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Northwest Georgia RESA Mathematics Academy

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Title: Northwest Georgia RESA Mathematics Academy


1
Northwest Georgia RESA Mathematics Academy
2
  • 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

3
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
Northwest Georgia RESA Mathematics Academy
4
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.
Northwest Georgia RESA Mathematics Academy
5
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
Northwest Georgia RESA Mathematics Academy
6
  • 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

Northwest Georgia RESA Mathematics Academy
7
Creating and Managing a Student-Centered
Classroom with the Workshop Model
Northwest Georgia RESA Mathematics Academy
8
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).

Northwest Georgia RESA Mathematics Academy
9
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.

Northwest Georgia RESA Mathematics Academy
10
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.

Northwest Georgia RESA Mathematics Academy
11
Managing the Workshop
Northwest Georgia RESA Mathematics Academy
12
Managing the Workshop
  • Rituals and Routines
  • Establish requirements for constructive
    individual attempts before pair or group work
    begins.
  • Use a timer.

Northwest Georgia RESA Mathematics Academy
13
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

Northwest Georgia RESA Mathematics Academy
14
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.

Northwest Georgia RESA Mathematics Academy
15
Managing the Workshop
  • Status of the Class

Northwest Georgia RESA Mathematics Academy
16
Planning the Workshop
Title_______________________________
Standard(s)________________________
Northwest Georgia RESA Mathematics Academy
17
Content Topic Algebra Pedagogy Topic
Questioning Strategies and Techniques
Northwest Georgia RESA Mathematics Academy
18
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
Northwest Georgia RESA Mathematics Academy
19
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.
Northwest Georgia RESA Mathematics Academy
20
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).
  •  
  •  

Northwest Georgia RESA Mathematics Academy
21
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.
  •  

Northwest Georgia RESA Mathematics Academy
22
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).
  •  
  •  
  •  

Northwest Georgia RESA Mathematics Academy
23
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.
  •  
  •  

Northwest Georgia RESA Mathematics Academy
24
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
  •  

Northwest Georgia RESA Mathematics Academy
25
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
Northwest Georgia RESA Mathematics Academy
26
  • 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

Northwest Georgia RESA Mathematics Academy
27
What do all of these skills have in common? They
can all be directly correlated to good
questioning.
Northwest Georgia RESA Mathematics Academy
28
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
Northwest Georgia RESA Mathematics Academy
29
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
Northwest Georgia RESA Mathematics Academy
30
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
Northwest Georgia RESA Mathematics Academy
31
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.

Northwest Georgia RESA Mathematics Academy
32
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.

Northwest Georgia RESA Mathematics Academy
33
Questioning
  • Require justification of true/false statements.
  • Explain how to

Northwest Georgia RESA Mathematics Academy
34
Questioning
  • Write your own problem and solve it.
  • Explain the mistakes in the given solution.

Northwest Georgia RESA Mathematics Academy
35
Questioning
  • What is this problem asking?
  • Is this answer reasonable? Why or why not?

Northwest Georgia RESA Mathematics Academy
36
Questioning
  • Give an example when this strategy would not work.
  • How can you make sure your answer is correct?

Northwest Georgia RESA Mathematics Academy
37
Questioning
  • Explain 3 ideas that you have learned in todays
    lesson.
  • Describe a type of problem that is still unclear
    to you.

Northwest Georgia RESA Mathematics Academy
38
Questioning
  • What would happen if
  • Tell me anything and everything you know about

Northwest Georgia RESA Mathematics Academy
39
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?

Northwest Georgia RESA Mathematics Academy
40
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.

Northwest Georgia RESA Mathematics Academy
41
Multiple Representations
Northwest Georgia RESA Mathematics Academy
42
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

Northwest Georgia RESA Mathematics Academy
43
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)

Northwest Georgia RESA Mathematics Academy
44
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)

Northwest Georgia RESA Mathematics Academy
45
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)

Northwest Georgia RESA Mathematics Academy
46
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.

Northwest Georgia RESA Mathematics Academy
47
Task time
lets collaborate!
Northwest Georgia RESA Mathematics Academy
48
Decorating for the Dance
Northwest Georgia RESA Mathematics Academy
49
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
50
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
51
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.
Northwest Georgia RESA Mathematics Academy
52
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.

Northwest Georgia RESA Mathematics Academy
53
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.

Northwest Georgia RESA Mathematics Academy
54
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?

Northwest Georgia RESA Mathematics Academy
55
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
56
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
57
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.
Northwest Georgia RESA Mathematics Academy
58
Opening
  • The following clip is entitled High-Priced
    Fashion.
  • As you view the clip, make note of 5 important
    and interesting ideas.

Northwest Georgia RESA Mathematics Academy
59
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?

Northwest Georgia RESA Mathematics Academy
60
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 .
Northwest Georgia RESA Mathematics Academy
61
Opening
  • Explain what these pictures mean in terms of
    supply and demand.

Northwest Georgia RESA Mathematics Academy
62
Opening
  • Explain what these pictures mean in terms of
    supply and demand.

Northwest Georgia RESA Mathematics Academy
63
Opening
  • Explain what these pictures mean in terms of
    supply and demand.

Northwest Georgia RESA Mathematics Academy
64
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?
Northwest Georgia RESA Mathematics Academy
65
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.

Northwest Georgia RESA Mathematics Academy
66
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!

Northwest Georgia RESA Mathematics Academy
67
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
68
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
69
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.
Northwest Georgia RESA Mathematics Academy
70
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
72
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
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