Northwest Georgia RESA Mathematics Academy

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Northwest Georgia RESA Mathematics Academy
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• Northwest Georgia RESA Mathematics Academy
• North Paulding High School
• Dallas, Georgia
• November 13, 2008
• Dexter Mills, Executive Director
• Karen Faircloth, Director of School
• Improvement Professional
• Learning

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Contact Information
Terry Haney, Math Coordinator Northwest Georgia
RESA 3167 Cedartown Hwy., SE Rome, Georgia
30161 706-295-6189 (EXT. 20) 706-295-6098
(FAX) 256-630-8362 (CELL) thaney_at_nwgaresa.com
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Purpose The purpose of the Northwest Georgia
RESA Mathematics Academy is to provide ongoing
professional learning experiences for district
teams in mathematics.  Each team should consist
of at least one representative from each of the
following curriculum bands  3-4, 5-6, 7-8 and
Math I.  Members of the teams may be teachers
and/or academic coaches, along with a
building-level and system-level administrator. 
Each of the meetings will begin with a brief
whole group session.  Each representative will
then attend a session based on his or her
appropriate curriculum band.  During this
extended session, instructors for all curriculum
bands will address one specific content strand
(algebra, geometry, numbers and operations, data
analysis) by facilitating work on performance
tasks and pedagogy.    Other topics may include
data-driven teaching and learning,
characteristics of the standards-based
classroom,  and ACTION planning for mathematics. 
Each system-level team will reassemble at the
end of the day to analyze the progression of
content across the grade bands and to plan
methods of redelivery within their system.
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Facilitators for each Curriculum Band Claire
Pierce, Math I Independent Consultant former
DOE Math Program Manager Terry Haney, Grades
7-8 Math Coordinator for Northwest Georgia
RESA Jason Pelham, Grades 5-6 Assistant
Principal at Lakeview Middle School in Catoosa
County RESA Math Consultant Danny Lowrance,
Grades 3-4 Math Specialist at W.L. Swain
Elementary School in Gordon County
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• Questions, concerns, and comments from our
  previous session
• Building the Data Analysis Ladder
• GAISE Report
• Instructional Framework The Workshop Model
• Instructional Framework Rituals and Routines
• Tasks Congress and Pizza
• People, Congress, and Pizza
• Predicting

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Creating and Managing a Student-Centered
Classroom with the Workshop Model
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Opening

• Teacher-centered
• The teacher is giving notes,
• explaining a process, modeling
• a process, etc.
• Students are involved
• -taking notes,
• -asking questions, and/or
• -sharing information
• NOT the longest portion of class
• Time will vary with the difficulty of
• subject matter and amount of time
• spent on content previously (approximately
• 20 minutes or less based on 90-minute block).

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Work Period

• Student-centered
• There are varying combinations of
• working alone, working in pairs, and
• working in small groups.
• There is a mix of
• authentic, real-world applications,
• multiple representations, showing
• work, explaining processes, inquiry,
• skills practice.
• Connections to standards are obvious to everyone
  .
• Teachers involved
• Constantly monitoring for engagement physically
  present in the work area, and/or holding
  individual or group conferences.

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Closing

• Student-centered
• Students take responsibility for teaching or
  sharing what
• they have learned. Students are speaking
  intelligently
• about work and standards, using the language of
  the
• standards and content terminology.
• Includes such activities as sharing work, sharing
  ideas, discussing what theyve learned,
  presenting solutions to problems, talking about
  how their work meets the standard.
• Teachers involved
• Choose students to share and let them prepare
  during the
• work period monitor and push discussion toward
  the standard.

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Managing the Workshop
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Managing the Workshop

• Rituals and Routines
• Establish requirements for constructive
  individual attempts before pair or group work
  begins.
• Use a timer.

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Managing the Workshop

• Rituals and Routines
• Create a systematic procedure
• for students to receive assistance
• SELF (notes, book, anchor charts, word wall,
  manipulatives, etc.)
• PARTNER OR GROUP MEMBERS
• TEACHER

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Managing the Workshop

• Rituals and Routines
• Teacher serves as facilitator during the work
  period and the closing.
• Monitor student progress using a status of the
  class form.
• Allow students to explain concepts and
  procedures
• to you.
• Respond to their questions with more probing
  questions.

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Managing the Workshop

• Status of the Class

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Planning the Workshop
Title_______________________________
Standard(s)________________________
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Content Topic Algebra Pedagogy Topic
Questioning Strategies and Techniques
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Essential Questions How do I effectively
integrate the Algebra standards into the
mathematics curriculum? How do the Algebra
standards build across the curriculum bands? How
do I effectively implement high- impact
questioning strategies in the mathematics
classroom
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Building the Algebra Curriculum Ladder

•  
•  

We will build the Algebra Curriculum Ladder to
show the scope of topics addressed in grades
K-10. Your handout contains a list of
statements taken directly from the Algebra strand
of the Georgia Performance Standards at each
grade level. The statements are listed in random
order. Cut the statements apart and reorder them
as they would be addressed in the K-10
curriculum. You will have about 15 minutes to
complete this process in your small groups. Be
prepared to share your thoughts on the process.
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Building the Algebra Curriculum Ladder

• K Students will identify, create, extend, and
  transfer patterns from one representation to
  another.
•  
• 1 Students will build number patterns using
  various concrete representations.
• 2 Students will represent and interpret
  quantities and relationships using mathematical
  expressions and symbols (, lt, gt).
•  
•  

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Building the Algebra Curriculum Ladder

• 3 Students will use mathematical expressions to
  represent relationships between quantities and
  interpret given expressions. This will include
  describing and extending patterns, describing and
  explaining a relationship represented by a
  formula, and using a symbol to represent an
  unknown and finding the value of the unknown.
• 4 Students will represent and interpret
  mathematical relationships in quantitative
  expressions. They will understand and apply
  patterns and rules, represent unknowns using
  symbols, and write and evaluate mathematical
  expressions.
•  
• 5 Students will represent and interpret the
  relationship between quantities algebraically.
  They will use variables for unknown quantities in
  algebraic expressions and investigate simple
  algebraic expressions. They will also determine
  that a formula will be reliable regardless of the
  type of number substituted for the variable.
•  

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Building the Algebra Curriculum Ladder

• 6 Students will understand the concept of ratio
  and use it to represent quantitative
  relationships. They will consider relationships
  between varying quantities which includes
  analyzing and describing patterns from rules,
  tables, and graphs using manipulatives and
  drawings to solve problems involving proportional
  relationships describing and graphing
  proportional relationships using y kx using
  proportional reasoning to solve problems.
• Students will also evaluate algebraic
  expressions, including those with exponents, and
  solve simple one-step equations using each of the
  four basic operations.
• 7 Students will represent and evaluate
  quantities using algebraic expressions. This
  includes translating verbal phrases to algebraic
  expressions simplifying and evaluating
  expressions using commutative, associative, and
  distributive properties adding and subtracting
  linear expressions. Students will also
  understand and apply linear equations in one
  variabledefine a variable, write an equation,
  solve the equation, and interpret the solution.
  Students will be able to use addition and
  multiplication properties of equality to solve
  one- and two-step linear equations.
• Students will understand relationships between
  two variables. They will plot points on the
  coordinate plane represent, describe, and
  analyze relations from tables, graphs, and
  formulas describe how change in one variable
  affects the other variable describe patterns in
  the graphs of proportional relationships, both
  direct (y kx) and inverse (y k/x).
•  
•  
•  

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Building the Algebra Curriculum Ladder

• 8 Students will use algebra to represent,
  analyze, and solve problems. This includes
  representing a situation using expressions or
  equations in one variable simplifying algebraic
  expressions solving algebraic equations in one
  variable (including absolute value) solving
  equations involving several variables for one
  variable in terms of the others interpreting
  solutions in problem contexts. Students will
  also understand and graph inequalities in one
  variable.
• Students will understand relations and linear
  functions. They will recognize a relation as a
  correspondence between varying quantities
  recognize a function as a correspondence between
  inputs and outputs where the output for each
  input must be unique use tables to describe
  sequences recursively. Students will graph and
  analyze graphs of linear equations and
  inequalities (interpreting slope as rate of
  change determining the meaning of slope in a
  given situation graphing equations of the form y
  mx b and ax by c solving problems
  involving linear relationships).
• Students will understand systems of linear
  equations and inequalities and use them
• to solve problems. This includes writing
  systems for a context, solving the system,
• and interpreting the solution in context.
•  
•  

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Building the Algebra Curriculum Ladder

• Math I Students will explore and interpret
  characteristics of functions, using graphs,
  tables, and simple algebraic techniques. They
  will also graph transformations (including
  vertical shifts, stretches and shrinks, and
  reflections across the x and y axes) investigate
  and explain characteristics of functions (domain,
  range, zeros, intercepts, intervals of increase
  and decrease, maximum and minimum values, and end
  behavior) determine graphically and
  algebraically whether a function has symmetry and
  whether it is even, odd, or neither.
• Students will factor expressions by GCF,
  grouping, trial and error, and special products.
  They will simplify and operate with radical
  expressions, polynomials, and rational
  expressions. They will also solve simple
  quadratic and radical equations
•  

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According to Wagner, seven survival skills are
imperative to our students success in the new
world of work. From Educational Leadership
October, 2008 Rigor Redefined by Tony Wagner
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• Critical Thinking and Problem Solving
• Collaboration and Leadership
• Agility and Adaptability
• Initiative and Entrepreneurialism
• Effective Oral and Written Communication
• Accessing and Analyzing Information
• Curiosity and Imagination
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner

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What do all of these skills have in common? They
can all be directly correlated to good
questioning.
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The heart of critical thinking and problem
solving is the ability to ask the right
questions. From Educational Leadership October,
2008 Rigor Redefined by Tony Wagner
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Read What role does teacher questioning play in
learning mathematics? In your small groups,
discuss specific ideas or strategies that your
have tried or ones that you feel will be most
important for you to implement in your classroom.
Make a list of these strategies on chart paper.
Be prepared for whole group discussion. From ED
Thoughts (2002) What We Know About Mathematics
Teaching and Learning J.S. Sutton and A. Krueger
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If you want to build a shipdont herd people
together to collect wood and dont assign them
tasks and work, but rather teach them to long for
the endless immensity of the sea. Antoine de
Saint-Exupéry
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Questioning

• Encourage and support questioning and discussion
  from the first day of class.

• Take multiple answers from students and allow
  them decide which one is correct.

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Questioning

• Stress the logic of mathematics and how
  mathematical definitions are very similar to
  meanings they already know.

• Require that students show all of their work.

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Questioning

• Require justification of true/false statements.

• Explain how to

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Questioning

• Write your own problem and solve it.

• Explain the mistakes in the given solution.

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Questioning

• What is this problem asking?

• Is this answer reasonable? Why or why not?

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Questioning

• Give an example when this strategy would not work.

• How can you make sure your answer is correct?

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Questioning

• Explain 3 ideas that you have learned in todays
  lesson.

• Describe a type of problem that is still unclear
  to you.

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Questioning

• What would happen if

• Tell me anything and everything you know about

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Sample QuestionsActivating Prior Knowledge

• AN INTRODUCTION TO THE CONCEPT OF IRRATIONAL
  NUMBERS
• Yesterday, Mr. Haney behaved in a rational way.
  He assigned 5 review problems for homework.
  Today, he was completely irrational and assigned
  75 problems. In your own words, explain what
  this means. How can you relate your explanation
  to mathematics and what you already know about
  rational numbers?

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Sample QuestionsActivating Prior Knowledge

• A WARM-UP TO INTRODUCE CIRCUMFERENCE
• Explain the meaning of each underlined word.
• Ferdinand Magellans crew was the first
• to circumnavigate the globe.
• Mr. Haney was born circa 1970.
• Mrs. Martin wants you to calculate the
• circumference of a circle.

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Multiple Representations
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Good questions should

• Monitor for meaning
• Activate prior knowledge
• Use sensory and emotional images
• Require students to make predictions and
  inferences
• Help determine importance
• Require students to synthesize information
• Adapted from 7 Metacognitive Strategies from
  Mosaic of Thought by Ellin Oliver Keene and Susan
  Zimmerman

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A Few SamplesPositive and Negative Numbers

• Tell me anything that you already know about
  positive and negative numbers. (activating prior
  knowledge)
• Imagine a thermometer at 15 degrees. What will
  the thermometer look like if the temperature
  falls 20 degrees? (visualizing)
• Find examples of positive and negative numbers in
  your text. Think of a time when you have worked
  with negative numbers or have seen them. Name 2
  situations in real life when you have seen
  positive and negative numbers. (making
  connections)

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A Few SamplesPositive and Negative Numbers

• What do you think will happen when you add,
  subtract, multiply, or divide positive and
  negative numbers? (make predictions--inferring)
• From the examples you have seen so far, what
  types of patterns are emerging? (inferring)

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A Few SamplesPositive and Negative Numbers

• What are integers? How are integers used?
  Demonstrate how to use a number line to make
  integer calculations. Do you think the patterns
  and rules that you have discovered will work with
  all numbers or only with integers. Say why.
  (explainingmaking predictions)
• Why do you think it is important to know about
  integers? Create 3 real-life situations in which
  a knowledge of integers would be required. Then
  solve the problems and show all of your work.
  (synthesizing)

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Designing Content-Specific Questions and Prompts

• Using specific topics from your current unit of
  study or an upcoming unit and strategies that we
  have discussed, design 5-10 questions and/or
  prompts. You may want to think about designing
  questions from simple to complex. You may also
  want to consider different ways to ask the same
  question as a means of differentiation.

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Task time
lets collaborate!
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Decorating for the Dance
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GEORGIA PERFORMANCE STANDARDS M7A3. Students
will understand relationships between two
variables. a. Plot points on a coordinate
plane. b. Represent, describe, and analyze
relations from tables, graphs, and
formulas. c. Describe how change in one
variable affects the other variable. d.
Describe patterns in graphs of proportional
relationships, both direct (y kx) and
inverse (y k/x). M8A4. Students will graph and
analyze graphs of linear equations and
inequalities. c. Graph equations of the
form y mx b. f. Determine the equation
of a line given a graph, numerical infor-
mation that defines the line, or a context
involving a linear relationship. g.
Solve problems involving linear relationships.
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GEORGIA PERFORMANCE STANDARDS M8A5. Students
will understand systems of linear equations and
inequalities and use them to solve problems.
a. Given a problem context, write an
appropriate system of linear equations
or inequalities. b. Solve systems of linear
equations graphically and algebraically
using technology as appropriate. d.
Interpret solutions in problem contexts.
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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Opening

• Take 5 minutes to answer these questions. Write
  your answers in complete sentences.
• What mathematical ideas would you need to
  consider and use if you were planning a 7th grade
  dance for your classmates? Give at least 3
  specific examples.
• Are these the same ideas that would need to be
  considered when planning a dance for the entire
  school? What are the similarities and
  differences?
• What other real life situations would involve the
  same mathematical ideas? Give at least 3
  specific examples.

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Work Period

• Begin working alone on the Decorating for the
  Dance activity. When the timer rings, you may
  begin working with your group.
• Be prepared to discuss your work with the whole
  class during our closing.

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Closing

• How did the items in this task relate to the
  examples you gave in your opening questions?
• What did you notice about the graphs your created
  in this task?
• If you were actually planning a dance, do you
  think the numbers and the information in this
  task would be accurate or would you have to make
  adjustments? Explain your thinking!
• What is meant by the term constant of
  proportionality?

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GEORGIA PERFORMANCE STANDARDS M7A3. Students
will understand relationships between two
variables. a. Plot points on a coordinate
plane. b. Represent, describe, and analyze
relations from tables, graphs, and
formulas. c. Describe how change in one
variable affects the other variable. d.
Describe patterns in graphs of proportional
relationships, both direct (y kx) and
inverse (y k/x). M8A4. Students will graph and
analyze graphs of linear equations and
inequalities. c. Graph equations of the
form y mx b. f. Determine the equation
of a line given a graph, numerical infor-
mation that defines the line, or a context
involving a linear relationship. g.
Solve problems involving linear relationships.
Northwest Georgia RESA Mathematics Academy
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GEORGIA PERFORMANCE STANDARDS M8A5. Students
will understand systems of linear equations and
inequalities and use them to solve problems.
a. Given a problem context, write an
appropriate system of linear equations
or inequalities. b. Solve systems of linear
equations graphically and algebraically
using technology as appropriate. d.
Interpret solutions in problem contexts.
Northwest Georgia RESA Mathematics Academy
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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Opening

• The following clip is entitled High-Priced
  Fashion.
• As you view the clip, make note of 5 important
  and interesting ideas.

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Opening

• In your opinion, what were the most interesting
  and most important points in the clip?
• How do you think this clip is related to
  mathematics?
• What is the meaning of the phrase supply and
  demand? How does this clip relate to the idea of
  supply and demand? How do you think this idea
  can be related to mathematics?

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John Stossel has 3 FREE DVDs available. All of
them feature clips of high-interest news stories
and interviews that can be used for a variety of
classes and lessons. Each one comes with a
supplemental teachers guide. You can request
free copies of the DVDs at www.stosselintheclassr
oom.org .
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Opening

• Explain what these pictures mean in terms of
  supply and demand.

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Opening

• Explain what these pictures mean in terms of
  supply and demand.

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Opening

• Explain what these pictures mean in terms of
  supply and demand.

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Opening
Based on the pictures you just saw, what kinds of
relationships exist with respect to supply and
demand? How could these relationships be related
to our study of equations? to our study of
systems of equations?
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Work Period

• Begin working in small groups on the Supply and
  Demand task.
• Be prepared to discuss your work with the whole
  class. Some students will be selected to present
  key problems and solutions to the class.

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Closing

• What do you notice about the graphs you created
  in this task?
• Explain how and why companies would need to
  understand systems of linear equations.
• Do you feel that these models will always provide
  exact information? reliable information?
  Explain!

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GEORGIA PERFORMANCE STANDARDS M7A3. Students
will understand relationships between two
variables. a. Plot points on a coordinate
plane. b. Represent, describe, and analyze
relations from tables, graphs, and
formulas. c. Describe how change in one
variable affects the other variable. d.
Describe patterns in graphs of proportional
relationships, both direct (y kx) and
inverse (y k/x). M8A4. Students will graph and
analyze graphs of linear equations and
inequalities. c. Graph equations of the
form y mx b. f. Determine the equation
of a line given a graph, numerical infor-
mation that defines the line, or a context
involving a linear relationship. g.
Solve problems involving linear relationships.
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GEORGIA PERFORMANCE STANDARDS M8A5. Students
will understand systems of linear equations and
inequalities and use them to solve problems.
a. Given a problem context, write an
appropriate system of linear equations
or inequalities. b. Solve systems of linear
equations graphically and algebraically
using technology as appropriate. d.
Interpret solutions in problem contexts.
Northwest Georgia RESA Mathematics Academy
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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GEORGIA PERFORMANCE STANDARDS M7A3. Students
will understand relationships between two
variables. a. Plot points on a coordinate
plane. b. Represent, describe, and analyze
relations from tables, graphs, and
formulas. c. Describe how change in one
variable affects the other variable. d.
Describe patterns in graphs of proportional
relationships, both direct (y kx) and
inverse (y k/x). M8A4. Students will graph and
analyze graphs of linear equations and
inequalities. c. Graph equations of the
form y mx b. f. Determine the equation
of a line given a graph, numerical infor-
mation that defines the line, or a context
involving a linear relationship. g.
Solve problems involving linear relationships.
Northwest Georgia RESA Mathematics Academy
71
GEORGIA PERFORMANCE STANDARDS M8A5. Students
will understand systems of linear equations and
inequalities and use them to solve problems.
a. Given a problem context, write an
appropriate system of linear equations
or inequalities. b. Solve systems of linear
equations graphically and algebraically
using technology as appropriate. d.
Interpret solutions in problem contexts.
Northwest Georgia RESA Mathematics Academy
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M7P1. Students will solve
problems. M7P2. Students will reason and
evaluate mathematical arguments. M7P3. Students
will communicate mathematically. M7P4. Students
will make connections among mathematical ideas
and to other disciplines. a. Recognize
and use connections among mathematical ideas.
b. Understand how mathematical ideas connect and
build on one another to produce a
coherent whole. c. Recognize and apply
mathematics in contexts outside of
mathematics. M7P5. Students will represent
mathematics in multiple ways. a. Create and
use representations to organize, record, and
communicate mathematical ideas. b.
Select, apply, and translate among mathematical
rep- resentations to solve problems.
c. Use representations to model and interpret
physical, social, and mathematical
phenomena.
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Essential Questions How do I effectively
integrate the Algebra standards into the
mathematics curriculum? How do the Algebra
standards build across the curriculum bands? How
do I effectively implement high- impact
questioning strategies in the mathematics
classroom
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Questions, Comments, and Concerns

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For our February session, read Never Say
Anything a Kid Can Say! If you are searching
for some simple strategies to increase student
efficacy and student achievement, try some
specifics from this article. Be prepared to
share your thoughts about the strategies that you
implement. From Mathematics Teaching in the
Middle School (2000) by Steven C. Reinhart
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Contact Information
Terry Haney, Math Coordinator Northwest Georgia
RESA 3167 Cedartown Hwy., SE Rome, Georgia
30161 706-295-6189 (EXT. 20) 706-295-6098
(FAX) 256-630-8362 (CELL) thaney_at_nwgaresa.com
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Northwest Georgia RESA Mathematics Academy