“The demands of the 21st century has created a
need for schools to become learning organizations
that focus on developing human capital and
creativity in their teachers to prepare them for
changing the educational landscape.”
“There is an exceptionally strong relationship
between communal learning, collegiality, and
collective action (key aspects of professional
learning communities) and changes in teacher
practice and increases in student learning.”
1
Learning Goals
Upon completion of this training, participants will…
 have increased their knowledge of the new Florida State Standards for
Mathematics (MAFS).
 recognize how the coherence of content standards within and across
the grades supports the learning progressions of students.
 encourage the integration of student writing in mathematics in order
to increase reasoning and problem solving skills.
 Identify resources that will provide assistance with implementation of
MAFS.
 be equipped to develop and facilitate Professional Learning
Communities (PLCs) at the school site in order to encourage a
continuation of collegial learning that supports the advancement of
student learning.
… is a group of people
working
interdependently toward
a common goal.
“I lift, You grab . . . . Was that concept
just a little too complex for you, Carl?”
3
Common Core State Standards
“The new Florida Math Standards ask us ALL to…
CCSSM
… rethink what it means to teach mathematics,
vs.
… understand
mathematics,
Mathematics
Florida State Standards
… and to learn mathematics.”
MAFS
Sherry Fraser
Faculty member of the Marilyn Burns Education Associates
 Cognitive Complexity of the Content Standards did NOT change.
 Amended, Deleted, Added Standards
 Standards for Mathematical Practice (SMP) remain for all grades.
 LITERACY embedded across ALL CONTENT AREAS.
MAFS Compared to CCSSM New and
Deleted Standards
www.flstandards.org
Vol. 108, No. 2, September 2014
NCTM, MATHEMATICS TEACHER
Why Teachers’ Mathematics Content
Knowledge Matters:
“Professional Learning Opportunities for teachers of
mathematics have increasingly focused on deepening
teachers’ content knowledge. Based on research studies…
Teachers’ content knowledge made a difference in their
professional practice and their students’ achievement.
 Teachers’ depth of knowledge meant problems were
presented in familiar contexts to the children and the
teacher linked them to activities they had previously
completed.
Teachers with stronger content knowledge were more likely
to respond to students’ mathematical ideas appropriately,
and they made fewer mathematical or language errors
during instruction.
Principle #1: Increases in
student learning occur only
as a consequence of
improvements in the level
of content, teachers’
knowledge and skill, and
student engagement.
Principle #2: If you
change one element of
the instructional core,
you have to change the
other two..
The Instructional Core
Alignment in Context:
Neighboring Grades and Progressions
Algebra: Reasoning with Equations and Inequalities (A-REI.1-12)
• Understand
solving equations
as a process
of reasoning
and explain
the reasoning
“You're
constantly
reusing
the same
concepts
in
• Solve equations and inequalities in one variable
of the staircase, leading to algebraic ways
•the
Solvegrowth
systems of equations
• Represent and solve equations and inequalities graphically
of thinking that you begin to master linear algebra in
Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.7-8
grade 8 and go on to a wider set of algebra in the high
Solve real-life and mathematical problems using numerical and algebraic
7.EE.3-4
school.”
expressions and equations.
6.EE.5-8
"Bringing the Common Core to Life"
Reason about and solve one-variable equations and inequalities.
David Coleman · Founder, Student Achievement Partners
5.OA.1-2
Write and interpret numerical expressions.
4.OA.1-3
Use the four operations with whole numbers to solve problems.
3.OA.1-4
Represent and solve problems involving multiplication and division.
2.OA.1
Represent and solve problems involving addition and subtraction.
1.OA.7-8
Work with addition and subtraction equations.
K.OA.1-5
Understand addition as putting together and adding to, and understand
subtraction as taking apart and taking from.
13
Mathematics Progressions Project
Progression
http://ime.math.arizona.edu/progressions/s Project
14
 Year at a Glance Nine Weeks Pacing
 Organized by Units of Instruction (related standards)
 Essential Questions and Vocabulary
 Teaching/Learning Goal(s) and Scales
 Rubric with Student Learning Target Details
 Progress Monitoring and Assessment Activities
 MFAS (Cpalms Formative Assessments)
 Unpacked Content Standards
 Unit/Critical Area
 Learning Objectives (Declarative and Procedural)
 DOK Level
 SMP
 Common Misconceptions
Mathematics Standards Flip Books
For questions or comments about the flipbooks please contact Melisa Hancock at
melisa@ksu.edu
http://www.katm.org
KG
Instructional Strategies for K.OA. 1-5
Concrete
Representational
Abstract
Learning
Progressions
Document,
“Operations and
Algebraic
Thinking”,
Grades K-5, pg. 9
Kg
Master in Grade 2
Explanations and Examples for 1.OA.7 and 1.OA.8
Students would have had prior learning within the grade understanding the
following priorities. MAFS.1.OA.2.3
1st
1st
Instructional Strategies for 1.OA.7
Think about how to explain the traditional…
FACT FAMILY.
Taken from CCFlipbook with Information compiled by Melisa Hancock melisa@ksu.edu
Learning
Progression
Document
“Operations
and
Algebraic
Thinking”
Grades K-5,
pg. 16
Explanations and Examples for
2.OA.1 and 2.OA.1a
Explanations and Examples for
2.OA.1 and 2.OA.1a
Developing Fact Fluency:
Phases of Understanding
Common Multiplication and Division Situations
Instructional Strategies (3.OA.1-4)
 Provide various contexts and tasks so that students will have more
opportunity to develop and use thinking strategies to support and
reinforce learning of basic mult. and div. facts.
 Encourage students to solve problems in different ways to show
the same idea and be able to explain their thinking verbally AND in
written expression.
Apply skills to solve word problems.
4th
4th
5th
6.EE.1
5th
Example of Using Writing to explain
thinking…
5th
H.Wu
Professor of Mathematics
University of California, Berkeley
Teachers need to be very careful to extend their own knowledge
“…when the ramp collapses, the
of what
a fraction is (IT IS NOT AN ACTIVITY),
well as how
to
“Is it as
reasonable
to expect
students aren’t able to scale a
approach
teaching
addition
and subtraction
of fractions
withiftheir
a person
to run well
his
gentle slope,
but rather
try and
walkare
is wobbly?”
students.
Theatdefinitions
impressed upon the
climb a wall
90 degrees.”and strategies that
students needs to be accurate and a continuum from what they
already know about whole numbers and their operations.
“No matter how much algebraic thinking“Early
is introduced
in the
early
grades
algebraic
thinking
algebra, generality and
grades“Inand
no matter how worthwhile such
exercises
might
be, the
approach
gives focus
on gaining
abstraction are expressed in symbolic
failure
rate Fluency
in algebra
will continue to be
high UNLESS
WE RADICALLY
conceptual
understanding
of
notation.
with symbolic
abstract
symbols.”
REVAMP
THE TEACHING
OFpart
FRACTIONS
AND
DECIMALS.”
manipulation
is an integral
of
algebra proficiency.”
H.Wu, Univ. of Calif., Berkeley
Fraction Progression Online Module
http://www.cgcs.org/site/Default.aspx?PageID=338
The Council of the Great City Schools, University of Arizona’s Institute for
Mathematics and Education (IM&E), and Achieve collaborated on the development of
an online professional development module to deepen understanding of the Fractions
Progression - a critical focus in the standards. This online, interactive module is
available free of charge to all users and takes about 60 minutes to complete.
The module features:
 Brief video segments that explain fraction concepts
 Illustrative tasks associated with the progression
 Built in, interactive checks for understanding throughout the module
 Supporting material that can be downloaded and printed
https://www.illustrativemathematics.org/fractions_progression
https://mathsolutions.wistia.com/projects/r4bjpdzb31
https://www.illustrativemathematics.org/
Rigor is defined as a process where students:
 Approach mathematics with a disposition to accept challenge and apply
effort.
 Engage in mathematical work that promotes deep knowledge of content,
analytical reasoning, and use of appropriate tools; and
 Emerge fluent in the language of mathematics, proficient with the tools39
of mathematics, and empowered as mathematical thinkers.
Focus on complexity of content
standards in order to successfully
complete an assessment or task.
The outcome (product) is the focus of
the depth of understanding.
RIGOR IS ABOUT COMPLEXITY
What is Depth-of-Knowledge?
DOK
 A scale of cognitive demand (thinking) based on the
research of Norman Webb (1997).
 Categorizes assessment tasks by different levels of
cognitive expectation required of a student in order
for them to successfully understand, think about, and
interact with the task.
 Key tool for educators so that they can analyze the
cognitive demand (complexity) intended by the
standards, curricular activities, and assessment
tasks.
41
Just the Facts – Low Level Processing
“Familiar” – Procedures & Routines, 2 + Steps
Real-World Problem – Develop Plan - Justification
Take what you learned and extend it to something
42
else – Make Judgments – WRITE!
http://www.fsassessments.org

Grades 3 Florida Standards Assessment
Test Item Specifications

Grades 4 Florida Standards Assessment
Test Item Specifications

Grades 5 Florida Standards Assessment
Test Item Specifications

Grades 6 Florida Standards Assessment
Test Item Specifications

Grades 7 Florida Standards Assessment
Test Item Specifications

Grades 8 Florida Standards Assessment
Test Item Specifications

Algebra 1 EOC Florida Standards
Assessment Test Item Specs

Geometry EOC Florida Standards
Assessment Test Item Specs

Algebra 2 EOC Florida Standards
Assessment Test Item Specs

Test Design Summary
MAFS + DOK = Math Standards & Math Practices
Standards for Mathematical Practice
Linking the Mathematical Practices with the Content Standards
Mathematical Practices Learning Community Templates
Tasks that Align with the Mathematical Practices
Resources to Support the Implementation of the
Standards for Mathematical Practice (SMP)
http://files.eric.ed.gov/fulltext/ED544239.pdf
“Writing in mathematics gives me a window into my
students’ thoughts that I don’t normally get when
they just compute problems. It shows me their
roadblocks, and it also gives me, as a teacher, a road
map.”
-Maggie Johnston
9th grade mathematics teacher, Denver, Colorado
“Using Writing in Mathematics to Deepen Student Learning”
by Vicki Urquhart
Why are we writing in math class?
David Pugalee (2005), who researches the relationship
between language and mathematics learning, asserts
that writing supports reasoning and problem solving
and helps students internalize the characteristics of
effective communication. He suggests that teachers
read student writing for evidence of logical conclusions,
justification of answers and processes, and the use of
facts to explain their thinking.
http://files.eric.ed.gov/fulltext/ED544239.pdf
Integrating writing into the mathematics
classroom
• Writing can provide valuable insight for teachers into their
students’ mastery of math concepts.
• Writing often reveals gaps in learning and misconceptions
which can help inform teachers for instructional planning and
intervention strategies.
• Communicating about mathematics through writing helps
strengthen student learning which can build conceptual
understanding.
• Students are able to clarify their thinking about a math topic
through writing.
• Integrating writing into the curriculum can be easy with a little
planning.
“Students write to keep
ongoing records about
what they’re doing and
learning.”
“Students write in order
to solve math problems.”
Benefit #1
Benefit #2
“Students write to
explain mathematical
ideas.”
Benefit #3
“Students write to
describe learning
processes.”
Benefit #4
http://www.readwritethink.org
Grade Levels: K-2
“Going on a Shape Hunt: Integrating Math and Literacy”
•
Students are introduced to the idea of shapes through a read-aloud session
with an appropriate book. They then use models to learn the names of shapes,
work together and individually to locate shapes in their real-world
environment, practice spelling out the names of shapes they locate, and
reflect in writing on the process. This lesson provides opportunities to engage
students using many different learning modalities.
Grade Levels: 1-2
“Draw a Math Story: From the Concrete to the Symbolic”
•
identify and use key mathematical terms in discussion and in writing.
•
draw a series of pictures telling a sequential story which depicts objects being
added or taken away.
•
tell and write a sequential story which corresponds to their drawings.
•
state or write equations that correspond to their stories.
http://www.readwritethink.org
Grades Levels 3-5
“Talking, Writing, and Reasoning: Making Thinking Visible
with Math Journals”
Getting Started with Math Journals
• Sharing a good math-related children’s book or exploring
puzzles – such as the Magic Triangle are good ways to
begin working with Math Journals.
• At the beginning stages of working with Math Journals, it
helps students if they are presented with an open-ended
prompt instead of having to develop an idea on their own.
This kind of prompt is best for revealing students’ thinking,
too.
• Teachers should collect and view journal entries and make
written comments to encourage the written dialogue
between the student. Teachers can ask specific questions.
Tasks to build literacy through mathematics and science content
Inspired and informed by the work of the Literacy Design Collaborative, the
Dana Center has created mathematics- and science-focused template tasks to
explicitly connect core mathematics and science content to relevant literacy
standards for students in grades 7–9. The mathematics template tasks were
built from the Common Core State Standards for Mathematics Standards for
Mathematical Practice.
MEAs are a collection of realistic problem-solving
activities aligned to multiple subject-area standards.
Model
Eliciting
Activities
Are you familiar with these “ready–to–use” activities?
Primary
Grades
MEA
LESSON
TITLES
Kg –
We Love Pets!
MAFS.K.CC.2.4
Flower Power
Flower Company
1st Grade –
MAFS.1.OA.1.1
MAFS.1.OA.3.5
MAFS.1.NBT.1.1
MAFS.1.MD.3.4
mea.cpalms.org
2nd Grade –
Carnival
MAFS.2.NBT.1.4
MAFS.2.NBT.2.5
Intermediate
Grades
MEA
LESSON
TITLES
3rd Grade - Spin Beyblades
MAFS.3.OA.2.6
MAFS.3.OA.3.7
4th Grade - Donuts and Decimals
MAFS.4.NF.3.6
5th Grade - X-treme Roller Coasters
mea.cpalms.org
MAFS.5.NBT.1.2
MAFS.5.NBT.1.3
MAFS.5.MD.1.1
"It takes a lot of courage
to release the familiar and seemingly secure,
and to embrace the new. But there is no real
security in what is no longer meaningful.
There is more security in the adventurous and
exciting, for in movement there is life,
and in change there is power.“
Alan Cohen