UCDMP Saturday Series 2013-14
The Vision of the Common Core:
Changing Beliefs,
Transforming Practice
Kindergarten – 6th Grade
Saturday, September 21, 2013
Agenda
Introductions and Overview
 Problem Solving: Jim and Jesse’s Money
 Review of SMP’s
 Assessment of and for Learning
Lunch
 Planning a Common Core Unit and Lesson
 Standards Analysis and Resource
Evaluation
 Sharing and Reflections

Wireless Access

Go to Moobilenet

Sign in information
 Email address: ucdmp@wireless.com
 Password: wireless
Introductions
The Staff
 Pam Hutchison, Director, UCDMP
 Andrea Williams, UCDMP Teacher Leader
and 4th grade teacher, FSUSD
 Diana Zaragoza, UCDMP Teacher Leader
and District Math Coach, DJUSD
 Renee Yeasted, UCDMP Teacher Leader
and Content Area Specialist, VUSD
Overview of Saturdays
November 2, 2013
 Assessment of and for learning
 Formative assessments
 Assessing students’ ability to
 Explain their reasoning,
 Construct viable arguments and
 Critique the reasoning of others.
 The use of games
 Planning for the CCSS-M
Overview of Saturdays
January 25, 2014
 The use of mathematical tasks
 As an instructional tool,
 As an assessment tool for
 Problem solving
 Explanations
 Connecting to prior knowledge
 Developing a deep understanding
 Planning for the CCSS-M
Overview of Saturdays
March 15, 2014
 Developing and using rubrics to assess
understanding, communication, and
problem solving
 General rubrics,
 Task specific rubrics
 CCSS rubrics
K-2 “Construct viable arguments and
critique the reasoning of others”
 3-5 Using technology to learn math
 Planning for the CCSS-M

Overview of Saturdays
May 3, 2014
 Summative Assessments
 Performance tasks
 Model with Mathematics
 K-2 Using technology to learn math
 3-5 “Construct viable arguments and
critique the reasoning of others”
 Planning for the CCSS-M
Units
Available for purchase
 Attend 3 sessions
 2 quarter units

Attend all 5 sessions
 3 quarter units
Online Course

Constructive Classroom Conversations:
Mastering the Language of the Common
Core State Standards
Standford Online
 October 21 – Dec 9

Andrea and Diana’s Money
Andrea and Diana each had the same
amount of money. Andrea spent $58
to fill the car up with gas for a roadtrip. Diana spent $37 buying snacks
for the trip. Afterward, Andrea had 1/4
as much money as Diana had. How
much money did each have at first?
The CCSS in Mathematics have two sections:
Standards for Mathematical CONTENT
and
Standards for Mathematical PRACTICE


The Standards for Mathematical Content
are what students should understand,
know, and be able to apply.
The Standards for Mathematical Practice
are what students should do.
 Mathematical “Habits of Mind”
1. Make sense of problems and persevere in
solving them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical Practices
REASONING AND EXPLAINING
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the
reasoning of others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND
GENERALIZING
7. Look for and make use of structure
8. Look for and express regularity in repeated
reasoning
Proficiency Matrix
Standards for Mathematical Practice
Initial
 Intermediate
 Advanced

PS, QW, GE, etc.
 Student engagement strategies
Self-Evaluation

Where are you on this matrix?
What SMP’s are you already overtly
fostering in students?
 Are you getting them to the initial,
intermediate, or advanced stage?


What SMP’s do you really not address at
this point?
Make a Plan
Pick 1 to 2 SMP’s that you want to focus on
in the next month or so.
 What are you going to do to support
students in developing those standards?
 Where are you (as the teacher) starting
from?
 What can you do to help “move” students
to the next stage on the matrix?
Share

Share your plan at your table.
What are your strategies and ideas?
 What are your concerns?

Assessments
 What
are various ways in which we
assess:
 what students know?
 what students understand?
Assessment and Learning
 “Assessment
should be an integral
part of teaching. It is the mechanism
whereby teachers can learn how
students think about mathematics as
well as what students are able to
accomplish.”
Assessment and Learning
 “Assessment
should allow all
students to show what they know,
understand and can do.”
(Cockcroft Report 1982)
Assessment and Learning
 “Assessment
for learning is one of
the most powerful ways of improving
learning and raising standards“
(Black and Wiliam 1998)
Assessment
 What
are characteristics of “good”
assessment?
According to the Shell Centre, high
quality assessment has:
 Curriculum balance
 Curriculum value
 Fitness for purpose
Formative Assessments
Assessment for learning
Occurs continuously in classroom both
within and between lessons
 Used to adjust teaching strategies
 Provides students with useful and
meaningful feedback

Formative Assessments
 Focus:
To determine what learning
comes next

Examples:






Feedback
Open questioning
Exit tickets
Observations
Discussions
Ungraded classwork/homeworks
Summative Assessments
Assessment of learning
Occur within, between, and among
instructional units
 Used to identify strengths and gaps in
curriculum and instruction
 Curriculum may be refined
 Teachers may modify instruction

Summative Assessments
Focus: To determine:
 how student groups are progressing
 how well program is working

Examples





Graded class work or homework
Quizzes
End of unit tests
Midterms
District benchmarks
Large Scale Assessments
Assessment of learning
Frequently high stakes
 Examine trends over time
 Used to develop long-term evaluation of
curriculum and programs
 Used to monitor school site, district and
state progress

Large Scale Assessments
 Focus:
To determine how schools,
districts and states are progressing
over time

Examples:





End of course exams
CST
NAEP
SAT/ACT Exams
AP Exams
Assessment

Think of how and when you assess your
students.

Which ones are assessments for learning?

Which ones are assessments of learning?
Assessment
“What a difference a word makes”
Read the article
Record
 1 thing with which you agree
 1 thing with which you might argue
 1 thing to which you aspire
 1 Aha!
Sharing
Go around the group and share one of the
following:
 the thing with which you agree
 the thing with which you might argue
 the thing to which you aspire
 your Aha!
Pick one thing from your group to share
with the whole group
Large Scale Assessment
WYTIWYG!
Large Scale Assessment
What you test is
what you get!
Goals of Assessment
“We must ensure that tests measure
what is of value, not just what is easy
to test. If we want students to
investigate, explore, and discover,
assessment must not measure just
mimicry mathematics.”
Everybody Counts
PARCC States
PARCC States
CCSS-M SMARTER Claims
Claim #1: Concepts and Procedures
“Students can explain and apply
mathematical concepts and interpret
and carry out mathematical
procedures with precision and
fluency.”
CCSS-M SMARTER Claims
Claim #2: Problem Solving
“Students can solve a range of
complex well-posed problems in pure
and applied mathematics, making
productive use of knowledge and
problem solving strategies.”
CCSS-M SMARTER Claims
Claim #3: Communicating
Reasoning
“Students can clearly and precisely
construct viable arguments to support
their own reasoning and to critique the
reasoning of others.”
CCSS-M SMARTER Claims
Claim #4: Modeling and Data
Analysis
“Students can analyze complex, realworld scenarios and can construct and
use mathematical models to interpret
and solve problems.”
Score Reporting-Individual
“Total Mathematics” score
 The composite mathematics score
will need to have scaling properties
that allow for the valid determination
of student growth over time. This
score will be a weighted composite
from the four claims
Claim #1: 40%
Claims #2-4: about 20% each.
Smarter Balanced
Assessment Consortium
Problem Types





SR – selected-response item
CR – constructed-response item
ER – extended-response item
TE – technology-enhanced item
PT – performance task
CCSS-M SMARTER Claims
Claim #1: Concepts and Procedures
“Students can explain and apply
mathematical concepts and interpret
and carry out mathematical
procedures with precision and
fluency.”
Claim 1
Selected Response
 Typical Multiple Choice
 Selected Response
Constructed Response
Extended Response
Technology Enhanced
Assessment Items Group 1
Claim 1 – Selected Response
Typical Multiple Choice
Answer the problems.
Assessment Items Group 1
Claim 1 – Selected Response
Typical Multiple Choice
How are these problems similar and/or
different from the typical CST questions?
Assessment Items Group 2
Claim 1 – Selected Response
Selected Response
Answer the problems.
Assessment Items Group 2
Claim 1 – Selected Response

How are these problems different from the
typical CST questions?

What do students have to know and/or
understand to do these problems that
they don’t have know/understand to do a
typical multiple choice question.
th
5
Grade Multiplication Models
Smarter Balanced
Assessment Consortium
Problem Types





SR – selected-response item
CR – constructed-response item
ER – extended-response item
TE – technology-enhanced item
PT – performance task
rd
3
Grade – CR
th
4
Grade – CR
th
5
Grade – CR
th
6
Grade – CR
Rubric Scoring
rd
3
Grade – ER
th
5
Grade – ER
th
4
Grade – TE
th
6
Grade – TE
th
6
Grade – TE, cont.
Claim 1
“Students can explain and apply
mathematical concepts and interpret and
carry out mathematical procedures with
precision and fluency.”

So what are the classroom implications if
we are assessing students in these ways?
Multiple Representations

Look at the standards for your grade
level.

Which standards clearly imply that
students need to be familiar with a variety
of models, representations, and/or
strategies?
Unit Planning
Unit Planning
Unit Planning Template
 Unit Planning Questions

2nd Grade
Unit Planning Questions
Topic:
 What is the big idea that you will be
addressing in this unit?
Unit Planning Questions
Content Standards:
 Which common core standards (or parts
of standards) will be addressed in this
unit?
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 addition and
subtraction.
6. Add up to four two-digit numbers using
strategies based on place value and
properties of operations.
7. Add and subtract within 1000, using
concrete models or drawings and strategies
based on place value, properties of
operations, and/or the relationship between
addition and subtraction; relate the strategy
to a written method. Understand that in
adding or subtracting three-digit numbers,
one adds or subtracts hundreds and
hundreds, tens and tens, ones and ones; and
sometimes it is necessary to compose or
decompose tens or hundreds.
7.1 Use estimation strategies to make
reasonable estimates in problem
solving. CA
8. Mentally add 10 or 100 to a given
number 100–900, and mentally subtract 10
or 100 from a given number 100–900.
9. Explain why addition and subtraction
strategies work, using place value and the
properties of operations.3
Explanations may be supported by
drawings or objects.
3
Unit Planning Questions
Practice Standards:
 What standards for mathematical practice
(1-2) do I want to focus on and promote
during this unit?
Unit Planning Questions
What should students already know?
 What have students learned in previous
grades?
 How does what they should already know
connect to what they are going to learn?
 Where does this unit fall on the continuum
of “Concrete – Representational –
Abstract”
Unit Planning Questions
What will students learn and how will I
know what they have learned?
 What should students understand by the
end of the unit? What are some ideas for
assessing student understanding?
Unit Planning Questions
What will students learn and how will I
know what they have learned?
 What should students know and be able to
do by the end of the unit? What are some
ideas for assessing procedural skills?
Unit Planning Questions
What will students learn and how will I
know what they have learned?
 How should students be able to
demonstrate their ability to apply what
they have learned by the end of the unit?
What are some possible assessment ideas
and/or tasks?
Unit Planning Questions
What will students learn and how will I
know what they have learned?
 Key Vocabulary
Unit Planning Questions
What tools, models, and materials are
necessary to fully address the
standards for this unit?
Unit Planning Questions
Anticipated Number of Days
 Approximately how many days do I
anticipate needing for this unit (including
all assessments)?
 How many days are needed for lessons
related to:
 Conceptual understanding
 Procedures and skills
 Applications and problem solving
Unit Planning Questions
Sketch of Unit by Days (Overview)
 Brief description of big ideas for each day
Lesson Planning Questions
Topic: What is the topic of the lesson?
Lesson Day: Where is this lesson in the
overall plan of the unit?
Lesson Planning Questions
OVERVIEW
Content Standard(s): What part of the
standard(s) is being addressed today? This
should be a brief statement or goal.
Practice Standard(s): What practice
standard will I be focusing on today?
Lesson Planning Questions
Type of Lesson:
 Concept Lesson
 Procedure or Skill Lesson
 Application or Problem Solving Lesson
 Review Lesson
Key Vocabulary: What vocabulary needs
to be introduced or reviewed today? How
and when will that take place?
Lesson Planning Questions

Materials Needed: What materials are
needed for this lesson? Materials include
(but are not limited to): textbook
resources, supplemental student activity
pages or worksheets, manipulatives,
rulers, protractors, strategies, models,
technology,…
Lesson Planning Questions
How and when will I support students
in connecting to prior knowledge? What
prior knowledge does this lesson build on
and extend? It could be from the prior day
or earlier in the year or the previous year.
How and when will I deal with
homework?
Lesson Planning Questions
Opening prompt or problem: Leads in
and connects to the topic of the day
Lesson Planning Questions
Lesson Part 1, 2, 3,…: Description of
what happens in each part of the lesson.
 What am I doing?
 What are students doing?
 What specific problems or activities are
involved?
 What are some key questions that I want
to ask?
 What materials are needed for this part?
Lesson Planning Questions
Closure: What prompt can I use to help
students review what they have learned?
How will I know what they have learned?
Collaboration
Lesson planning is easier and more efficient
when done with teams of teachers
 Share strategies
 Share workload (if need to create, copy or
collect materials)
 Share struggles and successes
 Reflect and revise
Resources
Illustrative Mathematics Website
http://illustrativemathematics.org
 A work in progress
 Designed to provide examples that help to
clarify what each CCSS means
Resources
Inside Mathematics Website
http://www.insidemathematics.org
 Resources on SMP’s, including:
 Classroom video examples illustrating the
math practice standards, including
commentary
 Videos of exemplary lessons integrating
multiple math practices
Resources
Inside Mathematics Website
 New resources on SMC’s, including:
 Common Core-aligned tasks, searchable
either by grade level or by Common Core
content area, such as “Operations and
Algebraic Thinking,” or “Geometry Congruence.”
Resources
Inside Mathematics Website
 Additional classroom videos of
Number Talks
 Four new classroom videos of “Number
Talks” showing students engaged in
mental math exercises and conversations
about math, including one from a bilingual
Spanish-English classroom.
Resources
NCTM Illuminations Website
http://illuminations.nctm.org/
 National Council of Teachers of
Mathematics
 Contains activities, lessons and links
related to the CCSS
Resources
Common Core Flip Books
http://katm.org/wp/wp-content/uploads/
flipbooks
 Grade level books with additional
examples, strategies and ideas for
teaching the CCSS-M
Resources
SBAC Website
 Sample Items
 http://www.smarterbalanced.org/smarterbalanced-assessments/
 Scroll down to “Mathematics”
 Find “Mathematics 3-5” (ZIP) or
“Mathematics 6-8” (ZIP)
 Folder of currently released sample
assessment items for the 4 claims
Resources
SBAC Website
 Practice Tests
 https://sbacpt.tds.airast.org/student/
Resources
California Department of Education
 Common Core State Standards – M
 http://www.cde.ca.gov/be/st/ss/documen
ts/ccssmathstandardaug2013.pdf
Mathematics Framework (DRAFT)
 http://www.cde.ca.gov/ci/ma/cf/draft2ma
thfwchapters.asp

Break-Out Groups

K-2:

3-5: