module 3b for middle/high school teachers
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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 - PowerPoint PPT PresentationTRANSCRIPT
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
2
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
3
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
4
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
5
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
6
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
7
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)
8
Module 2ELA
Module 1 Data Use
Module 3Math
Module 4 Data Use
Module 5 ELA
Module 6 Math
Module 7 ELA & Data
Use
Module 8Math &
Data Use
You Are Here
10
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
11
Pre-Assessment
Introductory Activity
12
Guide Page
5
Establishing a Positive Working Environment
Section 1
13
• 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?
14
Guide Page
7
Alignment to the Content Standards but not the Practice Standards
DOES NOT EQUAL Florida Standards Aligned
Important Point
15
Overview of the Florida Standards for Math
Section 2
16
Quick Write: What do you know about the Florida Standards for Math?
Activity 2a: What Do We Know?
17
Guide Page
9
Discuss: What does your group know about the Florida Standards for Math?
What’s in the Florida Standards for Math?
18
• 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
Focus
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
10
The Standards are designed around coherent progressions and conceptual connections.
Coherence
The Standards are designed around coherent progressions and conceptual connections.
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:
Rigor
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
24
Then Now In the Future
Guide Page
11
“A New Way to Work”
Florida’s Instructional Shifts
25
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
Teaching Mathematics
27
Then Now In the Future
Guide Page
11
Change Isn’t EasyStages of Change
Achievethecore.org
28
Guide Page
12
Let’s Take A Break…
29
Be back in 10 minutes…
Understanding the Standards for
Mathematical Practice: Developing
Mathematical Expertise
Section 3
30
Guide Pages14-23
31
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?
SMP 1: Make sense of problems and persevere in solving them
32
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
SMP 1: Make sense of problems and persevere in solving them
33
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.
SMP 1: Make sense of problems and persevere in solving them
34
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?
SMP 1: Make sense of problems and persevere in solving them
35
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.
36
SMP 2: Reason abstractly and quantitatively
What does it mean to reason
Abstractly? Quantitatively?
37
Mathematically proficient students:
Make sense of quantities and relationships Represent a problem symbolically Consider the units involved Understand and use properties of operations
SMP 2: Reason abstractly and quantitatively
Contextualize
Decontextualize
38
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?
SMP 2: Reason abstractly and quantitatively
39
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?
SMP 2: Reason abstractly and quantitatively
40
Instructional Supports Create ‘I Can’ statements for your students so they know what
is expected.
SMP 2: Reason abstractly and quantitatively
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
41
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
SMP 3: Construct viable arguments and critique the reasoning of others
42
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
43
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_____?
SMP 3: Construct viable arguments and critique the reasoning of others
44
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
45
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?
46
SMP 4: Model with mathematics
47
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.
SMP 4: Model with mathematics
48
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.
SMP 4: Model with mathematics
49
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.
SMP 4: Model with mathematics
50
Instructional Supports Create ‘I Can’ statements for your students so they know what
is expected.
SMP 4: Model with mathematics
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
51
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
52
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
SMP 5: Use appropriate tools strategically
53
Find all the ways you can divide a square in half.
SMP 5: Use appropriate tools strategically
54
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.
SMP 5: Use appropriate tools strategically
55
Instructional Supports Create ‘I Can’ statements for your students so they
know what is expected.
SMP 5: Use appropriate tools strategically
56
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
57
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.
58
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
SMP 6: Attend to precision
Explain why all squares are rectangles but not all rectangles are squares.
SMP 6: Attend to precision
59
60
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?
SMP 6: Attend to precision
61
Instructional Supports Create ‘I Can’ statements for your students so they know what
is expected.
SMP 6: Attend to precision
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
e”?
SMP 7: Look for and make use of structure
62
63
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
SMP 7: Look for and make use of structure
5 x 7 + 3 x 7 = (5+3) x 7
= 8 x 7
64
How is the algorithm for multiplying 32 x 41 like the procedure for multiplying
(x+1)(x+3)?
SMP 7: Look for and make use of structure
65
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?
SMP 7: Look for and make use of structure
66
Instructional SupportsCreate ‘I Can’ statements for your students so they
know what is expected.
SMP 7: Look for and make use of structure
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
67
68
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
SMP 8: Look for and express regularity in repeated reasoning
___ X ___ = ___
8 X 10 = 80
9 X 10 = 90
10 X 10 = 100
11 X 10 = 110
12 X 10 = ?
69
Guess my rule
SMP 8: Look for and express regularity in repeated reasoning
input output-1 10 31 52 73 9
70
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?
SMP 8: Look for and express regularity in repeated reasoning
71
Instructional Supports Create ‘I Can’ statements for your students so they know what
is expected.
SMP 8: Look for and express regularity in repeated reasoning
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.
72
Two Sentence Summary
Pause and Reflect
73
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
74
75
Lunch
Supporting Students to
"Make sense of problems and
persevere in solving them”
Section 4
76
Activity 4: Kites
77
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
25
I will….
78
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
79
80
Activity 5: Precision Video Observation
Guide Page
27Cathy Humphreys
81
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…
82
Be back in 10 minutes…
Teaching with the Standards for
Mathematical Practice
Section 6
83
84
Activity 6: Through the Lens
Guide Page
33
Sorting and classifying equations
85
Asking Effective Questions
Well structured questions include three parts:1. An invitation to think2. A cognitive process 3. A specific topic
Guide Pages34-35
86
Use of Multiple Representations
Van de Walle, Karp, & Bay-Williams 2013. 24.NCTM, 2001.
Guide Page
36
87
Promoting Student Discourse
Guide Page
37
Review Steps to Getting Students Talking on page 37 in the Participant Guide.
What would you addto this list?
Pause and Reflect
88
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
89
90
CPALMS Charter
Guide Page
39
http://www.cpalms.org/project/cpalmscharter.aspx
91
Teaching Channel
Guide Page
39
http://www.teachingchannel.org
92
Edutopia
Guide Page
40
http://www.edutopia.org
93
America Achieves
Guide Page
40
http://commoncoreamericaachieves.org
94
Illustrative Mathematics
Guide Page
41
http://www.illustrativemathematics.org
95
Inside Mathematics
Guide Page
41
http://www.insidemathematics.org
96
Achieve the Core
Guide Page
42
http://www.achievethecore.org
97
Edmodo
Guide Page
42
http://www.edmodo.com
Next Steps
Section 8
98
• 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?
99
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
100
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)
101
Closing Activities
102
Module 2ELA
Module 1 Data Use
Module 3Math
Module 4 Data Use
Module 5 ELA
Module 6 Math
Module 7 ELA & Data
Use
Module 8Math &
Data Use
What’s Next
Click to edit Master title style
Where Are You Now?
Assessing Your Learning
104
Post-Assessment and Session Evaluation
Guide Page
44
Thanks and see you next time!
105