Module 6A for Elementary Teachers

Module 6A for Elementary Teachers
Public Consulting Group 4/20/2017 Module 6A for Elementary Teachers Florida Standards for Mathematics: Focus on Content Standards Provide welcome to everyone. Give everyone an overview of the facility and where the restrooms are located. Set up the “Parking Lot” on a piece of chart paper so that participants have a place to post questions that may not be answered in a particular section. Explain that the questions posted will be answered throughout the day. Also, hang a piece of chart paper with the heading “Ideas”. This is a spot that participants can use to share ideas that they have found. Let participants know that all ideas will be compiled and shared after the session. Allow 15 minutes total for the introductory slides, #1-8 and the pre-assessment, #9.

Professional Development Session Alignment Set 1
Data Use Governing Board Data Use ELA Math School Leaders Data Use ELA Math Teachers This slide allows participants to see how the professional development fits together. Point out how the sessions on data and Florida Standards will provide teacher leaders, school administrators, and governing board members with many opportunities to deepen their understanding of the Florida Standards and provide strategies to ensure that participants see the connection between data use and the new standards and assessments that are being implemented. Leadership Teams Session 1 Session 2 Module 6 Florida Standards Math Module 7 ELA & Data Use

Professional Development Session Alignment Set 2
Governing Board Florida Standards Assessments Data Analysis VAM School Leaders Data Use ELA Math Data & ELA Data & Math Teachers In Year 2, there will be many more opportunities for the teachers and Leadership Teams to deepen their understanding and connect data use to their implementation of the Florida Standards. The Leadership Teams will also have the ability to build capacity, devise a Florida Standards Implementation Plan, and monitor implementation through the multi-metric monitoring system. Leadership Teams Session 3 Session 4 Session 5 Session 6 Module 6 Florida Standards Math Module 7 ELA & Data Use Module 8 Math & Data Use Module 5 Florida Standards ELA

You Are Here Module 2 ELA Module 1 Data Use Module 4 Module 3 Math
ELA & Data Use Module 8 Math & Data Use Module 5 ELA This slide allows participants to see how the PD fits together over the full project. They will see how the sessions on data and the Florida Standards will flow together to provide them with many opportunities to deepen their understanding of the Florida Standards in ELA and Math, as well as providing strategies to ensure that the participants see the connection between data use and the new standards and assessments that are being implemented.

8 Components of Full Florida Standards Implementation
This graphic shows eight components that describe what charter school educators need to consider as they move toward full Florida Standards implementation. Note the word “alignment” – the key message of the graphic is that all of these need to be aligned with the Florida Standards in the areas of ELA, Mathematics and Content Literacy. The four inner components are Curriculum Alignment, Instructional Materials Alignment, Instructional Practices Alignment, and Assessment Alignment. Without them, teaching and learning will NOT be Florida Standards-aligned. The four outer components are Data Use Alignment, Professional Development Alignment, Student Support Alignment and Resource, Policy and Procedures Alignment. When these are in place and aligned to the Florida Standards, they will support continuous improvement of teaching and learning. All of the professional development sessions and charter school leadership team sessions are aligned with this representation of full Florida Standards implementation, as are all of the tools the charter teams will use to monitor progress toward Florida Standards implementation as part of the Multi-Metric Monitoring System. Point out the areas highlighted in yellow; Instructional Practices Alignment, Instructional Materials Alignment, and Curriculum Alignment; and explain that these are the areas of focus for this session.

Focus on Content Standards Outcomes
Public Consulting Group 4/20/2017 Focus on Content Standards Outcomes Learn more about the Practice Standards Examine the language and structure of the Florida Standards for Math Content Create and solve standards-based tasks Observe Florida Standards for Math-aligned instruction Share implementation successes and challenges and plan next steps Summarize the outcomes for the day, sharing what you hope to accomplish throughout the full day session. Explain that the session will include an in-depth look at the progression of content across the different domains of the content standards, will examine how the Content and Practice Standards work together, and how rigorous tasks can be used to teach these standards at a high level for all students.

Public Consulting Group
4/20/2017 Today’s Agenda Welcome and Introductions Pre-Assessment Sharing Implementation Experiences The Language of the Content Standards The Progression of Mathematical Concepts Lunch Meeting the Expectations of the Content Standards by Teaching with High Level Tasks Teaching the Content Standards Through Problem Solving Next Steps Post-Assessment Wrap Up Review the agenda letting participants know that this is the pathway they will travel in order to accomplish the outcomes discussed earlier. Note that in addition to the one hour break for lunch there will be a 15 minute morning break. Emphasize the importance of coming back from breaks on time to ensure enough time to complete all the work of the day. Let them know that there is a separate copy of the agenda in addition to the one in their handouts to follow the day’s activities and use for proof of attendance, if required by their school.

4/20/2017 Introductory Activity Pre-Assessment This will be a short self-assessment, which is in the Participant Guide on page 3. It will assess where the teacher leaders are now with understanding and implementing the practice and content standards of the Florida Standards for Math. Explain that this is a self-assessment for them to reflect on where they are now with respect to the content of the day. Further explain that they will complete the same assessment at the end of the session to reflect on what they learned. The assessments will not be collected, they are for self-reflection. Guide Page 3

Sharing Implementation Experiences
Public Consulting Group 4/20/2017 Section 1 Sharing Implementation Experiences The goal of Section 1 is to briefly review the fundamentals of the Florida Standards for Math and the Practice Standards, and then have participants share their experiences thus far with implementing the Practice Standards. As participants work and discuss, a list of positive highlights, challenges, and lessons learned will be captured and summarized on chart paper. Capturing the positive highlights will allow the group to see and hear ideas that other participants are using to successfully implement the Practice Standards. Capturing the challenges and lessons learned will allow you, the facilitator, to determine what connections will need to be made during the discussion of the Content Standards so that participants who are finding the implementation challenging will have additional strategies that they can take back to their classroom to successfully implement both the Practice and Content Standards. Total Time on Section 1: 25 Minutes Materials Needed: Chart paper: 1 piece labeled Positive Highlights, 1 piece labeled Challenges, and 1 piece labeled Lessons Learned Markers and tape Handouts: “Moving Forward with the Practices” and “New Ideas for Implementing the Florida Standards for Math Practice” Mathematics Handout: Standards for Mathematical Practice (on tables for reference) Section 1 at a Glance Facilitator briefly reviews the three fundamentals of mathematics that are the foundation of the Florida Standards for Math: Focus, Coherence, and Rigor; and then reviews the 8 Practice Standards. (3 minutes) Each participant discusses their experiences implementing the Practice Standards, presenting one positive highlight, one continuing challenge, and one lesson learned to their table group. Each group will determine two positive highlights, one challenge, and one lesson learned that they will present to the larger group. Participants can record notes on the discussion on page 5 in the Participant Guide. (10 minutes) Table groups present their positive highlights, challenges, and lessons learned to the larger group. (5 minutes) Facilitator summarizes responses charted and wraps up activity. (2 minutes) Larger group provides final thoughts and possible solutions to common challenges. (3 minutes) Participants record “New Ideas” generated during the sharing of experiences implementing the Florida Standards for Math Practice on page 6 in the Participant Guide. (2 minutes)

Instructional Shifts for Mathematics
Public Consulting Group 4/20/2017 Instructional Shifts for Mathematics The Standards for Mathematical Content The Standards for Mathematical Practice Two Areas Focus Coherence Rigor There are two parts to the Florida Standards for Mathematics: Standards for Mathematical Content and Standards for Mathematical Practice. Together they define what students should understand and be able to do in their study of mathematics in order to be college and career ready. The Standards for Mathematical Practice are often simply called the Practice Standards or the Practices. The Practices include the mathematical habits of mind and mathematical expertise that students should develop such as reasoning, communication, making arguments, and modeling. These were the focus of Module 3. The Standards for Mathematical Content are very specific about concepts, procedures, and skills that are to be learned at each grade level, and contain a defined set of endpoints in the development of each. This will be the focus of this session. What’s New About the Florida Standards for Math? In order to meet both the Content Standards and the Practice Standards, the writers of the standards explicitly based them on three very important fundamentals of mathematics that were missing from or were not as explicit in different versions of mathematics standards. Those are: Focus, Coherence, and Rigor.

Focus Fewer standards allow for focusing on the major work for each grade Focus: The writers of the Standards worked very hard to reduce the number of expectations at each grade level. This work was not done arbitrarily. They focused on the different domains of mathematics, such as Operations and Algebraic Thinking, Number and Operations in Base Ten, Geometry, and Measurement and Data, and determined what work was critical for students at each grade level to address in order to develop the concepts in each domain over time. This reduction in number of standards allows teachers to shift their instruction to focus on the major work at their grade and to spend more time in each of these critical areas in order for students to develop a deep understanding through investigation, inquiry and problem solving.

Coherence Grade 1 Grade 2 Grade 3
The Standards are designed around coherent progressions and conceptual connections. Grade 1 Grade 2 Grade 3 Use place value understanding and properties of operations to add and subtract Use place value understanding and properties of operations to add and subtract fluently Use place value understanding and properties of operations to perform multi-digit arithmetic Coherence: Coherence means ensuring that there is a clear sequence of concepts and skills that build on each other across the grades.

Coherence The Florida Standards for Math are designed around coherent progressions and conceptual connections. All Roads Lead to Algebra…… Coherence: The chart on the slide shows one of the progressions in the Florida Standards for Math that builds up to Algebra in High School. Note that the Operations and Algebraic Thinking standards in grades K–5 lead up to and are designed to help middle school students work with Expressions and Equations, which will then help students to be successful in high school Algebra. This same progression takes place with the Number and Operations domains. In K–5 the Number and Operations standards are split over two domains, Base Ten and Fractions. This does not mean that the standards within the domains are not connected, but that there is a focus on each. The intent of the coherence and progressions is that students will all be ready for algebra at either the 8th grade or high school level. Section 3 of this module will include an in-depth examination of coherent progressions. Math Concept Progression K-12

CONCEPTUAL UNDERSTANDING APPLICATION OF MATHEMATICS
Rigor The major topics at each grade level focus equally on: CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding APPLICATION OF MATHEMATICS Using math in real-world scenarios Choosing concepts without prompting Rigor: Rigor means learning that is based in the deep understanding of ideas AND fluency with computational procedures AND the capacity to use both to solve a variety of real world and mathematical problems. Section 2 of this module will include an in-depth examination of the three aspects of rigor.

Developing Mathematical Expertise
The Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the National Council of Teachers of Mathematics process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

Activity 1: Sharing Experiences Implementing Math Practice Standards
Sharing Implementation Experiences Each participant will discuss with their table group one positive highlight, one challenge, and one lesson learned from their personal implementation of the Practice Standards thus far. Each table group will then determine two positive highlights, one common challenge, and one common lesson learned that they will present to the larger group. Participants will record notes and “New Ideas” generated from the discussion. Positive Highlights Challenges Lessons Learned A copy of the Practice Standards is available as a Mathematics Handout on each table for reference. Have each participant discuss with their table group one positive highlight, one challenge, and one lesson learned from their personal implementation of the Practice Standards thus far. Each table group will then determine two positive highlights, one common challenge, and one common lesson learned that they will present to the larger group. They can record notes from their discussion on page 5 in the Participant Guide. As table groups present, record the participants’ responses on the chart paper titled Positive Highlights, Challenges, and Lessons Learned. After all groups have presented, summarize what has been charted and then ask the large group if anyone has a solution to any of the common challenges. Encourage participants to record “New Ideas” on page 6 in the Participant Guide. (Allow 20 minutes total) Wrap up the activity by explaining that the challenges will be revisited periodically throughout the day as the discussion of the Content Standards ensues. Note: Be sure that the connections are made when discussing how to teach the Content Standards so that participants understand how implementing the Practice Standards goes hand-in-hand with implementing the Content Standards in a rigorous, focused, and coherent lesson. Transition to the next activity by explaining that participants will now start looking at the connections of the Content and Practice Standards by looking at the language of the Content Standards. Guide Pages 5-6 Guide Pages 8-9

The Language of the Mathematical Content Standards
Public Consulting Group 4/20/2017 Section 2 The Language of the Mathematical Content Standards The goal of Section 2 is to define and understand the difference between conceptual understanding, procedural skill and fluency, and application of mathematics. Total Time for Section 2: 40 minutes Materials Needed: Handouts: “Who Knows Math” and “Notes on Conceptual Understanding, Procedural Skill and Fluency, and Application of Mathematics” Section 2 at a Glance: In table groups, participants will read and analyze, and record their ideas on the “Who Knows Math” handout. Participants will discuss the students’ work and make observations about what the students know and are able to do. They will also determine what is unknown about what the students know. (15 minutes) The large group will briefly discuss their findings. (5 minutes) The facilitator will remind participants that, according to the standards, rigorous content addresses conceptual understanding AND procedural skills AND application. The facilitator will note that this handout is about conceptual understanding and procedural skill and fluency. Facilitator will go through information to build background understanding of conceptual understanding, procedural skill and fluency, and application of mathematics. (5 minutes) Participants will label the students’ work on the “Who Knows Math” handout as conceptual understanding and/or procedural skill and will answer additional follow-up questions as a large group. (8 minutes) Participants will watch a short video on fluency. (2 minutes) Activity concludes with participants reflecting on how the Florida Standards for Math approach to the Content Standards is similar and/or different to other standards that they have taught to in the past. (5 minutes)

Activity 2: What Do These Students Understand? – Part 1
Read and analyze the “Who Knows Math” handout on page 8 in the Participant Guide. Record your observations on what these students know and what they can do on page 9 in the Participant Guide. Would you be comfortable with his/her understanding if s/he continued to approach division in his/her particular way? Explain your reasoning. 2 412 1 2 X 412 What do these students understand? Ask table groups to read and analyze the “Who Knows Math” handout on pages 8-9 in the Participant Guide. Ask them to decide what each student on the sheet knows and doesn’t know. Ask participants to also determine what is unknown about what the students know. Participants can record their ideas on the handout. They do not need to fill out the last column, “Conceptual Understanding and/or Procedural Skill and Fluency?” yet. Tell them that they will return to the worksheet to complete that column after exploring the language of the content standards in more detail. (Allow 15 minutes) As table groups finish discussing, bring the whole group together and discuss participants’ observations. (5 minutes) Guide Pages 8-9 Guide Pages 8-9

CONCEPTUAL UNDERSTANDING APPLICATION OF MATHEMATICS
Rigor The major topics at each grade level focus equally on: CONCEPTUAL UNDERSTANDING More than getting answers Not just procedures Accessing concepts to solve problems PROCEDURAL SKILL AND FLUENCY Speed and accuracy Used in solving more complex problems Comes after conceptual understanding APPLICATION OF MATHEMATICS Using math in real-world scenarios Choosing concepts without prompting Rigor: Remind participants that the big shift in the content standards is that at all ages students are to be taught with rigor as defined on the slide. Review the three aspects of rigor: conceptual understanding, procedural skill and fluency, and application of mathematics. Repeat that rigor means learning based in the deep understanding of ideas AND fluency with computational procedures AND the capacity to use both to solve a variety of real world and mathematical problems. Explain to participants that you will now go over each aspect of rigor in more depth.

Conceptual Understanding
Public Consulting Group 4/20/2017 Conceptual Understanding “Conceptual understanding refers to an integrated and functional grasp of mathematical ideas.” (Adding it Up: Helping Children Learn Mathematics. 2001) Ask participants to turn to pages in the Participant Guide where space is provided for them to take notes on Conceptual Understanding, Procedural Skill and Fluency, and Application of Mathematics. Conceptual Understanding As participants read the quote on the slide, explain that conceptual understanding can be difficult to define. Ask participants to read the following description on page 10 in the Participant Guide that is an overlap of the National Research Council and NCTM definitions of conceptual understanding: “Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples of concepts; use and interrelate models, diagrams, manipulatives, and varied representations of concepts; identify and apply principles; know and apply facts and definitions; compare, contrast, and integrate related concepts and principles; recognize, interpret, and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding reflects a student’s ability to reason in settings involving the careful application of concept of definitions, relations, or representations of either.” (Balka, D., Hull, T., & Harbin Miles, R.(n.d.). What is conceptual understanding. Retrieved Oct. 15, 2013 from Just as they looked at “I Can” statements with each of the Practices, use the next slides to show examples of student responses that demonstrate conceptual understanding. Guide Pages 10-11

Public Consulting Group 4/20/2017 Conceptual Understanding Example Question: What is ? Student Response: 20 is 2 tens and 70 is 7 tens. So, 2 tens and 7 tens is 9 tens. 9 tens is the same as 90. Conceptual Understanding Go over the example on the slide as one way that a student might begin to demonstrate conceptual understanding of Content Standard MAFS.1.NBT.2.2c: The Numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Public Consulting Group 4/20/2017 Conceptual Understanding Example Question: What is 5 + 6? Student Response: I know that = 10; since 6 is 1 more than 5, then much be 1 more than more than 10 is 11. Conceptual Understanding Go over example on the slide as one way that a student might begin to demonstrate conceptual understanding of Content Standard MAFS.1.OA.3.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10, use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13-4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g.; knowing that = 12, one knows 12 – 8 = 4); and creating equivalent but easier or know sums (e.g.; adding by creating the known equivalent = = 13).

Public Consulting Group 4/20/2017 Conceptual Understanding Example Question: Why is 7 an even or odd number? Explain how you know. Student Response: 7 is odd because I cannot make pairs with all of the cubes like I can with 8 cubes. When I can make pairs with all of the cubes it is an even number. Conceptual Understanding Go over example on the slide as one way that a student might begin to demonstrate conceptual understanding of Content Standard MAFS.2.OA.3.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s write an equation to express an even number as a sum of two equal addends.

Procedural Skill and Fluency
Public Consulting Group 4/20/2017 Procedural Skill and Fluency “Procedural skill and fluency is demonstrated when students can perform calculations with speed and accuracy.” (Achieve the Core) “Fluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for higher-level thinking.” (Engage NY) Procedural Skill and Fluency Highlight the two key points on the slide. Ask participants for their thoughts on the fact that the Florida Standards for Math ask students to develop their conceptual understanding prior to developing procedural skill and fluency. Ask why they think this is the case. If it does not come out in the conversation, explain that teaching students procedures and how to use an algorithm or any type of short cut prior to developing some conceptual understanding for why those things work mathematically is akin to teaching answer getting vs. problem solving.

Procedural Skill and Fluency
Check all the equations that are true. 8 x 9 = 81 54 ÷ 9 = 24 ÷ 6 7 x 5 = 25 8 x 3 = 4 x 6 49 ÷ 7 = 56 ÷ 8 Mariana is learning about fractions. Show how she can divide this hexagon into 6 equal pieces. Write a fraction that shows how much of the hexagon each piece represents. Adding / subtracting with tens [Ask orally] (a) Add 10 to 17 (b) Add 10 to 367 (c) Take 10 away from 75 (d) Take 10 away from 654 Procedural Skill and Fluency Go over the examples on the slide. Each of the these is a variation on the traditional skill and drill activities that teachers are used to using to help students develop mathematical fluency.

Application of Mathematics
Public Consulting Group 4/20/2017 Application of Mathematics The Standards call for students to use math flexibly for applications. Teachers provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content. Application of Mathematics Go through points on the slide. Ask participants how they have had students apply mathematics. Get two or three examples. Ask participants why this is important. Application of mathematics is important because without this step or expectation students are learning math as a set of rules, procedures, etc. that have no real meaning in the world outside of the classroom. Students need to learn how math works and how it is used. Note here that when the conversation of application of mathematics typically comes up the phrase ‘real world problems’ is usually somewhere in the conversation. As teachers think about the types of problems that students will solve in order to apply their mathematical understanding, have them think about problems that would be ‘real world’ to their students. This means that the problems should be contextually relevant and easily understood by the students at their particular grade level. Before moving to the next slide that has examples of contextually relevant problems, highlight the third bullet on the slide and ask for one or two volunteers to give examples of how the Florida Standards for Math can be supported and ‘chunked’ with the standards from other content areas in order for students to see and apply mathematics outside of their typical math lesson time. (Frieda & Parker, 2012) (Achieve the Core, 2012)

Public Consulting Group 4/20/2017 Application of Mathematics Example There are 9 cookies left in the pan. Five students want to share the cookies equally. How many cookies will each student get? Application of Mathematics Have participants examine the example on the slide. As time permits have them discuss ways that conceptual understanding and procedural skill and fluency can be applied when solving this problem. Standards addressed by the problem: MAFS.3.NF.1.1 – Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned in b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. MAFS.3.NF.1.3a – Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (a) Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. MAFS.3.G.1.2 – Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape. (Investigations Grade 3 Unit 7, Session 1.5)

Public Consulting Group 4/20/2017 Application of Mathematics Example 5.MD – Minutes and Days What time was it 2011 minutes after the beginning of January 1, 2011? (Illustrative Mathematics) Application of Mathematics Have participants examine the example on the slide. As time permits have them discuss ways that conceptual understanding and procedural skill and fluency can be applied when solving this problem. If needed, clarify, as a group, that the beginning of January 1, 2011 is 12:00 am January 1, 2011. Standards addressed by the problem: MAFS.5.NBT.2.6 – Find whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculations by using equations, rectangular arrays, and/or area models. MAFS.5.MD.1.1 – Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g. convert 5 cm to .05 m), and use these conversions in solving multi-step, real world problems.

Activity 2: What Do These Students Understand? – Part 2
Return to the “Who Knows Math” handout on pages 8-9 in the Participant Guide. Which students have shown conceptual understanding, which have shown procedural skill and fluency, which have shown both, and which pieces of work would you need to know more to make the determination? 2 412 1 2 X 412 What do these students understand? Have participants look back at the “Who Knows Math” student work and ask them to determine which students have shown conceptual understanding, which have shown procedural skill and fluency, which have shown both, and which pieces of work they would need to know more about in order to make the determination. Have volunteers share their thinking. Things to note about each student’s piece of work: Abie: Produced two correct answers, but lacks the conceptual understanding of the operations and that would allow the connection to be made between division and multiplication of fractions. Ceedee: Is able to make the conceptual connections, but did not perform the calculations in a way that produced the correct answer. Also, as she performed the calculations she was not paying attention to the precision of her answer and asking herself, ‘does my answer make sense?’ Effie: Is able to make the conceptual connections, but does not have a way to get an answer. Gigi: More information on Gigi’s thinking and understanding would be needed to determine if there was conceptual understanding. Hi: Seems to have an efficient way for finding the answer, but more information is needed to determine what ‘it’ is. An important point to bring up here is that teachers should not assume what students know and understand. They need to probe deeper to really determine where students are with their understanding. Transition to the video by pointing out that this lens of looking at student work will be necessary as students develop and meet the mathematical expectations of the Florida Standards for Math. Guide Pages 8-9

Mathematics Fluency: A Balanced Approach
Public Consulting Group 4/20/2017 Mathematics Fluency: A Balanced Approach Click on “Watch Video” to play the video Mathematics Fluency: A Balanced Approach from here: The video is 1:57 long. After the video has played, ask participants for their thoughts. Watch Video

Think About It… How does the approach of the Florida Standards for Math Content differ from previous approaches to mathematics teaching and learning? Think About It Finally, wrap up this section by asking participants to reflect on the question on the slide. Allow 5 minutes for discussion. You can also use this question to transition to the next activity after the break by linking this discussion on the Florida Standards for Math approach to rigor and now looking specifically at the standards to see how conceptual understanding, procedural skill and fluency, and application of mathematics is developed over and within grade levels. As time permits, ask for volunteers to share their responses to the question.

4/20/2017 Let’s Take A Break… The break should be 15 minutes. Remind the participants to try to be timely in their return. Be back in 15 minutes…

The Progression of Mathematical Concepts
Public Consulting Group 4/20/2017 Section 3 The Progression of Mathematical Concepts The goal of Section 3 is to see how concepts are developed within and across grade levels and to be able to group or ‘chunk’ standards across content domains. Total Time on Section 3: 75 minutes Materials Needed: Sets of Standard Progression Cards (1 set per five table groups) Handouts: “Exploring the Content Standards Observation Sheet” and “Activity 3 Reflection” Mathematics Handout: Standards for Mathematical Practice (on tables for reference) Sticky notes Chart paper, markers, tape: signs made for K, 1, 2, 3, 4, and 5 and hung around the room for participants to gather in grade-level groups during Activity 3, Part 3 Section 3 at a Glance: Review the organization, domain distribution, and domain progression of the Florida Standards for Math. (5 minutes) Watch video Gathering Momentum for Algebra. (5 minutes) Explore the Standards Part 1: Participants explore Content Standards for one domain and determine which focus on Conceptual Understanding, Procedural Skill and Fluency, and Application of Mathematics. (20 minutes) Explore the Standards Part 2: Participants explore Content Standards for one domain across grade levels and record five general observations and two connections to the Practice Standards. (20 minutes) Explore the Standards Part 3: Participants explore all of the Content Standards for one grade level to create ‘clusters’ of standards across multiple domains that can be taught together in a lesson or unit. (20 minutes) Participants reflect on teaching and learning with the Florida Standards for Math. (5 minutes)

The Organization of the Standards
Domain Cluster Standards The Organization of the Standards Quickly go through the organization of the Content Standards with the participants. Each grade level is organized by domains and within each domain there are associated groups of standards that make up a cluster. There can be multiple clusters within a domain. Explain that Florida has a unique numbering scheme. There are 5 character places in the alphanumeric coding- the subject, grade level, domain and/or conceptual category, cluster, and standard. Use the code on the slide as an example: MAFS.3.NF.1.2 MAFS = Subject: Mathematics Florida Standards 3 = Grade: Third NF = Domain: Number and Operations Fractions 1 = Cluster: Develop understanding of fractions as numbers. 2 = Standard: Understand a fraction as a number on the number line, represent fractions on a number line diagram. Remind participants that there is no importance to the order of the domains in the grade, nor should the domains necessarily be taught separately. On the contrary, they should be taught in cross domain chunks wherever possible. Transition to the next slide by explaining that domains span several grade levels.

4/20/2017 Domain Distribution Domain Distribution Explain that in K-5 there are four domains that span all of the grades and Kindergarten has a unique domain of Counting and Cardinality. The standards here are foundational to both Number and Operations in Base Ten and Operations and Algebraic Thinking. When students are developmentally ready and have a solid foundation in Number and Operations in Base Ten, Number and Operations – Fractions is layered on beginning in third grade. Transition to the next slide by reminding participants that the domains were determined based on a very specific and coherent roadmap for learning called a progression.

Domain Progression Domain Progression
Remind participants that the domains were written so concepts build on each other grade after grade so that, in this particular progression, there is a clear pathway to high school Algebra. The video on the next slide is an explanation of the progressions from Math Team coordinator Bill McCallum.

Gathering Momentum for Algebra
Click on “Watch Video” to play the video Gathering Momentum for Algebra from here: The video is 2:08 long. After playing the video, ask participants how domains differ from strands. If it does not come up in the brief discussion, explain that strands typically span elementary, middle, and high school and are far more broad than domains. For example, and as we have heard Professor McCallum explain, the domain of Number and Operations in Base Ten cover how students learn about numbers and the Domain of Operations and Algebraic Thinking is where students develop meanings for addition, subtraction, multiplication, and division. To get a better understanding of the progressions, participants will now explore a progression. Watch Video

Exploring the Content Standards
Number and Operations in Base Ten Number and Operations in Fractions Counting and Cardinality & Operations and Algebraic Thinking Measurement and Data Geometry Exploring the Content Standards Participants will complete the first two parts of this activity as table groups and will work in grade level alike groups for the third part. Signs for each grade, K-5, should be posted around the room so participants can gather together for the third part. Assign each table one of the K-5 Content Standard domains and pass out the color coded domain cards to each group.

Activity 3 (part 1): Explore a Progression
Examine your assigned domain and determine which standards focus on: Conceptual Understanding (CU) Procedural Skill and Fluency (PSF) Application (A) 2.NBT.1 Understand that three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g equals 7 hundreds, 0 tens, and 6 ones. K.NBT.1 Compose and decompose numbers from 11to19 into ten ones and some further ones e.g. by using objects, drawings, and record each composition or decomposition by a drawing or equation. 4.NBT.4 Fluently add and subtract multi-digit whole numbers to any place. Exploring a Progression For Part 1 of Exploring the Content Standards ask participants to examine their assigned domain and determine which standards focus on Conceptual Understanding, Procedural Skill and Fluency, and Application of Mathematics. Participants should use sticky notes to mark the card with either CU, PSF, or A according to how they sorted the cards. After sorting and marking the cards, have participants answer the following questions on page 13 in their Participant Guide: What are the expectations around conceptual understanding at your grade level? What are the fluency expectations at your grade level? What are the opportunities for application at your grade level? After 15 minutes bring the groups back together to discuss their answers to the questions. Guide Page 13

Activity 3 (part 2): Explore a Progression
Examine your assigned domain across the K-5 grade band and record five general observations about the progression and two observations about the relationship between the Content and Practice Standards. 2.NBT.1 Understand that three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g equals 7 hundreds, 0 tens, and 6 ones. K.NBT.1 Compose and decompose numbers from 11to19 into ten ones and some further ones e.g. by using objects, drawings, and record each composition or decomposition by a drawing or equation. 1.NBT.2a Understand that numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Exploring a Progression Now, ask participants to examine the Content Standards in their assigned domain across grade levels and, on pages in the Participant Guide, complete the observation worksheet on which they record five general observations about the progression and two observations about how the Practices are integrated into the content. Allow participants 10 minutes to observe and 10 minutes to discuss. During discussion each domain group will share their observations. The goal here is for participants to see the progression of and how conceptual understanding, procedural skill and fluency, and application of mathematics are developed across grade levels. Because they are using the cards, participants should be able to line up the grade level domain standards side by side so that the vertical alignment can be seen horizontally across their table allowing for a continuous comparison. Transition to Part 3 of the activity by explaining to participants that teaching the standards is not just about understanding how the Content Standards progress across a domain, but also about understanding how the standards of different domains work together. Guide Pages 14-15 Guide Pages 13-14

Activity 3 (part 3): ‘Chunking’ the Standards
Examine all of the Content Standards for your assigned grade level. Make connections across domains and create clusters that can be taught as part of a lesson or unit. 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. ‘Chunking’ the Standards Ask participants to separate their domain cards by grade level. Direct participants to the areas around the room designated for each grade, K-5. They should take the cards for their grade level from the table to the designated area. For each grade, the cards for all five domains will be combined so there is a complete set of Content Standards for each grade level. In larger groups there may be several complete sets so the grade groups can be broken into two or three smaller groups. Once they have their complete set of standards, ask participants to examine all of the Content Standards for their grade level and make connections across the domains thereby creating clusters that can be taught together as part of a lesson or unit. Allow participants 10 minutes to create and record the clusters and then take 10 minutes to allow each grade level the opportunity to share one or two of their clusters. They can record their thoughts on page 15 in the Participant Guide. Guide Page 15

Reflect What domains of the Florida Standards for Math do you think will be the most exciting and/or productive for you to teach to your students? 2. What domains of the Florida Standards for Math do you think will be the most challenging for your students to learn? Reflect Now that participants have a deeper understanding of the Florida Standards for Math expectations around conceptual understanding, procedural skill and fluency, and application of mathematics at their grade level, ask them to reflect on the two questions on the slide and record their answers on page 16 in their Participant Guide. As time permits ask for volunteers to share their responses. Allow 5 minutes. Then, set-up the after lunch activities by explaining to participants that they will build off of their understanding of the Content Standards to explore the implications for teaching and learning in the classroom. Guide Page 16

Lunch Lunch: Go over any lunch procedures with participants and be sure to give them a specific time that you will start the second half of the day.

4/20/2017 Section 4 Meeting the Expectations of the Content Standards by Teaching with High Level Tasks The goal of Section 4 is to have teachers understand how to create open questions and parallel tasks so that all students are provided a pathway into the mathematics of a rich and high level task. Total Time on Section 4: 85 minutes Materials Needed: -Chart paper, markers, tape -Handouts: “Characteristics of Higher Level Tasks”, “Strategies for Creating Open Questions”, “Examples of Parallel Tasks”, “Creating Open Questions and Parallel Tasks”, and “Activity 4 Reflection” -Mathematics Handout: Standards for Mathematical Practice (on tables for reference) -Standard Progression Cards Section 4 at a Glance: Review characteristics of higher level tasks then play Dan Meyer video Math Class Needs a Makeover. (15 minutes) Participants examine a sample assessment task. (5 minutes) Go over and allow participants time to examine Strategies for Creating Open Questions. (10 minutes) Go over and allow participants time to examine Examples of Parallel Tasks. (10 minutes) In table groups participants create Open Questions and Parallel Tasks around a chosen set of Content and Practice Standards. Participants put their work on chart paper. (20 minutes) Table groups present their work to the larger group. (20 minutes) Participants answer reflection questions. (5 minutes)

High Level Tasks Don’t have a predictable, well-rehearsed approach or pathway to the solution. Require students to explore and understand the nature of mathematical concepts, processes, or relationships. Demand self-monitoring or self-regulation of one’s own cognitive processes. Require students to access relevant knowledge and experiences and make appropriate use of them in working through the task. There are two slides for the list of characteristics of high level tasks. This list is in the Participant Guide on page 18. The slides have animation so each bullet point will appear on the mouse click. Go over the list. Guide Page 18

High Level Tasks Require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions. Require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required. Adapted from (Stein, Smith, et al (2000). Implementing Standard-Based Mathematics Instruction) Finish reviewing the list.

Math Class Needs a Makeover Dan Meyer
Public Consulting Group 4/20/2017 Math Class Needs a Makeover Dan Meyer Math Class Needs a Makeover Begin the activity by explaining to participants that they are going to watch a video in which math expert Dan Meyer discusses the types of problems that students should be doing in math class. Further set-up the video by explaining that the examples given in the video are from a secondary classroom. Ask participants to not focus so much on the task itself but the message that is being delivered as it will be the topic of the discussion that will follow. Click on “Watch Video” to play the video Math Class Needs a Makeover from here: The video is 11:39 long. After viewing, debrief the video with participants by first asking for their thoughts on Dan Meyer’s message. After two or three volunteers share, tell participants to keep the type of tasks that Dan Meyer spoke of in mind. If students are going to be expected to work at this level as they enter middle and high school, it is our obligation to them to determine, “How can we help students in K-5 work with high level tasks so that they are prepared to work with mathematics at this level in middle and high school?” This is the question they will focus on now. Watch Video

Take a Look… Take a Look Have participants examine the Florida Standards Assessments third grade task and give their first impressions. Ask participants what challenges they face everyday when trying to implement high level tasks with students? Most will answer that not all students are ready to work tasks such as this. Use this answer to this question to transition to the next slide.

The Big Question How can I incorporate high-level mathematics tasks that will benefit ALL of my students? The Big Question Explain to participants that they will now learn more about two strategies that can be used to provide multiple pathways into the mathematics of high level tasks so that all students can benefit from its use.

Strategies for Differentiating High Level Tasks
Open Questions Parallel Tasks Strategies for Differentiating High Level Tasks Explain that the two strategies that will be looked at are Open Questions and Parallel Tasks. These two strategies are from Marian Small’s book Good Questions: Great Ways to Differentiated Mathematics Instruction. Begin the discussion by first going over Open Questions.

What are Open Questions?
An open question is framed in such as way that multiple responses and approaches can correctly answer the question. An open question allows students at varying developmental and readiness levels to equally participate in and grow from thought provoking tasks. An open question provides multiple pathways into the mathematics. What are Open Questions? Summarize the three points on the slide by explaining that open questions provide multiple pathways into the mathematics by allowing all students to participate no matter their developmental or readiness level by allowing for multiple responses and approaches to yield a correct answer.

Example of an Open Question
Question 1: To which fact family does the fact 3 x 4 = 12 belong? Question 2: Describe the picture below by using a mathematical equation. X X X X Example of an Open Question Go over this example of an Open Question as it allows for different answers. “If the student does not know what a fact family is, there is no chance he or she will answer Question 1 correctly. In the case of Question 2, even if the student is not comfortable with multiplication, the question can be answered by using addition statements (e.g., 4+4+4=12 or 4+8=12). Other students might use multiplication statements (e.g., 3x4=12 or 4x3=12), division statements e.g., 12÷3=4 or 12÷4=3), or even statements that combine operations (e.g., 3x2+3x2=12). (Small, 2012) After students come up with their answer, the teacher connects answers by finding those that form a fact family based on similarities, or having students find connections in the answers. (Small.2012, 7)

Guidelines for Using Open Questions
An open question should be mathematically meaningful by focusing on the expectations of the content standards. An open question needs just the right amount of ambiguity. An open question is most effectively used when followed up by a whole class discussion in which the teacher strategically calls on students, conveys the message that multiple answers are welcomed, and builds connections between students’ answers. Guidelines of Using Open Questions This slide has animation so each of the three bullet points will appear on the mouse click. Introduce the three points on the slide by using the following to support each bullet. While participants read the first bullet further explain that questions such as, ‘What do you think of when I say the number 12? ‘ Can be used to launch an open question but should not be the actual open question because by answering just this question students would not meet any of the content goals of the Florida Standards for Math. While participants read the second bullet, clarify that ‘the right amount of ambiguity’ means that the question is vague enough to allow for multiple correct answers but is not so vague that students do not understand what the question is asking. While participants read the third bullet follow up with these points: Calling on students with the simplest and/or least complex answer/approach early in the discussion will help to ensure that their answer is not given by someone else. Thus, making the chances greater that all students, even those that have struggled in the past, are able to participate in a vital way within the conversation. Students knowing that multiple answers are appropriate also means that multiple answers are valid. However, do note that precision is still important. While there is no ‘one right answer’ to the actual open question, there are correct answers based on each students’ interpretation of the question. For example, if the question is ‘Create an equation that consists of three three-digit numbers’, no matter what three numbers are used, they must each be three digits and whatever operations are applied to the numbers must be done so in a way that makes the equation true. All answers should be mathematically sound and because each answer belongs to the same question there should always be inter-answer connections that can be made either explicitly or through the use of follow-up questions. If one student answers the question how are 6 and 10 alike by saying that ‘they are both doubles’, and another answers with ‘they are both even’, follow-up questions such as ‘how do you know that these are doubles?’ and ‘how do you know that they are even?’ can help to make the connect between repeating the same addend and multiplying and dividing by 2.

Strategies for Writing Open Questions
Turning Around a Question Asking for Similarities and Differences Replacing a Number with a Blank Creating a Sentence Using “Soft” Words Changing the Question Strategies for Writing Open Questions Have participants work in their table groups to examine the specific Strategies for Creating Open Questions that are described on pages in the Participant Guide and the examples provided. Allow table groups 10 minutes to examine the strategies and discuss how they could use these strategies in their classroom. As a large group have volunteers share their thoughts on implementation. Guide Pages 19-21

4/20/2017 Parallel Tasks Parallel Tasks are sets of tasks, usually two or three, that get at the same big idea and are close enough in context that they can be discussed simultaneously. Parallel Tasks Explain to participants that the second strategy for differentiating tasks for students is to create parallel tasks. Go over the statement on the slide and then further explain that parallel tasks can be used in conjunction with open questions by allowing the open question to launch the task itself. (Small. 2012, 10)

Example of Parallel Tasks
Public Consulting Group 4/20/2017 Example of Parallel Tasks Choice 1: Create a word problem that could be solved by multiplying two one-digit numbers. Choice 2: Create a word problem that could be solved by multiplying two numbers between 10 and 100. Example of Parallel Tasks Go over the example on the slide by explaining that: “Both choices focus on the concept of recognizing when multiplication is appropriate, but Choice 1 is suitable for students only able to work with smaller factors. Further, the tasks fit well together because questions such as the ones listed below suit a discussion of both tasks and thus can be asked of all students in the class: What numbers did you choose to multiply? How did you know how many digits the product would have? What about your problem made it a multiplying problem? What was your problem? How could you solve it? (Small 2012, 11)” (Small. 2012, 10)

Creating Parallel Tasks
Public Consulting Group 4/20/2017 Creating Parallel Tasks Consider the following: Different developmental levels What operations students can use What size numbers students can handle Conceptual understandings that students have developed Creating Parallel Tasks Explain to participants that when they are creating parallel tasks they need to consider the developmental levels of their students, what operations students can use, what size numbers student are able to work with, and conceptual understandings that students have developed up to this point.

Implementing Parallel Tasks
Public Consulting Group 4/20/2017 Implementing Parallel Tasks Things to Do: Create the parallel tasks Create parallel questions Manage task choice Hold a follow-up discussion Implementing Parallel Tasks Explain to participants that when they are implementing parallel tasks they need to be sure to create questions that will be used as part of the follow-up discussion that can be answered by any student, no matter their choice in task. To manage task choice, teachers can assign tasks to students, allow students to choose, or suggest tasks for specific students but allow the final choice to be the student’s discretion. Before moving on to having participants create open questions and parallel tasks, allow participants 10 minutes to examine the Examples of Parallel Tasks on pages in the Participant Guide and then ask for final questions about either parallel tasks or open questions. Guide Pages 22-24

Activity 4: Teaching with High Level Tasks
Public Consulting Group 4/20/2017 Activity 4: Teaching with High Level Tasks Teaching with High Level tasks Choose a grade level. Choose which content and practice standards you want to work with. Create Open Questions and one set of Parallel Tasks that can be used in your instruction of the Content Standards. Write your final version of both the Open Questions and the Parallel Tasks on a piece of chart paper. Be prepared to present your ideas to the full group. Teaching with High Level Tasks In this activity participants will work together in table groups to create Open Questions and Parallel Tasks around a chosen set of Content and Practice Standards. There is space in the Participant Guide on pages for groups to record their thinking. Each group should transfer their thinking onto chart paper because at the end of their work time each group will have an opportunity to present their work to the larger group. Explain the activity to participants using the following directions: As a group, choose which content and practice standards you want to work with. (They can use the Standard Progression Cards to choose content standards and the Mathematics Handout on their tables to choose practice standards.) For your chosen set of standards create Open Questions and a set of Parallel Tasks that can be used with students. Use the space in your Participant Guide for brainstorming ideas. Write your final version of both the Open Questions and the Parallel Tasks on a piece of chart paper. When asked, present your questions and tasks to the larger group and then hang your piece of chart paper on the wall. After going over the directions, use the following slide to provide a short list of things that participants should keep in mind while working. Guide Pages 25-26

Principles to Keep in Mind
Public Consulting Group 4/20/2017 Principles to Keep in Mind All open questions must allow for correct responses at a variety of levels. Parallel tasks need to be created with variations that allow struggling students to be successful and proficient students to be challenged. Questions and tasks should be constructed in such a way that will allow all students to participate together in follow-up discussions. Principles to Keep in Mind Go through each of the points on the slide and allow participants 20 minutes to work. At the end of the work time, or when participants have finished if they do not need the full 20 minutes, have each group present their work. Allow 20 minutes for group presentations. During the presentations, as time permits, allow other groups to ask questions about the thought process behind the creation of the Open Questions and Parallel Tasks. Wrap up the activity by having participants complete the Reflection Questions on the next slide.

Reflect How does teaching with high level tasks relate to conceptual understanding, procedural skill and fluency, and application of mathematics? 2. How does teaching with high level tasks support Florida’s ‘New Way of Work’? Reflect Allow participants 5 minutes to respond to the reflection questions on the slide in their Participant Guide on page 27. As time permits have volunteers share their thinking and remind participants that Florida’s New Way of Work requires the ‘chunking’ of standards and high level tasks can be used to teach more than one individual standard when appropriate. Transition to the next section by telling participants that they will now observe two lessons and reflect on the instructional strategies that the teacher is using and will then examine additional strategies in four centers that will be set up around the room. Because participants will be moving from table to table in the next activity ask participants to put their personal belongings to the side. Guide Page 27

Teaching the Content Standards Through
Public Consulting Group 4/20/2017 Section 5 Teaching the Content Standards Through Problem Solving The goal of Section 5 is for participants to examine multiple instructional strategies for teaching the content standards through problem solving. Total Time on Section 5: 75 minutes Materials Needed: Handout: “Video Observation Sheet” Two sample lesson plans from each grade level for review at Center 1 (12 plans total) Activity 5 handouts -Center 1: Lesson Plan Sources handout – 1 per participant -Center 2: Math Journals handout – 1 per participant -Center 3: Concept Cards handout – 1 per participant -Center 4: Developing Fluency handout – 1 per participant Index cards – 1 per participant Chart paper- signs made indicating the location of each center and one sheet hung at each center labeled – “Leave One” Markers and tape Section 5 at a Glance: Watch and discuss video Skip Counting with Counting Collections. (15 minutes) Watch and discuss video What Fraction of this Shape is Red. (5 minutes) Participants visit each of the four workstations in small groups. Each group will have 12 minutes at each workstation. While at each workstation participants will “Take One, Leave One” meaning that they will take away a strategy or resource and should then, as a group, write an additional (one or more) strategy or resource on the index card provided on the table and then tape that index card to the chart paper labeled Leave One so that the additional resources are also shared. (50 minutes) Debrief the workstation activity as a large group and highlight the additional resources posted on the chart papers. (5 minutes)

4/20/2017 Counting Collections: Kindergarten To begin the activity explain to participants that they will watch two videos, one showing parts of a primary lesson and one showing parts of an intermediate lesson. While watching the videos, participants should makes notes on the Video Observation sheet provided in the Participant Guide on pages After each video, pause for a short discussion centered around participants’ observation notes. The goal of watching the videos is to get participants looking for examples of the important aspects of teaching the Content Standards that have been discussed throughout this session, but to also look at additional teaching strategies that they want to try in their own classroom. Begin by watching the first video, Skip Counting with Counting Collections, that shows part of a Kindergarten lesson. Click on “Watch Video” to play the video from here: The video is 12 minutes long. Guide Pages 29-31 Watch Video

4/20/2017 What Fraction of this Shape is Red? Following the discussion of the Kindergarten lesson, watch the video What Fraction of this Shape is Red that takes place in a fifth grade classroom. Click on “Watch Video” to play the video from here: The video is 5 minutes long. After the discussion on the second video, explain to participants that they will now have an opportunity to explore some additional strategies and resources for teaching the Florida Standards for Math Content. Guide Page 29-31 Watch Video

Activity 5: A New Spin on Old Strategies
Public Consulting Group 4/20/2017 Activity 5: A New Spin on Old Strategies Center 1: Sample Lesson Plans Center 2: Math Journals Center 3: Concept Cards You will have 12 minutes at each work station. Center 4: Developing Fluency A New Spin on Old Strategies Participants will work in small groups to examine Math strategies and/or resources at 4 different workstations that support Math Practices and Content Standards. Participants will need to number each table until everyone has a number representing 1, 2, 3, or 4. Participants will have 12 minutes at each workstation. After each 12 minute segment you will need to call time and have participants move to the next numbered center (clockwise, moving up in count). While at each workstation participants will “Take One, Leave One” meaning that they will take away a strategy or resource and should then, as a group, write an additional (one or more) strategy or resource on the index card provided on the table and then tape that index card to the chart paper labeled Leave One so that the additional resources are also shared. Notes about setting up and managing centers: • In cases where you are working with a large number of participants, create multiple centers (e.g., two to three tables labeled as Center 1, two to three tables labeled as Center 2, etc.) so that there are no more than six participants at any one center at any one time. • Each group of six teachers should travel from center to center together so that the movement is fluid. •Make sure that each center is clearly labeled so that groups are not trying to figure out where they are going as they move. •Even though there may be multiples of each center set up, be sure that consecutive centers are set up within close proximity to each other (i.e. Center 1 is next to Center 2, Center 2 is next to Center 3, etc.). •Give participants a 1 minute wrap up warning at each center so that they can conclude their conversations and prepare to move to the next center. “Set up” this activity to participants by explaining that they might explore strategies they already know. However, a new spin has been put on each strategy in order to meet the challenges presented by the Florida Standards. Also, explain that at each workstation there is a “take-home” handout for their future planning. After the last center is visited, debrief the centers as a large group and highlight some of the Leave Ones (strategies left behind on index cards by each group) posted on the chart paper. Transition to the last activity by asking participants how they will now share this information back at their school site.

4/20/2017 Section 6 Next Steps The goal of Section 6 is for participants to determine how they will take the key information back to their peers at their school so that everyone gains a shared understanding. Total Time on Section 6: 15 minutes Materials Needed Handout: “Next Steps” Chart paper, markers, tape – one sheet labeled “Like to Do”, one labeled “Can Do”, and one labeled “Challenges & Work-Arounds” Section 6 at a Glance: Discuss and answer questions on the Next Steps handout in the Participant Guide. (15 minutes)

4/20/2017 What's Your Plan? What do we think should happen at school to promote implementation of the Florida Standards for Math? What can we do now in our classrooms and in the school to promote implementation of the Florida Standards for Math? What are some expected challenges? How can we work around the challenges? What’s Your Plan? Ask participants to look over their work of the day and generate a list of implementation steps they would like to do, think they can do, challenges they might face, and ways to work around the challenges. They can record their answers on page 33 in the Participant Guide. While groups are talking, put up three charts with the labels, “Like to Do”, “Can Do”, and “Challenges & Work-Arounds”. After about 10 minutes of table work, ask participants to share some of what they’ve written. Chart what they say. Guide Page 33

Closing Activities

Focus on Content Standards Outcomes
Public Consulting Group 4/20/2017 Focus on Content Standards Outcomes Learned more about the Practice Standards Examined the language and structure of the Florida Standards for Math Practice Created and solved standards-based tasks Observed Florida Standards for Math-aligned instruction Shared implementation successes and challenges and planned next steps Review each session outcome and discuss how each was met. Utilize the work on the walls to point out specific activities that led to the outcome being addressed. (5 minutes)

Post-Assessment and Session Evaluation
Public Consulting Group 4/20/2017 Post-Assessment and Session Evaluation Where Are You Now? Assessing Your Learning This Post-Assessment, on page 35 in the Participant Guide, will be the same as the Pre-Assessment they took in the beginning of the session. This assessment is to gauge their learning based on the activities of the full day session. Remind the participants to fill out their session evaluation form as well. Guide Page 35

What’s Next? Module 4 Data Use Module 4 Data Use Module 1 Data Use
ELA Module 3 Math Module 4 Data Use Module 6 Math Module 7 ELA & Data Use Module 8 Math & Data Use Module 5 ELA Module 7 ELA & Data Use End the module with this slide, which is entitled, “What’s Next?” This will remind the participants where they are on the continuum of learning. The professional development series will also ensure that by having a stronger understanding of data use, there will be support for their charter school’s transition to the Florida Standards. The data use process will enable charter schools that may not be doing well on the new Florida Standards to have a defined process to use to identify concerns and problem solve around the issues.

Module 6A for Elementary Teachers

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