Transcript Diapositiva 1 - Educational Cents

Sailing the Seas of Change:
CCSS Mathematics K-5
Bay District Schools
Common Core Summer Institute
2013
Presenters
Jeremy Centeno, K-5 Staff Training Specialist
Ilea Faircloth, K-5 Staff Training Specialist
Teacher Presenters
Ashley French
Michelle Spencer
Candice Wilds
Group Norms
1.
2.
3.
4.
Start/End on Time
Be Respectful of Agenda
Use Parking Lot
Silence Cell Phones
Agenda
1. Think Share and Pair – “Why I became a teacher”
2. CCSS video
3. Common Vocabulary overview
4. Visual (will be referring back for each section)
5. Introduction and Review of Instructional Shifts of CCSS
A. Review slide with shifts from NGSSS to CCSS with the focus
on the Standards Based Instruction
B. Review Instructional shifts of ELA/ literacy standards/ Math
C. It all begins with Course Descriptions – first look at CPALMS
6. Grouping Course descriptions under organizing principals (units)
A. Show “chunking or grouping” example
B. Each participant group organizes /chunks standards in course
descriptions under an organizing principle (unit). Demonstrate how this
process forms learning goals. Show learning goal example.
Continued….
Agenda Continued…
7. Follow a CCSS shift or skill or anchor standard or concept from elementary to high
school (if applicable for your content area).
8. Write a scale from a Learning Goal
A. Explain learning goals with scales – tied to teacher evaluation framework
B. Participants write a progression scale from a given goal. Groups share.
9. Align instructional shifts to model CCSS lessons/tasks or learning strategies. What
does this look like in the classroom? (This will look different for each content area.)
A. Watch video on what this may look like (if applicable).
B. Model lessons/tasks /strategies aligned to instructional shifts (may only be able to
do 2-3 depending on time).
C. Discuss necessary classroom norms. Establishing the classroom culture,
physical
environment, collaborative spaces, etc.
10. Assessments
A. PARCC prototype
B. Discussion about different types of assessments (interim, summative, formative) .
11. Resources – common ones and add additional ones.
Why did you become a teacher?
Think Pair Share!
2 minutes
Think Time: Think about why you became a
teacher.
When the signal word is given share your
thoughts with your shoulder partner
Video
Click picture to start video
Bay District Learning Goal
By the end of the Common Core Summer Institute,
participants will have an increased knowledge of the
Common Core State Standards (CCSS) and shifts in
instruction to enhance learning opportunities and
instructional delivery to support student success.
8
Common Vocabulary
• Learning Goals
• Formative
Assessment
• Scales
• Learning Activities
• Interim
Assessment
• Differentiated
Instruction
• Summative
Assessment
Model for Instructional Planning
10
English Language Arts and Literacy
Standards “Roadmap”
Standards-Based
Teaching and Learning
The standards come alive when teachers
study student work, collaborate with other
teachers to improve their understanding of
subjects and students’ thinking, and develop
new approaches to teaching that are relevant
and useful for them and their students.
-Linda Darling-Hammond
12
Course Descriptions
CPALMS
www.cpalms.org
Course Description
14
“Blended” Courses for Math and ELA
• A blended course description is comprised primarily of
Common Core standards (CCSS) with a few additional Next
Generation (NGSSS) standards blended in.
• Mathematics and English language arts courses are the only
content areas that may have blended course descriptions.
• The blended course descriptions will only be used for the
2013-14 school year to ensure course content fidelity for the
spring 2014 FCAT 2.0 in mathematics, reading, and writing,
as well as the Algebra 1 End of Course assessment.
15
Florida’s Coding of
the Common Core State Standards
MACC.4.NBT.2.5
Subject Grade Domain Cluster Standard
Breaking the Code of CCSS
in Florida Course Descriptions
Find in the CCSS Mathematical Practices
Locate each on the page: (What is the page number?).
– Mathematics Common Core (Where on the page is this found?).
– Grade Band K-12 (What is this called in the CCSS document?).
– First Domain (What is the title of this domain?).
– First Cluster (What is the title of this cluster?).
– First Standard (How do you know it is the first standard?).
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Why Are Multiple Content Area
Standards in My Course Description?
• The Common Core State Standards (CCSS) in
both English/Language Arts (ELA) and
Mathematics are designed to be robust and
relevant to the real world reflecting the knowledge
and skills that students need for success in
college and careers.
• Appropriate CCSS in the course descriptions of
content areas other than ELA and Mathematics
provides a framework for teachers to ensure that
students are applying what they learn in a way
that enhances their literacy or mathematical skills
in those content areas.
18
RIGOR
Common Core
Instructional Shifts
• Focus strongly where the Standards focus
• Coherence: Think across grades, and link to major topics within
grades
• Fluency: Speed and Accuracy with simple calculations
• Deep Understanding: Students access concepts from a number of
perspectives so they are able to “SEE THE MATH”
• Applications: Use math and choose appropriate concept for
application even when they are not prompted to do so. Apply to
“Real-World” situations.
• Dual Intensity - Practice and Understand. Opportunity for both.
Talking Chips
• Think Time: After looking at the instructional
shifts, “How will these shifts affect your
teaching?”
• When signal is given anyone may place their
chip in the middle to start
• Share your idea
• As participants share place chips in the middle
• Once all chips are in the middle continue
conversation by removing chips
Instructional Shift #1
FOCUS strongly where the Standards focus
“… standards must address the problem of a
curriculum that is ‘a mile wide and an inch
deep.’ These Standards are a substantial
answer to that challenge” (CCSS, 2010, p. 3).
Mathematics – Grades K
• 5 Domains
– Counting and Cardinality (CC)
– Operations and Algebraic Thinking (OA)
– Number and Operations in Base Ten
(NBT)
– Measurement and Data (MD)
– Geometry (G)
Mathematics – Grades 1st – 5th
• 4 Domains
– Operations and Algebraic Thinking(OA)
– Number and Operations in Base
Ten(NBT)
– Measurement and Data(MD)
– Geometry(G)
Let’s examine coherence in
Operations and algebraic thinking
Kindergarten: Understand addition as putting together and adding to, and
understand subtraction as taking apart and taking from.
1st Grade: Represent and solve problems involving addition and subtraction.
2nd grade: Represent and solve problems involving addition and subtraction.
2nd grade: Work with equal groups of objects to gain foundations for
multiplication.
3rd grade: Represent and solve problems involving multiplication and
division.
3rd grade: Solve problems involving the four operations, and identify and
explain patterns in arithmetic.
4th grade: Use the 4 operations with whole numbers to solve problems.
4th grade: Generate and analyze patterns.
A Picture Says a Thousand
Words
• As a grade group locate your critical areas
• Once you locate the critical areas in your
grade level create a picture that
represents those critical areas
• Once done be prepared as a grade group
to share and explain your pictures
Two Critical Areas in
Kindergarten
• In Kindergarten, instructional time should focus
on two critical areas:
• (1) representing, relating, and operating on
whole numbers, initially with sets of objects
(2) describing shapes and space.
• More learning time in Kindergarten should be
devoted to number than to other topics.
http://www.corestandards.org/the-standards/mathematics/kindergarten/introduction/
Four Critical Areas in
1st Grade
• In Grade 1, instructional time should focus on four critical
areas:
– (1) developing understanding of addition, subtraction, and
strategies for addition and subtraction within 20;
– (2) developing understanding of whole number
relationships and place value, including grouping in tens
and ones;
– (3) developing understanding of linear measurement and
measuring lengths as iterating length units; and
– (4) reasoning about attributes of, and composing and
decomposing geometric shapes.
http://www.corestandards.org/the-standards/mathematics/grade-1/introduction/
Four Critical Areas in
2nd Grade
• In Grade 2, instructional time should focus on
four critical areas:
– (1) extending understanding of base-ten
notation
– (2) building fluency with addition and
subtraction;
– (3) using standard units of measure; and
– (4) describing and analyzing shapes.
http; ://www.corestandards.org/the-standards/mathematics/grade-2/introduction/
Four Critical Areas in
3rd Grade
• In 3rd Grade, instructional time should focus on four critical
areas:
– Developing understanding of multiplication and division
strategies for multiplication and division within 100
– Developing understanding of fractions, especially unit
fractions (fractions with numerator 1)
– Developing understanding of the structure of rectangular
arrays and of area
– Describing and analyzing two-dimensional shapes.
http://www.corestandards.org/the-standards/mathematics/grade-3/introduction/
Three Critical Areas in
4th Grade
• In 4th Grade, instructional time should focus on
three critical areas:
– Developing understanding and fluency with multi-digit multiplication,
and developing understanding of dividing to find quotients involving
multi-digit dividends.
– Developing an understanding of fraction equivalence, addition and
subtraction of fractions with like denominators, and multiplication of
fractions by whole numbers.
– Understanding that geometric figures can be analyzed and classified
based on their properties, such as having parallel sides, perpendicular
sides, particular angle measures, and symmetry.
http://www.corestandards.org/the-standards/mathematics/grade-4/introduction/
Three Critical Areas in
5th Grade
• In 5th Grade, instructional time should focus on
three critical areas:
– Developing fluency with addition and subtraction of fractions, and
developing understanding of the multiplication of fractions and of
division of fractions in limited cases.
– Extending division to 2-digit divisors, integrating decimal fractions
into the place value system and developing understanding of
operations with decimals to hundredths, and developing fluency with
whole number and decimal operations.
– Developing understanding of volume.
http://www.corestandards.org/the-standards/mathematics/grade-5/introduction/
Essential Question #1
• How will unpacking and chunking
the Mathematical Content
Standards improve my math
instruction?
Chunks/Units/Organizing Principles
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Critical Areas
There are 2-4 Critical Areas for instruction in the Introduction
for each grade level
1st Grade Critical Areas – Introduction
They bring focus to the standards at each grade by grouping
and summarizing the big ideas that educators can use to
build their curriculum and to guide instruction.
Critical Areas Activity
–The goal of this activity is to help
teachers:
Become familiar with the Critical
Areas and Content Standards
Understand chunking standards
into Critical Ideas (Big Ideas)
Directions
• In Grade-level groups, read through the Critical
Areas and their descriptions on the Introduction
page.
• Then, read each of the content standards and
mark on the recording sheet with a:
X - when a standard strongly matches a
Critical Area or
•
? - when you are not sure
•
1.OA.1. Use addition and subtraction within 20 to solve word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using objects, drawings,
and equations with a symbol for the unknown number to represent the
problem.1
3.OA.1.Interpret products of whole numbers, e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7 objects each. For example, describe a
context in which a total number of objects can be expressed as 5 × 7.
Questions to Consider
• Did every standard fall within a Critical
Area?
• Are there standards that fall within more
than one Critical Area?
• Do all standards within a cluster fall within
the same Critical Area?
What’s a Learning Goal?
BACK
Clear learning goals are statements that communicate to teachers and
students exactly what the student will understand and be able to do
at the conclusion of instruction.
• Learning goals encompass two broad categories of knowledge:
declarative and procedural.
• Declarative knowledge is student recall of information about
facts, generalizations, or principles, while procedural
knowledge involves skills, strategies, or processes.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
40
What’s a Learning Goal?
As a rule of thumb, declarative learning goals begin with:
The student will understand . . .
Procedural learning goals begin with:
The student will be able to . . .
Complex tasks may involve both declarative and procedural
knowledge. Learning goals of this nature are written as:
The student will understand ―x and be able to ―y.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
41
Learning Goals
The learning goals and the accompanying scales focus
on what the student will understand or be able to do.
The learning activities focus on enabling them to do so.
Learning Goals are the endpoint; they are not activities, assignments, or
assessments.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
42
Learning Goals
• Learning Goals target key learning at the unit or “big
picture” level.
• Learning Goals are statements that communicate to
teachers and students exactly what the student will
understand and be able to do at the conclusion of
instruction.
• Learning Goals take a standard(s) that will take
students weeks, months, or even all year to master.
• Learning goals are written with scales that guide
students toward successful mastery.
43
Scales
BACK
Scales provide a clear learning progression of what a student should
understand or be able to do. The terms scale or rubric relate to the same
concept: an explicit set of criteria used for assessing progress toward a
learning goal. A scale typically has several criteria, each focused on some
important aspect of mastering the goal. The progress points built into the
scale are appropriately sequenced, usually based on a logical order or
progression of learning or ascending levels of difficulty. The points in the
scale must directly support the learning goal. Learning activities are
needed that are directly tied to the learning goal(s) and the state
standard(s) on which the learning goal is based.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
44
Kindergarten
Learning Goal/Scale Example
See Learning Goals and Progression Scale
Course/Grade: Math Kindergarten
Looking at “chunked”
relatable standards- write into Learning Goals.
Standard(s): MACC.K.CC.1.1, MACC.K.CC.1.2, MACC.K.CC.1.3, LACC.K.SL.1.1, LACC.K.SL.1.2, LACC.K.SL.1.3, MACC.K12.MP.6.1, MACC.K12.MP.7.1,
MACC.K12.MP.8.1
Learning Goal 1: Students will be able to count forward to 100 by ones and tens from a given number and be able to write/represent numbers 0 to 20.
Essential Question(s): (Optional)
Step 4.0
In addition to Step 3.0, in-depth inferences and applications that go
beyond what was taught.
 Count forward beyond 100 by ones, fives, tens, and hundreds
from a given number
 Write numbers 0-100
 Represent numbers 0-100
 Recognize numbers 0-100
Step 3.0
(Target)
The student exhibits no major errors or omissions.
Step 2.0
The student exhibits major errors or omissions regarding the more
complex ideas and processes.
Step 1.0
The student will be able to:
 Count forward to 100 by ones and tens from a given number
 Write numbers 0 to 20
 Represent numbers 0 to 20
The student will be able to:
 Count by Ones and Tens to 50
 Recognize numbers 0-20
 Write numbers 0-20
 Represent numbers 0-20 with objects
With help, a partial understanding of some of the simpler details and
processes and some of the more complex ideas and processes.
The student will be able to:
Sample Progress Monitoring and Assessment Activities
Have students count from 103 by ones, then fives, then
tens, then 100.
 Show students numbers 0-100 on index cards and ask
them to correctly identify.
 Have students write numbers 0-100 on desk using expo or
on paper using pencil.
 Display several numbers on board (77, 14, 37, 49, 63, 22).
Have students choose 3 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 100 from 73 by ones.
 Have students count forward to 100 from 55 by tens.
 Have students write numbers 0-20 on desk using expo or
on paper using pencil.
 Display several numbers on board (3, 11, 17). Have
students choose 2 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 50 from 47 by ones.
 Have students begin at 30 and count to 50 by tens.
 Show students numbers 0-20 on index cards and ask them
to correctly identify.
 Display several numbers on board (2, 12, 18). Have
students choose 2 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 20 from 6 by ones.
 Show students numbers 11-20 on index cards and ask
them to correctly identify.
 Have students write numbers 0-10 on desk using expo or

Lesson Plans
46
Lesson Plan/Strategy Models
What are Learning Activities?
BACK
Learning activities are purposeful exercises that engage
the student with explicit content to promote mastery of the
learning goal. Simply stated, learning activities are the
tasks you have students do during school time. Learning
activities are not the same as learning goals. While a
learning goal is where the student needs to be at the end of
a lesson or unit, much like a destination, learning activities
are the vehicles and paths the student uses to get there.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
48
How to select learning activities?
Learning activities are deliberately planned and require the student to be
engaged at a level of cognitive demand that is consistent with the learning goal.
An activity may be fun or engaging but lack the rigor necessary to meet the
standard. Teachers need to be cognizant of the difference between tasks that are
difficult due to content and those that are difficult due to the demand placed on
the thinking skills of an individual student. In short, only select activities that
support the learning goal and engage the learner at an appropriately demanding
level. Some learning activities may focus on a specific learning goal or stage of
progression. Other learning activities may support more than one learning goal or
more than one standard.
http://learninggoals.nefec.org/learning-goals/module/media/modules/Complete%20Module.pdf
49
Targeting Student Success
We are moving from thinking only about
what we want to do and need to accomplish as
teachers to thinking about what the student the end user of our design - will need to do to
achieve understanding.
Wiggins, Grant & McTighe, Jay (1998) Understanding by Design (p. 116). Alexandra, VA:
Association for Supervision and Curriculum Development
50
Kindergarten
Learning Activities/Assessment Example
Looking at “Sample Progress Monitoring and Assessment” ActivitiesCourse/Grade: Math Kindergarten
Standard(s): MACC.K.CC.1.1, MACC.K.CC.1.2, MACC.K.CC.1.3, LACC.K.SL.1.1, LACC.K.SL.1.2, LACC.K.SL.1.3, MACC.K12.MP.6.1, MACC.K12.MP.7.1,
MACC.K12.MP.8.1
Learning Goal 1: Students will be able to count forward to 100 by ones and tens from a given number and be able to write/represent numbers 0 to 20.
Essential Question(s): (Optional)
Step 4.0
In addition to Step 3.0, in-depth inferences and applications that go
beyond what was taught.
 Count forward beyond 100 by ones, fives, tens, and hundreds
from a given number
 Write numbers 0-100
 Represent numbers 0-100
 Recognize numbers 0-100
Step 3.0
(Target)
The student exhibits no major errors or omissions.
Step 2.0
The student exhibits major errors or omissions regarding the more
complex ideas and processes.
Step 1.0
The student will be able to:
 Count forward to 100 by ones and tens from a given number
 Write numbers 0 to 20
 Represent numbers 0 to 20
The student will be able to:
 Count by Ones and Tens to 50
 Recognize numbers 0-20
 Write numbers 0-20
 Represent numbers 0-20 with objects
With help, a partial understanding of some of the simpler details and
processes and some of the more complex ideas and processes.
The student will be able to:
Sample Progress Monitoring and Assessment Activities
Have students count from 103 by ones, then fives, then
tens, then 100.
 Show students numbers 0-100 on index cards and ask
them to correctly identify.
 Have students write numbers 0-100 on desk using expo or
on paper using pencil.
 Display several numbers on board (77, 14, 37, 49, 63, 22).
Have students choose 3 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 100 from 73 by ones.
 Have students count forward to 100 from 55 by tens.
 Have students write numbers 0-20 on desk using expo or
on paper using pencil.
 Display several numbers on board (3, 11, 17). Have
students choose 2 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 50 from 47 by ones.
 Have students begin at 30 and count to 50 by tens.
 Show students numbers 0-20 on index cards and ask them
to correctly identify.
 Display several numbers on board (2, 12, 18). Have
students choose 2 numbers to represent. (They may
choose how they wish to represent, eg. Drawing, using
counters, etc.
 Have students count forward to 20 from 6 by ones.
 Show students numbers 11-20 on index cards and ask
them to correctly identify.
 Have students write numbers 0-10 on desk using expo or

Differentiated Instruction
BACK
In all classrooms, teachers deal with at least three curricular elements:
(1) content – input, what students learn
(2) process – how students go about making sense of ideas and
information
(3) product – output, how students demonstrate what they have
learned
By differentiating these three elements, teachers offer different
approaches to what students learn, how they learn it, and how they
demonstrate what they’ve learned. What these different approaches
have in common, however; is that they are crafted to encourage
substantial growth in all students.
Tomlinson, Carol Ann (2001) How to Differentiate Instruction in Mixed Ability Classrooms, 2nd Edition (pgs. 4-5). Alexandra, VA: Association for
Supervision and Curriculum Development
52
Classroom Norms
•
•
•
•
Establishing the classroom culture
Physical environment
Collaborative spaces
Classroom management
Assessment
54
Beginning with the end in mind
The backward design approach encourages us
to think about a unit or course in terms of the
collected assessment evidence needed to
document and validate that the desired
learning has been achieved, so that the course
is not just content covered or a series of
learning activities.
•Wiggins, Grant & McTighe, Jay (1998) Understanding by Design (p. 12). Alexandra, VA: Association for Supervision and Curriculum Development
55
Formative Assessments
BACK
• Formative assessment is a process used by
teachers and students during instruction that
provides feedback to adjust ongoing teaching and
learning to improve students' achievement of
intended instructional outcomes. Formative
assessments are questions, tools, and processes
that are embedded in instruction. They are used
by teachers and students to provide timely
feedback for purposes of adjusting instruction
and/or learning efforts to improve learning.
“The Common Language Project.” The Florida School Leaders Project.
56
BACK
Interim Assessments
• An interim assessment is an assessment that is
given at regular and specified intervals throughout
the school year, is designed to evaluate students'
knowledge and skills relative to a specific set of
academic standards, and produces results that
can be aggregated (e.g., by course, grade level,
school, or LEA) in order to inform teachers and
administrators at the student, classroom, school,
and LEA levels.
“The Common Language Project.” The Florida School Leaders Project.
57
BACK
Summative Assessments or
Measures
• Assessments typically administered near
the end of the school year or academic
term to give an overall perspective of the
effectiveness of the instructional program.
They typically are cumulative in that they
cover content from previous interim
assessments and the term or year.
“The Common Language Project.” The Florida School Leaders Project.
58
Assessments
• Differences between formative,
summative, interim
• PARCC prototype
Resources
•
•
•
•
•
Cpalms
Educational Impact
The Teaching Channel
PARCC Website
Bay District CCSS Website
Resources