Module 3B for Middle/High School Teachers

Module 3B for Middle/High School

Teachers

Florida Standards for Mathematics: Focus on

Practice Standards

Transitioning to Florida Standards: Project Overview

• Project is Race to the Top funded until June 2014• All charter schools eligible to participate• Develop and deliver targeted training and technical assistance

specific to charter schools in two major areas: 1) Implementation of the Florida Standards2) Access and use of a Local Instructional Improvement System (LIIS)

to analyze student achievement data to drive instruction and increase student academic achievement

• No cost to charter schools

Project Activities• Professional development for teachers, administrators, and governing board

members (Delivered regionally)• Data Literacy and Use • Florida Standards (English Language Arts & Literacy, Math)• Value-Added Model (VAM)

• Training of Trainers Model for Teacher Leaders• K-5 (Up to 5 Teachers & 1 Administrator Per School)• 6-12 (Up to 5 Teachers & 1 Administrator Per School)

• Training for charter school teams (Delivered regionally)• Self-assessment tool • Creating a Florida Standards Implementation Plan• Progress monitoring templates

Professional Development Session Alignment Set 1

Governing Board

School Leaders Module 3PARCC

Module 6 Florida Standards Math Module 7

ELA & Data Use

Teachers Math

Leadership Teams Session 2

Session1

ELAData Use

Data Use ELA Math

Data Use

Professional Development Session Alignment Set 2

Governing Board

School Leaders

Module 5 Florida Standards ELA

Module 6 Florida Standards Math Module 7

ELA & Data Use

Module 8 Math & Data Use

Teachers Math

Leadership Teams

Session 4

Session3

ELAData Use

AssessmentsData

AnalysisVAM

Florida Standards

Data &ELA

Data &Math

Session 5

Session 6

Travel Notes

• Mileage to/from the trainings will be reimbursed to the school at $.445/mile (documentation with map and mileage required)

• Parking and tolls will also be reimbursed with receipt• Reimbursement is limited to two cars per school• Forms and directions to request reimbursement are available

under “Resources” on www.flcharterccrstandards.org• There are specific instructions included with the form to help

fill it out correctly• Reimbursements for substitutes are NOT an eligible expense

By the end of this session you will have:• Gained an initial understanding of the Florida Standards for Math

and the embedded changes and instructional shifts.

• Explored all eight of the Standards for Mathematical Practice and identified how they are related.

• Explored how practices can be clustered and examined why Practice 1: “Make sense of problems and persevere in solving them” and Practice 6: “Attend to precision” are considered the two “umbrella” standards that describe the habits of mind of successful mathematical thinkers.

Focus on Standards for Mathematical Practice Outcomes

By the end of this session you will have:• Identified evidence of the Practices, with focus on Practices 1 and

6, in Florida Standards aligned mathematics tasks.

• Discussed descriptors for all eight Practices, and created formal grade level descriptions for Practice 1 and Practice 6.

• Explored how specific instructional strategies (e.g., questioning, engaging students in mathematical discourse, and requiring multiple representations) can help students meet the major learning goals identified as part of Florida’s “New Way to Work.”

• Identified relevant resources for implementing the Florida Standards for Math and created a peer support network.

Focus on Standards for Mathematical Practice Outcomes (cont'd)

Module 2ELA

Module 1 Data Use

Module 3Math

Module 4 Data Use

Module 5 ELA

Module 6 Math

Module 7 ELA & Data

Module 8Math &

Data Use

You Are Here

8 Components of Full Florida Standards Implementation

Welcome and Introductions• Pre-Assessment• Establishing a Positive Working Environment• Overview of the Florida Standards for Math• Understanding the Standards for Mathematical

Practice: Developing Mathematical ExpertiseLunch• Supporting Students to Make Sense of Problems

and Persevere in Solving Them• Attending to Precision in Every Lesson• Teaching the Standards for Mathematical Practice• The Right Support at the Right Time• Next Steps• Post-AssessmentWrap Up

Today’s Agenda

Pre-Assessment

Introductory Activity

Guide Page

Establishing a Positive Working Environment

Section 1

• In a conversation, what is something that encourages you to speak your mind?

• What is something that deters you from expressing your ideas?

Activity 1: Setting Norms for Productive Work

How can we work well together?

Guide Page

Alignment to the Content Standards but not the Practice Standards

DOES NOT EQUAL Florida Standards Aligned

Important Point

Overview of the Florida Standards for Math

Section 2

Quick Write: What do you know about the Florida Standards for Math?

Activity 2a: What Do We Know?

Guide Page

Discuss: What does your group know about the Florida Standards for Math?

What’s in the Florida Standards for Math?

• The Standards for Mathematical Content• The Standards for Mathematical Practice

What’s New About the Florida Standards for Math?

Focus Coherence Rigor

Fewer standards allow for focusing on the major work for each grade

The Standards are designed around coherent progressions and conceptual connections.

Coherence

Grade 7 Grade 8 AlgebraAnalyze proportional relationships and use

them to solve real-world and mathematical

problems.

Understand the connections between

proportional relationships, lines, and linear equations.

Create equations that describe numbers or

relationships.

Guide Page

Coherence

Expressing Geometric Properties with Equations G-Gpe

Translate between the geometric description and the equation for a conic section

Use coordinates to prove simple geometric theorems algebraically

The major topics at each grade level focus equally on:

Much more on this in the next Florida Standards for Math Sessions:

Modules 6 & 8

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

Activity 2b: Then, Now and in the Future

Teaching Mathematics

Then Now In the Future

Guide Page

“A New Way to Work”

Florida’s Instructional Shifts

Before planning units:

1. Refer to the way the standards have been “chunked” within the course description

2. Identify the major learning goals for the unit

3. Create progress scales for each goal

4. Develop lesson plans and formative assessments to differentiate instruction

Much more on this in Modules 6 & 8

Phil Daro

Phil Speaks

Teaching Mathematics

Then Now In the Future

Guide Page

Change Isn’t EasyStages of Change

Achievethecore.org

Guide Page

Let’s Take A Break…

Be back in 10 minutes…

Understanding the Standards for

Mathematical Practice: Developing

Mathematical Expertise

Section 3

Guide Pages14-23

SMP 1: Make sense of problems and persevere in solving them

What does it mean to make sense of a

problem?

What does it mean to persevere in

solving a problem?

Mathematically proficient students:

Understand the meaning of the problem

• Look for ways to start working on the problem

Analyze the information

• Design a plan

Monitor and evaluate their progress

• Change course as necessary

Check their answers to problems

• Know if their answer makes sense

Farmer Lebowski has some chickens and some cows in her yard. Together, the animals have a total of 90 heads and

286 legs. How many chickens and how many cows are in the yard? Find a way

to solve this problem that does not involve algebra.

Instructional SupportsDon’t be afraid to challenge students! Ask clarifying questions such as:

What is the problem asking? How could you start the problem?What tools might be helpful? How can you check this?Does your answer make sense? How could you make this easier to

solve?

Instructional Supports Create ‘I Can’ statements for your students so they know what

is expected. Example 1

• I can tell you what the problem is asking me to do.

Example 2

• I can keep working on a problem even when I encounter difficulties.

SMP 2: Reason abstractly and quantitatively

What does it mean to reason

Abstractly? Quantitatively?

Mathematically proficient students:

Make sense of quantities and relationships Represent a problem symbolically Consider the units involved Understand and use properties of operations

Contextualize

Decontextualize

Eighth graders are going on a field trip. There are 167 students going. How many buses are needed for the trip if each bus can hold 48 students?

Instructional Supports Don’t be afraid to challenge students!

Ask clarifying questions such as:What does the number___ represent in the problem?How can you represent the problem with symbols and numbers?Does your answer fit what the problem is asking?

is expected.

Example 1

• I can represent the problem with math symbols and numbers.

Example 2

• I can explain how my answer fits the problem.

“(Students) make conjectures and build a logical progression of statements to explore the truth of their conjectures.”

“Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.” Mathematics Standards

SMP 3: Construct viable arguments and critique the reasoning of others

Two more points…

Mathematically proficient students: Use definitions and previously established results in constructing

arguments Make conjectures and attempts to prove or disprove through examples

and counterexamples

Continuous

• In 2009, the maintenance budget for a school was $30,000 of a total budget of $500,000. In 2010, the figure was $31,200 of a total budget of $520,000. Inflation between 2009 and 2010 was 8 percent.

• Parents complain that the money spent on maintenance has increased.

• The maintenance manager for the school complains that the money for maintenance has decreased.

• The Principal maintains that, in fact, there has been no change in spending patterns at the school.

• Is it possible that everybody's opinion could be valid? Why or why not? Where do you stand?

SMP 3: Construct viable arguments and

critique the reasoning of others

Instructional Supports Don’t be afraid to challenge students! Create tasks that directly involve argumentation and

critique. Ask questions such as:

How can you prove that your answer is correct?What examples could prove or disprove your argument?How is your answer different from _____’s answer?What questions do you have for_____?

Instructional Supports Create ‘I Can’ statements for your students so they know

what is expected.

SMP 3: Construct viable arguments and

critique the reasoning of others

Example 1

• I can use mathematical language to explain my thinking.

Example 2

• I can prove my answer is right.

Example 3

• I can ask questions about others’ work.

What does it mean to model

with mathematics?

SMP 4: Model with mathematics

Mathematically proficient students: Apply reasoning to create a plan or analyze a real world

problem Apply formulas/equations Make assumptions and approximations to make a problem

simpler Check to see if an answer makes sense and change a model

when necessary Use all kinds of physical models, images and drawings,

graphs, tables, equations, etc.

On its menu, a restaurant has 3 different appetizers, 4 different entrées, and 2 different desserts. How many distinct meals of 1 appetizer, one entrée, and 1 dessert could you make from this menu? Show how you know.

Instructional Supports Don’t be afraid to challenge students! Do not interpret the standard too narrowly. Provide a problem and explicitly ask students to write the

equation or number sentence called for in the situation. Provide a model and ask students to create a situation that

matches. Apply a C-R-A sequence when helping students to progress their

thinking.

is expected.

Example 1

• I can record my thinking in many ways.

Example 2

• I can use mathematical notation as a tool to solve problems.

Two Sentence Summary

With your grade level team create a two sentence summary of what the Practice will look like in YOUR classroom.

Write your summary on the designated chart paper.

What tools do students have available?

SMP 5: Use appropriate tools strategically

Mathematically proficient students: Identify relevant math resources and use them to pose or solve

problems Make sound decisions about the use of specific tools Use technological tools to explore and deepen understanding of

concepts

Find all the ways you can divide a square in half.

Instructional Supports Don’t be afraid to challenge students! Have students brainstorm tools that they might use to

solve the problem during the problem introduction. Use students’ prior knowledge about how they used tools

to solve other problems. Make a variety of math tools available. Have students evaluate their choice of tool after they

have solved the problem.

Instructional Supports Create ‘I Can’ statements for your students so they

know what is expected.

Example 1

• I can appropriately use a variety of mathematical tools.

Example 2

• I can explain how and why a particular tool was useful to solve a problem

SMP 6: Attend to precision

Two things we know to be true

The study of mathematics entails the use of academic

language and the more it is used, the better the communication.

Getting a correct answer is still

important.

Mathematically proficient students: Communicate precisely using clear definitions State the meaning of symbols, calculate accurately and

efficiently Provide carefully formulated explanations Label accurately when measuring and graphing

Explain why all squares are rectangles but not all rectangles are squares.

Instructional Supports Don’t be afraid to challenge students! Be vigilant. Precision should become habit. Model the standard. Students will speak the language that you

speak. Ask questions such as:

What does the term/symbol ____ mean?What math words can you use?What labels will you need to use? Have you labeled everything correctly?

is expected.

Example 1

• I can work carefully and check my work.

Example 2

• I can use mathematical terminology to describe my work.

Example 3

• I can use math vocabulary and symbols, appropriately, correctly, and precisely.

What do they

mean by “structur

SMP 7: Look for and make use of structure

Mathematically proficient students: Look for patterns or structure Recognize the significance in concepts and models and can

apply strategies for solving related problems Look for the big picture or overview

5 x 7 + 3 x 7 = (5+3) x 7

= 8 x 7

How is the algorithm for multiplying 32 x 41 like the procedure for multiplying

(x+1)(x+3)?

Instructional Supports Don’t be afraid to challenge students! Take your time with this – it WILL come. Ask questions such as:

Why does this happen?How is ___ related to ___?What do you know about ___ that can help you figure this out?What patterns do you see?

Instructional SupportsCreate ‘I Can’ statements for your students so they

know what is expected.

Example

• I can use what I already know about numbers to solve new problems.

What does repeated

reasoning look like?

SMP 8: Look for and express regularity in repeated reasoning

Mathematically proficient students: Notice repeated calculations and look for general methods

and shortcuts Continually evaluate the reasonableness of their results

while attending to details and make generalizations based on findings

Solve problems arising in everyday life

___ X ___ = ___

8 X 10 = 80

9 X 10 = 90

10 X 10 = 100

11 X 10 = 110

12 X 10 = ?

Guess my rule

input output-1 10 31 52 73 9

Instructional Supports Don’t be afraid to challenge students! Take your time -- it WILL come. Ask questions such as:

What generalizations can you make?Can you find a shortcut to make the problem easier?How could this problem help you solve another problem?

is expected.

Example 1

• I can discover and use shortcuts.

Example 2

• I can generalize and articulate a pattern as a mathematical rule or function.

With your grade level team create a two sentence summary of what the Practice will look like in YOUR classroom.

Write your summary on the designated chart paper.

Two Sentence Summary

Pause and Reflect

Look back at all eight Practices. • Is there anything that you

want to add to your notes?• Do you have additional

questions right now?

Finding Relationships

Supporting Students to

"Make sense of problems and

persevere in solving them”

Section 4

Activity 4: Kites

A store sells kits to make kites. All the kites are quadrilaterals. Some are what we call “kite-shaped.” Others are rectangles, squares, rhombi, and four sided shapes with no particular characteristics. A kit has string, paper and two sticks to form the skeleton of the kite.

The store owner needs to know what sticks to put in the kits for each shape, and how to tell the purchaser how to put the sticks together for each shape.

Your job is to give the store owner information about making squares, rectangles, trapezoids, and typical kite shapes. For each shape list the sticks needed and how they should be put together.

Guide Page

I will….

Write three to four commitment statements that

will help students learn to ‘make sense of problems and persevere in solving them.’

Attending to Precision in Every Lesson

Section 5

Activity 5: Precision Video Observation

Guide Page

27Cathy Humphreys

Let’s Plan

With your grade level or course group, examine your task and determine the precise language, calculations, notations, and labeling you will expect to see and hear.

Precision does not mean that all students must solve the problem the exact same way. Students can still attend to precision while developing a personal strategy.

Guide Pages28-31

Let’s Take A Break…

Be back in 10 minutes…

Teaching with the Standards for

Mathematical Practice

Section 6

Activity 6: Through the Lens

Guide Page

Sorting and classifying equations

Asking Effective Questions

Well structured questions include three parts:1. An invitation to think2. A cognitive process 3. A specific topic

Guide Pages34-35

Use of Multiple Representations

Van de Walle, Karp, & Bay-Williams 2013. 24.NCTM, 2001.

Guide Page

Promoting Student Discourse

Guide Page

Review Steps to Getting Students Talking on page 37 in the Participant Guide.

What would you addto this list?

Pause and Reflect

Look back at all of your notes. • Is there anything that you

want to add to your notes?• Do you have additional

questions right now?

The Right Support at the Right Time

Section 7

CPALMS Charter

Guide Page

http://www.cpalms.org/project/cpalmscharter.aspx

Teaching Channel

Guide Page

http://www.teachingchannel.org

Edutopia

Guide Page

http://www.edutopia.org

America Achieves

Guide Page

http://commoncoreamericaachieves.org

Illustrative Mathematics

Guide Page

http://www.illustrativemathematics.org

Inside Mathematics

Guide Page

http://www.insidemathematics.org

Achieve the Core

Guide Page

http://www.achievethecore.org

Edmodo

Guide Page

http://www.edmodo.com

Next Steps

Section 8

• Determine how you will bring what you did today back to your school.

• Determine what questions your colleagues may have.

• What questions do you still have?

What's Your Plan?

By the end of this session you will have:• Gained an initial understanding of the Florida Standards for Math

and the embedded changes and instructional shifts.

• Explored all eight of the Standards for Mathematical Practice and identified how they are related.

• Explored how practices can be clustered and examined why Practice 1: “Make sense of problems and persevere in solving them” and Practice 6: “Attend to precision” are considered the two “umbrella” standards that describe the habits of mind of successful mathematical thinkers.

Focus on Standards for Mathematical Practice Outcomes

By the end of this session you will have:• Identified evidence of the Practices, with focus on Practices 1 and

6, in Florida Standards aligned mathematics tasks.

• Discussed descriptors for all eight Practices, and created formal grade level descriptions for Practice 1 and Practice 6.

• Explored how specific instructional strategies (e.g., questioning, engaging students in mathematical discourse, and requiring multiple representations) can help students meet the major learning goals identified as part of Florida’s “New Way to Work.”

• Identified relevant resources for implementing the Florida Standards for Math and created a peer support network.

Focus on Standards for Mathematical Practice Outcomes (cont'd)

Closing Activities

Module 2ELA

Module 1 Data Use

Module 3Math

Module 4 Data Use

Module 5 ELA

Module 6 Math

Module 7 ELA & Data

Module 8Math &

Data Use

What’s Next

Click to edit Master title style

Where Are You Now?

Assessing Your Learning

Post-Assessment and Session Evaluation

Guide Page

Thanks and see you next time!

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