below.
Domain
Cluster
Standard
Graph proportional relationships, interpreting
the unit rate as the slope of the graph. Compare
two different proportional relationships
represented in different ways. For example,
compare a distance-time graph to a distancetime equation to determine which of two moving
objects has greater speed.
Compute unit rates associated with ratios of
fractions, including ratios of lengths, areas and
other quantities measured in like or different
units. For example, if a person walks 1/2 mile in
each 1/4 hour, compute the unit rate as the
complex fraction 1/2/1/4 miles per hour,
equivalently 2 miles per hour.
Know that numbers that are not rational are
called irrational. Understand informally that
every number has a decimal expansion; for
rational numbers show that the decimal
expansion repeats eventually, and convert a
decimal expansion which repeats eventually into
a rational number.
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“The Standards for
Mathematical Practice
describe varieties of
expertise that
mathematics educators at
all levels should seek to
develop in their students.”
CCSS page 6
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1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in
solving them
Reason abstractly and quantitatively
Construct viable arguments & critique the
reasoning of others
Refer to the
Model with mathematics
standards
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated
reasoning
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Investigating the Standards for
Mathematical Practice
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What is it?
How can you use it?
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Grad
eK
Counting
&
Cardinality
Grad
e1
Grad Grade Grade Grade Grade Grade Grade
3
4
5
6
7
8
e2
The Number System
Operations & Algebraic Thinking
Number & Operations in Base 10
Number Operations – Fractions
Measurement & Data
Geometry
Ratios &
Proportional
Relationships
Function
s
Expressions & Equations
Statistics & Probability
Vertical Connections
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All Standards in
mathematics have a
connection to early
and subsequent
concepts and skills
The flow of those
connections is
documented by how
a student develops
the concepts
Future Standards
Future Standards
Current Standard
Prior Standards
Prior Standards
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TEAM TAKE AWAY 2
Investigating
Vertical Connections
Investigating Vertical Connections
Task:
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Find a standards to insert in the chart , find corresponding prior and future standards that focus
on the learning progressions one level above or below the given standard (if they exist). Note
that you will be looking for standards prior to the given grade level and after the given the grade
level.
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Discuss and note these connected standards in the chart below.
EXAMPLE:
Prior Standard
Cluster/ Grade Level Standard
Future Standard
th
7 Grade. Ratios & Proportional Relationships.
2. Recognize and represent proportional relationships
between quantities.
 Decide whether two quantities are in a proportional
relationship, e.g., by testing for equivalent ratios in a
table or graphing on a coordinate plane and
observing whether the graph is a straight line
through the origin.
 Identify the constant of proportionality (unit rate) in
tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
 Represent proportional relationships by equations.
For example, if total cost ( t) is proportional to the
number (n) of items purchased at a constant price
(p), the relationship between the total cost and the
number of items can be expressed as t = pn.
 Explain what a point (x, y) on the graph of a
proportional relationship means in terms of the
situation, with special attention to the points (0, 0)
and (1, r) where r is the unit rate.
8th Grade Functions. 4. Construct a function to model
a linear relationship between two quantities.
Determine the rate of change and initial value of the
function from a description of a relationship or from
two (x, y) values, including reading these from a table
or from a graph. Interpret the rate of change and
initial value of a linear function in terms of the
situation it models, and in terms of its graph or a table
of values.
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Investigating the Standards
Through Vertical Connections
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Properties of operations: their role in arithmetic and
algebra
Mental math and algebra vs. algorithms (Inspection)
Units and unitizing
Operations and the problems they solve
Quantities
Variables
Functions
Modeling (As a
sequence across grades)
Number
Operations
Expressions
Equations
(As a sequence across grades)
Modeling
Practices
(from Phil Daro, one of three lead writers on the
Common Core Standards for Mathematics)
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So how will you use this in your school or district?
PowerPoint
Activities 1 - 4
2 Takeaway Activities
Today’s Materials are all Available at:
http://www.cesa4.k12.wi.us/
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(Today’s slides and materials were adapted from Investigating the Standards,
©2010 Wisconsin Cooperative Educational Service Agencies (CESAs) School
Improvement Services statewide roll-out initiative)
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Please complete your Exit Ticket.
Nicki
Pope
Thanks for
coming!
Sherri
Torkelson
Billie
Finco
Julie
Jensen
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