1. No category

“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.
www.flstandards.org
“The new access points in
mathematics identify the most salient
grade-level, core academic content
for students with a significant
cognitive disability.”
IMPORTANT TO NOTE:
“These access points are NOT ‘extensions’
to the standards, but rather they illustrate
the necessary core content, knowledge,
and skills that students with a significant
cognitive disability need at each grade to
promote success in the next grade.”
Bureau of Exceptional Education and Student Services
Spring 2014
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
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.
16
Mathematics Progressions Project
http://ime.math.arizona.edu/progressions/s Project
17
 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 [email protected]
http://www.katm.org
Mathematics Teaching in the Middle School
● Vol. 14, No. 8, April 2009
Proficiency Scale
6th
Instructional Strategies for
6.EE.5 - 8
In order for students to understand equations:
The skill of solving an equation must be developed conceptually
before it is developed procedurally.
 Students should think about what numbers could be a solution BEFORE
solving the equation.
 Experience is needed solving equations with a single solution, as well as
with inequalities having multiple solutions.
 Conceptual understanding of positive and negative numbers and
operation rules is introduced in grade 6.
 Students need to practice the process of translating between
mathematical phrases and symbolic notation. (ie. write equations
from situations/stories, write a story that references a given
equation/inequality)
Explanations and Examples for 6.EE.7
Students create and solve equations that are based on real world
situations. It may be beneficial for students to draw pictures that illustrate
the equation in problem situations. Solving equations using reasoning and
prior knowledge should be required of students in order to allow them to
develop effective strategies.
Learning
Progression
Document
“Expressions and
Equations”
Grades 6-8, pg. 7
As word problems grow more complex in grades 6
and 7, analogous arithmetical and algebraic solutions
show the connection between the procedures of
solving equations and the reasoning behind those
procedures.
7th
It is appropriate to expect students to show the steps in their work.
Students should be able to explain their thinking using the correct terminology for
the properties and operations. Continue to build on students’ understanding and
application of writing and solving one-step equations from a problem situation to
multi-step problem situations.
Progression Document
“Expressions and Equations Grades 6-8”
pgs. 13-14
Instructional Strategies for
8.EE.7 - 8
 Pairing contextual situations with equation solving allows
students to connect mathematical analysis with real-life events.
 Experiences should move through the stages of concrete,
conceptual and algebraic/abstract.
 System-solving in Grade 8 should include estimating solutions
graphically, solving using substitution, and solving using
elimination.
Progression Document
“Expressions and Equations Grades 6-8"
pg. 14
Write an equation that represent the growth rate of
Plant A and Plant B.
Solution:
Plant A H = 2W + 4
Plant B H = 4W + 2
• At which week will the plants have the same height?
Solution:
The plants have the same height after one week.
Plant A: H = 2W + 4 Plant B: H = 4W + 2
Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2
Plant A: H = 6 Plant B: H = 6
After one week, the height of Plant A and Plant B are
both 6 inches.
Two domains in middle school are important
in preparing students for Algebra in high school.
 Number System (NS) – Students become fluent in finding and using
the properties of operations to find the values of numerical
expressions. (Began as Number Operations with Fractions, NF grades 3-5.)
 Expressions and Equations (EE) – Students extend their use of
these properties to linear equations and expressions with letters.
(Began as Operations and Algebraic Thinking, OA grades K-5.)
Algebra: Reasoning with Equations and Inequalities (A-REI.1-12)
• Understand solving equations as a process of reasoning and explain the reasoning
• Solve equations and inequalities in one variable
• Solve systems of equations
• Represent and solve equations and inequalities graphically
Proficiency Scale
HS
Scope and Sequence Curriculum Blueprints
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 tools38
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.
Content Complexity
Florida Standards: Definitions
July 2014
“Content complexity ratings reflect the level of
cognitive demand that standards and corresponding
instruction impose upon a student. The evolution of
Florida’s standards and assessment alignment is illustrative
of the state’s ongoing effort to support the development of
a curriculum and assessment system that exemplifies the
qualities of focus, coherence, and rigor embodied by the
new FL standards.”
40
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
41
else – Make Judgments – WRITE!
MAFS + DOK = Math Standards & Math Practices
Standards for Mathematical Practice
Mathematics Assessment Project
http://map.mathshell.org
“I would say that CCs are
collaborative lessons that are built
around one concept and are
structured in ways to allow an initial
entry point that every student can
access in some way. They really allow
a group of students to explore their
understanding of the concept.”
http://mathpractices.edc.org/
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
“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
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?
Middle
School
MEA
LESSON
TITLES
6th Grade - The Best Domestic Car
MAFS.6.RP.1.1
MAFS.6.RP.1.2
7th Grade - Run For Your Life
MAFS.7.NS.1.1
MAFS.7.NS.1.3
mea.cpalms.org
8th Grade -
Pack It Up
MAFS.8.G.3.9
CollegeReview.com
High School
MAFS.912.A-CED.1.1
MAFS.912.S-ID.1.1
MEA
LESSON
TITLES
Plants versus
Pollutants
MAFS.912.F-BF.1.1
MAFS.912.F-BF.1.2
MAFS.912.S-ID.2.5
MAFS.912.S-IC.1.2
MAFS.912.S-IC.2.6
Shopping for a Home Mortgage Loan
Which Brand of
Chocolate Chip Cookie
Would You Buy?
MAFS.912.S-IC.2.6
MAFS.912.N-Q.1.1
MA.912.F.3.9
MA.912.F.3.10
MA.912.F.3.11
MA.912.F.3.12
MA.912.F.3.13
MA.912.F.3.14
MA.912.F.3.17
mea.cpalms.org
MAFS.912.N-Q.1.3
"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