Northwest Georgia RESA Mathematics Academy

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• Northwest Georgia RESA Mathematics Academy
• Heritage High School
• Ringgold, Georgia
• March 5, 2009
• 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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Content Topic Algebra Pedagogy Topic
Assessing the Algebra of Math I
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Essential Questions Why should I post the
standards in my classroom? How do I effectively
integrate the Algebra standards into the
mathematics curriculum? How can I maximize the
positive impact of assessment on students
learning?
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Agenda

• 900 DOK Review
• 915 Poster Task
• 1130 Lunch
• 1215 Assessing to Learn and Learning to
  Assess
• 1245 Fairfield Aviation
• 215 Final sharing

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How are the questions categorized? Questions are
coded by DOK (Depth of Knowledge) Levels.
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Depth of Knowledge

• Powerful tool to determine the relationship
  between Instruction and Assessment in terms of
  cognitive demand
• Initially developed in collaboration with CCSSO
  (Council of Chief State School Officers)
• By late 2005, used in over 17 states and other
  countries More have joined since then.
• Aligns state tests, standards, curriculum

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Table Talk

• Read the descriptors for each level of
  mathematics. Annotate/highlight key terms and
  ideas.
• Discuss the progressions of cognitive complexity
  evidenced in the levels.
• How might this tool be used to impact classroom
  assessment and instruction?
• Be prepared to briefly share with the whole group.

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More About Level 4

• DOK 4 requires high cognitive demand and is very
  complex. Students are expected to make
  connections relate ideas within the content or
  among content areasand have to select or devise
  one approach among many alternatives on how the
  situation can be solved.
• Due to the complexity of cognitive demand, DOK 4
  often requires an extended period of time.

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Depth of Knowledge Levels
Given the equation below, find the x and y
intercepts.
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Depth of Knowledge Levels
In the adjacent figure, a camera is positioned in
front of a mural on a wall. Letting the wall
represent the x axis and the camera lens lie on
the y axis, the line of site for the photographer
can be modeled by the function
.
How far from the mural is the camera? How wide is
the part of the mural the photograph will capture?
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Based on the rigor of our Georgia Performance
Standards Mathematics Curriculum, 55 of the
questions on the CRCT/EOCT must be at DOK 2 or
above.
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Where do I find sample assessments?

• OAS Mathematics I Midterm
• Mathematics I Teacher Edition
• NAEP Sample Items
• Unit Assessments
• GaDOE Testing Site EOCT Student Guide
• Released Test Items on Massachusetts and Virginia
  state websites
• Phillips Exeter website

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Task 2 Creating a EOCT Poster
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Warm-up

• Answer the following questions in complete
  sentences. You have 5 minutes.
• What are some strategies that you use when taking
  a test like the EOCT?
• How do you approach a problem when you are
  uncertain of the correct answer.
• Most tests like the EOCT have one correct answer
  and three incorrect answers for each item. How
  do you think test writers get their incorrect
  answer choices?

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Opening

• You will be assigned four problems from the
  benchmark test that you have been given. All
  problems address algebra standards from Units 1
  and 2 of Math I. For each problem you will
• Work the problem
• Determine the DOK level
• Give a brief description of the standards
  addressed by the problem
• Give an explanation for the correct answer,
  showing all work
• For each distracter, give a detailed description
  of why the
• answer is incorrect. Include any thoughts you
  may have related to student misconceptions or
  misunderstandings.

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Work Period

• Begin working with your group to create and/or
  solve problems for your poster.
• You should work through each problem on notebook
  paper and make certain that your group members
  agree on the answer before writing it on the
  poster.
• Discuss information about common mistakes and
  misconceptions with your group members.

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Closing

• During the worktime, your group received a card
  with a DOK level. Choose a problem from your
  poster with the indicated DOK level and be
  prepared to present this problem to the class.
  Each member of your group should discuss at least
  one specific aspect of the problem (DOK level,
  correct answer, standards addressed, common
  mistakes and misconceptions, or descriptions of
  the distracters). All areas should be addressed.

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GEORGIA PERFORMANCE STANDARDS Mathematics 1
ALGEBRA Students will explore functions and
solve simple equations. Students will simplify
and operate with radical, polynomial, and
rational expressions. MM1A1. Students will
explore and interpret the characteristics of
functions, using graphs, tables, and simple
algebraic techniques. a. Represent functions
using function notation. b. Graph the basic
functions f(x) xn, where n 1 to 3, f(x) ,
f(x) x, and f(x) . c. Graph
transformations of basic functions including
vertical shifts, stretches, and shrinks, as well
as reflections across the x- and y-axes. d.
Investigate and explain the characteristics of a
function domain, range, zeros, intercepts,
intervals of increase and decrease, maximum and
minimum values, and end behavior.
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• GEORGIA PERFORMANCE STANDARDS
• Mathematics 1
• e. Relate to a given context the characteristics
  of a function, and use graphs and tables to
  investigate its behavior.
• f. Recognize sequences as functions with domains
  that are whole numbers.
• g. Explore rates of change, comparing constant
  rates of change (i.e., slope) versus variable
  rates of change. Compare rates of change of
  linear, quadratic, square root, and other
  function families.
• h. Determine graphically and algebraically
  whether a function has symmetry and whether it is
  even, odd, or neither.
• i. Understand that any equation in x can be
  interpreted as the equation f(x) g(x), and
  interpret the solutions of the equation as the
  x-value(s) of the intersection point(s) of the
  graphs of y f(x) and y g(x).
•  

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GEORGIA PERFORMANCE
STANDARDSMathematics 1 MM1A2. Students will
simplify and operate with radical expressions,
polynomials, and rational expressions. a.
Simplify algebraic and numeric expressions
involving square root. b. Perform
operations with square roots. c. Add, subtract,
multiply, and divide polynomials. d. Expand
binomials using the Binomial Theorem. e. Add,
subtract, multiply, and divide rational
expressions.
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GEORGIA PERFORMANCE STANDARDSMathematics 1 f.
Factor expressions by greatest common factor,
grouping, trial and error, and special products
limited to the formulas below. (x y)2 x2
2xy y2 (x - y)2 x2 - 2xy y2 (x y)(x -
y) x2- y2 (x a)(x b) x2 (a b)x ab
(x y)3 x3 3 x2y 3xy2 y3 (x - y)3 x3
- 3x2y 3xy2 y3 g. Use area and volume
models for polynomial arithmetic.
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GEORGIA PERFORMANCE
STANDARDSMathematics 1MM1A3. Students will
solve simple equations. a. Solve quadratic
equations in the form ax2 bx c 0, where a
1, by using factorization and finding
square roots where applicable. b. Solve
equations involving radicals such as x b c,
using algebraic techniques. c. Use a
variety of techniques, including technology,
tables, and graphs to solve equations
resulting from the investigation of x2 bx c
0. d. Solve simple rational equations that
result in linear equations or quadratic
equations with leading coefficient of 1.

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Northwest Georgia RESA Mathematics Academy
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Assessing to LEARN

• Read the article Assessing to Learn and Learning
  to Assess.
• List five ideas discussed in the article that
  you feel are important factors in raising student
  achievement.

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• What we have done so far
• A better way to prepare for THE TEST
• Examined testing strategies
• Re-enforced concepts and skills from Units 1 and
  2
• Examined the underpinnings for Unit 5
• Ways to increase the positive impact of assessing
• Where we are going
• Using the culminating activity of Unit 5 to
  explore the depth and rigor of the algebra in
  Math I
• Developing our own benchmark items
• Sharing items

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• Fairfield Aviation
• Putting It All Together

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Opening

• Your group has been given a problem from the
  culminating task of Math I, Unit 5 Algebra in
  Context.
• Work your problem, showing all work.
• List the standard(s) and any specific
  mathematical concepts, skills, and vocabulary
  addressed in the problem.
• Write 3 multiple choice assessment items (a DOK
  level 1, 2, and 3) related to the mathematical
  content of your problem. Carefully consider the
  depth and rigor addressed in your items as
  compared to the task.

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Worktime

• As you work
• Be conscious of the how you are incorporating the
  process standards into your assessment items.
• Think about the number of steps that a student
  would need to take to answer your items
  successfully.
• List any questions that you still have related to
  content, depth, or rigor of the algebra standards
  in Math I.

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Closing

• Share your problem from the task.
• Be sure to address standard(s), concepts,
  skills, and vocabulary addressed in the problem.
  
• Share your assessment items.
• Include
• the DOK level
• why you chose the distracters that you did
• how your item does (or does not) incorporate the
  process standards
• the steps that a student would need to take to
  answer your items successfully.

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Questions, Comments, and Concerns

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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
Northwest Georgia RESA Mathematics Academy