“There is an exceptionally strong relationship between,, and (key aspects of professional learning communities) and.” “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.” “The demands of the 21 st century has created a that focus on developing human capital and creativity in their teachers to prepare them for changing the educational landscape.” “The demands of the 21 st 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.” 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.

3 “I lift, You grab.... Was that concept just a little too complex for you, Carl?” … is a group of people working interdependently toward a common goal.

Common Core State Standards CCSSM vs. Mathematics Florida State Standards MAFS Cognitive Complexity of the Content Standards did NOT change.  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. “The new Florida Math Standards ask us ALL to… teach  … rethink what it means to teach mathematics, understand  … understand mathematics, learn  … and to learn mathematics.” Sherry Fraser Faculty member of the Marilyn Burns Education Associates MAFSMAFS Compared to CCSSM New and Deleted Standards

Vol. 108, No. 2, September 2014 NCTM, MATHEMATICS TEACHER

Why Teachers’ Mathematics Content Knowledge Matters 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…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.

The Instructional Core Principle #1: 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: Principle #2: If you change one element of the instructional core, you have to change the other two..

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 8.EE.7-8 Analyze and solve linear equations and pairs of simultaneous linear equations. 7.EE.3-4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 6.EE.5-8 Reason about and solve one-variable equations and inequalities. 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. Alignment in Context: Neighboring Grades and Progressions 13 “You're constantly reusing the same concepts in the growth of the staircase, leading to algebraic ways of thinking that you begin to master linear algebra in grade 8 and go on to a wider set of algebra in the high school.” "Bringing the Common Core to Life" David Coleman · Founder, Student Achievement Partners

Mathematics Progressions Project Progression Project 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

KG

Instructional Strategies for K.OA. 1-5

RepresentationalConcrete Abstract

Kg Learning Progressions Document, “Operations and Algebraic Thinking”, Grades K-5, pg. 9 Master in Grade 2

Explanations and Examples for 1.OA.7 and 1.OA.8 MAFS.1.OA.2.3 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 st

Instructional Strategies for 1.OA.7 Taken from CCFlipbook with Information compiled by Melisa Hancock Think about how to explain the traditional… FACT FAMILY. 1st

Learning Progression Document “Operations and Algebraic Thinking” Grades K-5, pg. 16

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.

4 th

6.EE.1 5 th

Example of Using Writing to explain thinking… 5 th

H.Wu Professor of Mathematics Professor of Mathematics University of California, Berkeley University of California, Berkeley “…when the ramp collapses, the students aren’t able to scale a gentle slope, but rather try and climb a wall at 90 degrees.” “In algebra, generality and abstraction are expressed in symbolic notation. Fluency with symbolic manipulation is an integral part of algebra proficiency.” “Is it reasonable to expect a person to run well if his walk is wobbly?” “Early grades algebraic thinking approach gives focus on gaining conceptual understanding of abstract symbols.” Teachers need to be very careful to extend their own knowledge of what a fraction is (IT IS NOT AN ACTIVITY), as well as how to approach teaching addition and subtraction of fractions with their students. The definitions and strategies that are impressed upon the 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 is introduced in the early grades and no matter how worthwhile such exercises might be, the failure rate in algebra will continue to be high UNLESS WE RADICALLY REVAMP THE TEACHING OF FRACTIONS AND DECIMALS.” H.Wu, Univ. of Calif., Berkeley

Fraction Progression Online Module 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

39 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 tools 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 41  A scale of () based on the research of Norman Webb (1997).  A scale of cognitive demand (thinking) based on the research of Norman Webb (1997).  Categorizes assessment tasks by different levels of required of a student in order for them to successfully,, and with the task.  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 () intended by the standards, curricular activities, and assessment tasks.  Key tool for educators so that they can analyze the cognitive demand (complexity) intended by the standards, curricular activities, and assessment tasks.

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 else – Make Judgments – WRITE! 42

 Grades 3 Florida Standards Assessment Test Item Specifications Grades 3 Florida Standards Assessment  Grades 4 Florida Standards Assessment Test Item Specifications Grades 4 Florida Standards Assessment  Grades 5 Florida Standards Assessment Test Item Specifications Grades 5 Florida Standards Assessment  Grades 6 Florida Standards Assessment Test Item Specifications Grades 6 Florida Standards Assessment  Grades 7 Florida Standards Assessment Test Item Specifications Grades 7 Florida Standards Assessment  Grades 8 Florida Standards Assessment Test Item Specifications Grades 8 Florida Standards Assessment  Algebra 1 EOC Florida Standards Assessment Test Item Specs Algebra 1 EOC Florida Standards  Geometry EOC Florida Standards Assessment Test Item Specs Geometry EOC Florida Standards  Algebra 2 EOC Florida Standards Assessment Test Item Specs Algebra 2 EOC Florida Standards  Test Design Summary 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)

“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.

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.

Benefit #1Benefit #2 Benefit #3Benefit #4 “Students write to keep ongoing records about what they’re doing and learning.” “Students write in order to solve math problems.” “Students write to explain mathematical ideas.” “Students write to describe learning processes.”

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.

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.

Model Eliciting Activities MEAs are a collection of realistic problem-solving activities aligned to multiple subject-area standards. Are you familiar with these “ready–to–use” activities?

Kg – We Love Pets! MAFS.K.CC.2.4 We Love Pets! 1 st Grade – Flower Power Flower Company Flower Power Flower Company MAFS.1.OA.1.1 MAFS.1.OA.3.5 MAFS.1.NBT.1.1 MAFS.1.MD nd Grade – Carnival Carnival MAFS.2.NBT.1.4 MAFS.2.NBT.2.5 MEA LESSON TITLES PrimaryGrades mea.cpalms.org

3 rd Grade - Spin Beyblades Spin Beyblades MAFS.3.OA.2.6 MAFS.3.OA th Grade - Donuts and Decimals Donuts and Decimals MAFS.4.NF th Grade - X-treme Roller Coasters X-treme Roller Coasters MAFS.5.NBT.1.2 MAFS.5.NBT.1.3 MAFS.5.MD.1.1 MEA LESSON TITLES Intermediate Grades Grades mea.cpalms.org

"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 Alan Cohen