# Common Core State Standards in Mathematics

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```					     Common Core State
Standards in Mathematics
For Cluster 2 Network Leaders and Teams
Prepared and presented by Louise Antoine, Kerry Cunningham, Linda Curtis-Bey,
George Georgilakis, Carol Mosesson-Teig, Rose Shteynberg, Suzanne Werner
9/21/10
What are Standards?
   Standards define what students should
understand and be able to do.

   Standards must be a promise to students
of the mathematics they can take with
them.
CCSS Mathematical Practices

The Common Core proposes a set of
Mathematical Practices that all teachers
should develop in their students. These
practices are similar to the mathematical
processes that NCTM addresses in the
Process Standards in Principles and
Standards for School Mathematics.
CCSS Mathematical Practices

The Common Core proposes a set of
Mathematical Practices that all teachers
should develop with their students. These
practices are similar to the mathematical
processes that NCTM addresses in the
Process Standards in Principles and
Standards for School Mathematics and
informed by the Strands of Proficiency from
Adding it Up from the National Research
Council.
CCSS Mathematical Practices
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
Common Core Format
K-8                              High School

Domain                          Domain
Cluster                       Cluster
Standards                Standards
(There are no Pre-K Standards)

Cross-
Cutting
Themes

Critical Area
Format of K-8 Standards

Standard

Cluster

Standard

Cluster
Format of High School Standards
Domain

Standard

Cluster
Common Core - Domain

   Overarching “big ideas” that connect topics

   Descriptions of the mathematical content to
be learned, elaborated through clusters and
standards
Common Core - Standards

   Content statements

   Progressions of increasing complexity from
High School
Conceptual Categories
   The big ideas that connect mathematics
across high school

   A progression of increasing complexity

   Description of the mathematical content to
be learned, elaborated through domains,
clusters, and standards
High School Conceptual Categories

   Number & Quantity
   Algebra
   Functions
   Modeling
   Geometry
   Statistics & Probability
High School Pathways

   The CCSS Model Pathways are NOT required. The
two sequences are examples, not mandates
   Two models that organize the CCSS into coherent,
rigorous courses
   Four years of mathematics:
◦ One course in each of the first two years
◦ Followed by two options for year 3 and a variety of relevant
courses for year 4
   Course descriptions
◦ Define what is covered in a course
◦ Not prescriptions for the curriculum or pedagogy
High School Pathways
   Pathway A: Consists of two algebra courses and a
geometry course, with some data, probability, and

   Pathway B: Typically seen internationally,
consisting of a sequence of 3 courses, each of
which treats aspects of algebra; geometry; and
data, probability, and statistics.
Mathematics
United States
How can I teach my kids to get the
Easy, reliable, works with bottom half,
good for classroom management.
Japan
How can I use this problem to teach
know?
How might a fourth grader solve
these problems?

145-100=          145
-100

145-98=           145
- 98
D. Schifter and M. Riddle

 Read pages 28, 29, 30.
 STOP at Dig into Content
 Go back to Mathematical Practices in the
Standards
 Find evidence for students’ use of some of
the Practices described in the CCSS
document.
Domain Trace: Number and
Operations in Base Ten: Grade 2
Use place value understanding and
properties of operations to add and
subtract
5. Fluently add and subtract within 100 using
strategies based on place value, properties of
operations, and/or the relationship between
Domain Trace Number and
Operations in Base Ten Grade 3

Use place value understanding and
properties of operations to perform multi-
digit arithmetic.
2. Fluently add and subtract within 1000 using
strategies and algorithms based on place value,
properties of operations, and/or the relationship
Trail Mix Problem

 At your tables, begin solving the problem
 Discuss and share solutions and strategies
 Choose one solution to share. Put it on
chart paper.
Take a BREAK
Sharing Strategies

   Listen

   Connect

   Compare
Looking at Student Work:
Trail Mix Problem

 Look   at samples of student work

 Analyzefor evidence of
understanding through the CCSS
Mathematical Practices
LUNCH
Using Video to
Examine Teacher
Practice
Framework for Viewing

 What does the teacher do to foster
learning?

 What is the impact on student
learning?

Mathematical tasks are a set of
problems or a single complex problem
the purpose of which is to focus
students’ attention on a particular
mathematical idea.
Why Focus on Mathematical

   Tasks form the basis for students’
opportunities to learn what mathematics
is and how one does it;
   Tasks influence learners by directing their
attention to particular aspects of content
and by specifying ways to process
information;
Why Focus on Mathematical
   The level and kind of thinking required by
influences what students learn; and
   Differences in the level and kind of
thinking of tasks used by different
teachers, schools, and districts, is a major
source of inequity in students’
opportunities to learn mathematics.
“Not all tasks are created equal, and
levels and kinds of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in
which students engage determines
what they will learn.”
Hiebert et al., 1997
 Memorization
 Procedures without connections

 Procedures with connections
 Doing mathematics

highlight important words, phrases or
ideas for each level.

   What type of task was the Trail Mix
problem? Why?
   Choose a standard from the 4th Grade or
from the 8th Grade CCSS in Mathematics.
   As a group, write a low-level demand task
on a large post-it note.
   Discuss why the task is low-level demand
Three Stay-One Stray
• Designate one person as the Traveler.
The Traveler takes the group’s low-level
demand task and moves to the next
table. The rest of the group stays.
•   The Traveler explains why the task is a
low- level demand task to the new
group.
   The new group creates a high-level
demand task from the low-level demand
the CCSS Standards for Mathematical
Practices and writes their new task on
chart paper.
Facilitator Walk

•    Facilitators move the charted tasks from
table to table.
Facilitator Walk (continued)
•   Table groups evaluate the cognitive level of
each task presented by the facilitator using the
criteria from the Task Analysis Guide and writes
the demand level (M, PwoC, PwC, DM) on a
post-it note.

•   The facilitator moves from table to table adding
the post-it notes from each group to their
charts.

•   The facilitators discuss feedback on the tasks
with the whole group.
Reflection
   Review of the CCSS in Mathematics
   Article - Students Ideas About Math
   Trail Mix Problem
   Looking at Student Work
   Using Video to Examine Teacher
Practice
A Sample Plan for Year 1
   Explore and integrate at least one Mathematical
Practice, into your students’ repertoire of doing
mathematics.
   Integrate a Mathematical Practice into an existing unit
of study in your curriculum map.
   Explore and collect mathematical tasks that will
support students’ use of the CCSS Mathematical
Practices.
   Collect student work and integrate looking at student
work into your school’s inquiry team work.
   Use classroom talk to support the CCSS Mathematical
Practices.
   Develop one Domain strand trace covering the grade
spans of your school (e.g. K-5, K-8, 6-8, 6-12, etc)

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