Northwest Georgia RESA Summer Mathematics Institute

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Northwest Georgia RESA Summer Mathematics
Institute
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• Northwest Georgia RESA
• Summer Mathematics Institute
• Coosa Valley Technical College
• Rome, Georgia
• June 24, 2009
• Dexter Mills, Executive Director
• Karen Faircloth, Director of School
• Improvement Professional
• Learning

3
Contact Information
Danny Lowrance, Math Specialist W.L. Swain
Elementary 2505 Rome Rd SW Plainville, GA
30733 706-629-0141 dlowrance_at_gcbe.org
Northwest Georgia RESA Summer Mathematics
Institute
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Facilitators for each Curriculum Band Claire
Pierce, Math I and II Independent Consultant
former DOE Math Program Manager Linda Segars,
Math I and II School Improvement Specialist for
Metro RESA Terry Haney, Grades 6-8 Math
Coordinator for Northwest Georgia RESA Danny
Lowrance, Grades 3-5 Math Specialist at W.L.
Swain Elementary School in Gordon County
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Institute
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Purpose The purpose of the Northwest Georgia
RESA Summer Mathematics Institute 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  3-5, 6-8, and
Math I II.  Members of the teams may be
teachers and/or academic coaches, along with a
building-level and system-level
administrator.  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. 
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Institute
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Content Topic Numbers and Operations
(Fractions) Pedagogy Topic Questioning
Strategies and Techniques
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Institute
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Essential Questions How do I effectively
integrate the Numbers and Operations, fractions,
standards into the mathematics curriculum? How
do I purposefully and effectively implement high-
impact questioning strategies in the mathematics
classroom?
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Institute
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A closer look at fractions vertically

• 1 Identify, label and relate fractions (halves,
  fourths) as equal parts of a whole using
  pictures and models.
• 2 Students will understand and compare
  fractions.
• Model, identify, label, and compare fractions
  (thirds, sixths, eighths, tenths) as a
  representation of equal parts of a whole or of a
  set.
• Know that when all fractional parts are
  included, such as three thirds, the result is
  equal to the whole.

Northwest Georgia RESA Summer Mathematics
Institute
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A closer look at fractions vertically

• 3 Students will understand the meaning of
  decimal fractions and common fractions in simple
  cases and apply them in problem-solving
  situations. They will understand a common
  fraction represents parts of a whole. They will
  understand the fraction a/b represents a equal
  sized parts of a whole that is divided into b
  equal parts. They will understand the concept of
  addition and subtraction of common fractions with
  like denominators. They will solve problems
  involving fractions. They will understand a one
  place decimal fraction represents tenths, i.e.,
  0.3 3/10.
• 4 Students will further develop their
  understanding of the meaning of common fractions
  and use them in computations. They will
  understand representations of simple equivalent
  fractions. They will add and subtract fractions
  and mixed numbers with common denominators.
  (Denominators should not exceed twelve.) They
  will convert and use mixed numbers and improper
  fractions interchangeably.
•  

Northwest Georgia RESA Summer Mathematics
Institute
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A closer look at fractions vertically

• 5 Students will continue to develop their
  understanding of the meaning of common fractions
  and compute with them. They will understand the
  value of a fraction is not changed when both its
  numerator and denominator are multiplied or
  divided by the same number because it is the same
  as multiplying or dividing by one. They will find
  equivalent fractions and simplify fractions. They
  will model the multiplication and division of
  common fractions. They will add and subtract
  common fractions and mixed numbers with unlike
  denominators.
• 6 Students will add and subtract fractions and
  mixed numbers with unlike denominators. They will
  multiply and divide fractions and mixed numbers.
  They will use fractions, decimals, and percents
  interchangeably. They will solve problems
  involving fractions, decimals and percents.
•  
•  
•  

Northwest Georgia RESA Summer Mathematics
Institute
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How close can you get to filling 8 containers?
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Institute
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Opening

• M4N6 b. Add and subtract fractions and mixed
  numbers with common denominators. (Denominators
  should not exceed twelve.)
• Take 5 minutes to answer the question. Write
  your answers in complete sentences.

Make sure to illustrate your answer.
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Institute
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GEORGIA PERFORMANCE STANDARDS M3N5. Students will
understand the meaning of decimal fractions and
common fractions in simple
cases and apply them in problem-solving
situations. d. Know and use decimal fractions
and common fractions to represent the size of
parts created by equal divisions of a whole. e.
Understand the concept of addition and
subtraction of decimal fractions and common
fractions with like denominators. f. Model
addition and subtraction of decimal fractions and
common fractions with like
denominators. g. Solve problems involving
fractions. M4N6. Students will further develop
their understanding of the meaning of common
fractions and use them in computations. a.
Understand representations of simple equivalent
fractions. b. Add and subtract fractions and
mixed numbers with common denominators.
(Denominators should not exceed twelve.) c.
Convert and use mixed numbers and improper
fractions interchangeably.
Northwest Georgia RESA Summer Mathematics
Institute
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M4P1. Students will solve
problems. a. Build new mathematical knowledge
through problem solving. c. Apply and adapt a
variety of appropriate strategies to solve
problems. M4P2. Students will reason and
evaluate mathematical arguments. d. Select and
use various types of reasoning and methods of
proof. M4P3. Students will communicate
mathematically. M4P4. 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. M4P5. 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- representations to solve
problems. c. Use representations to model
and interpret physical, social, and
mathematical phenomena.
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Institute
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Work Period

• Lets begin
• Each container holds 6 boxes. Each pair gets
  10 rolls to attempt to fill up their 8
  containers. Record each roll as a fraction. For
  example if you roll a 4 on a six sided dice for
  your first roll then you record 4/6 in the spot
  labeled Roll 1.
• Be prepared to discuss your work with the whole
  class during our closing. Some of you may be
  asked to present your work to the class.

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Institute
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Closing

• How are the results from Part A and Part B the
  same?
• How are the results from Part A and Part B
  different?
• Explain your thinking!
• How does your work meet the standard?
• Explain what each of the following terms means in
  relation to this task mixed number, proper
  fraction, improper fraction, numerator,
  denominator.

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Institute
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GEORGIA PERFORMANCE STANDARDS M3N5. Students will
understand the meaning of decimal fractions and
common fractions in simple
cases and apply them in problem-solving
situations. d. Know and use decimal fractions
and common fractions to represent the size of
parts created by equal divisions of a whole. e.
Understand the concept of addition and
subtraction of decimal fractions and common
fractions with like denominators. f. Model
addition and subtraction of decimal fractions and
common fractions with like
denominators. g. Solve problems involving
fractions. M4N6. Students will further develop
their understanding of the meaning of common
fractions and use them in computations. a.
Understand representations of simple equivalent
fractions. b. Add and subtract fractions and
mixed numbers with common denominators.
(Denominators should not exceed twelve.) c.
Convert and use mixed numbers and improper
fractions interchangeably.
Northwest Georgia RESA Summer Mathematics
Institute
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M4P1. Students will solve
problems. a. Build new mathematical knowledge
through problem solving. c. Apply and adapt a
variety of appropriate strategies to solve
problems. M4P2. Students will reason and
evaluate mathematical arguments. d. Select and
use various types of reasoning and methods of
proof. M4P3. Students will communicate
mathematically. M4P4. 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. M4P5. 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- representations to solve
problems. c. Use representations to model
and interpret physical, social, and
mathematical phenomena.
Northwest Georgia RESA Summer Mathematics
Institute
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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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Institute
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These seven survival skills for the world of work
can be directly correlated to Georgias
Standards-Based Classrooms Rubric.
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Institute
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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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Institute
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• Critical Thinking and Problem Solving
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Teaching and learning reflect a balance of
  skills, conceptual understanding, and problem
  solving.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher supports students as they work
  through challenging tasks without taking over the
  thinking process for them.
• Students are engaged in tasks aligned to the GPS
  that develop mathematical concepts and skills,
  require students to make connections, involve
  problem solving, and encourage mathematical
  reasoning.
• Students can explain why a mathematical idea is
  important and the types of contexts in which it
  is useful.

Northwest Georgia RESA Summer Mathematics
Institute
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• Collaboration and Leadership
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Students will communicate mathematically.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher creates an environment where students
  feel comfortable engaging in conversations,
  discussions, and debating using mathematical
  vocabulary and/or the language of the standards
  when communicating mathematical reasoning.
• Students use mathematical vocabulary and/or the
  language of the standards to communicate their
  mathematical thinking and ideas coherently and
  precisely to peers, teachers, and others.
• Students analyze and evaluate the mathematical
  thinking and strategies of others.

Northwest Georgia RESA Mathematics Academy
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• Agility and Adaptability
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Students will solve a variety of real-world
  problems.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher provides students with opportunities
  to engage in performance tasks that allow
  students to discover new mathematical knowledge
  through problem solving.
• Students apply their mathematical understanding
  to interpret and solve real-world problems.
• Students apply and adapt a variety of appropriate
  strategies to solve problems.
• Students monitor and reflect on their process of
  mathematical
• problem solving.

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Institute
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Initiative and Entrepreneurialism From
Educational Leadership October, 2008 Rigor
Redefined by Tony Wagner Students will justify
their reasoning and evaluate mathematical
arguments of others. From Teaching and Learning
in the Mathematics Classroom (Addendum to the
Standards-Based Classroom Rubric) Georgia
Department of Education

• The teacher provides opportunities for students,
  who solve the problems differently from others,
  to share their procedures, thus encouraging
  diverse thinking.
• The teacher ensures that reasoning and proof are
  a consistent part of a students mathematical
  experience.
• Students make and investigate mathematical
  conjectures (mathematical statements that appear
  to be true, but not formally proven) about
  solutions to problems.
• Students use their mathematical understanding to
  evaluate and debate their own mathematical
  arguments as well as those of others. Students
  offer various methods of proof to support their
  positions.

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Institute
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• Accessing and Analyzing Information
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Students will represent mathematical solutions in
  multiple ways.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher releases responsibility by providing
  opportunities for students to independently
  select and use various representations to
  organize, record, and communicate mathematical
  ideas.
• Students select and apply appropriate
  mathematical representations to solve problems,
  and explain and interpret the connections between
  those representations.

Northwest Georgia RESA Summer Mathematics
Institute
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• Effective Oral and Written Communication
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Students will communicate mathematically.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher creates and environment where
  students feel comfortable engaging in
  conversations, discussions, and debating using
  mathematical vocabulary and/or the language of
  the standards when communicating mathematical
  reasoning.
• Students use mathematical vocabulary and/or the
  language of the standards to communicate their
  mathematical thinking and ideas coherently and
  precisely to peers, teachers, and others.
• Students analyze and evaluate the mathematical
  thinking and strategies of others.

Northwest Georgia RESA Summer Mathematics
Institute
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• Curiosity and Imagination
• From Educational Leadership October, 2008
  Rigor Redefined by Tony Wagner
• Students will make connections among mathematical
  ideas and to other disciplines.
• From Teaching and Learning in the Mathematics
  Classroom (Addendum to the Standards-Based
  Classroom Rubric) Georgia Department of
  Education
• The teacher expects students to independently
  make connections without prompting.
• Students make connections between mathematical
  ideas and other content areas and connect new
  concepts to those within previous strands or
  domains.
• Students understand how mathematical ideas
  interconnect and build on one another to
  produce a coherent whole.
• Students recognize and apply mathematics in
  contexts outside
• of the mathematics classroom.

Northwest Georgia RESA Summer Mathematics
Institute
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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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Institute
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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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Institute
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Think about it

• Customer
• What is your biggest difficulty in hiring people
  for your business?
• Owner
• It is impossible to find people who can think.
  If most of my employees come across anything out
  of the ordinary, I have to help them past that
  part so they can get to the basic process or
  routine.
• A portion of a conversation on which I
• eavesdropped at Westmoreland
• Tire Center in Fort Payne, Alabama
• October 3, 2008

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Think about it
Any subject be it physics, art, or auto repair
can promote critical thinking as long as
teachers teach in intellectually challenging
ways. Nel Noddings Educational Leadership,
February, 2008
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Institute
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(No Transcript)
34
(No Transcript)
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Taking our temperature with respect to
establishing a standards-based
classroom
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Institute
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Perception vs. Reality
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Institute
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Common Perceptions Openings, work periods, and
closings must meet exact time constraints.
While there are time suggestions for each
portion of the instructional framework, times
will vary depending on the type of lesson and
the content. Every concept must be completely
discovered by students. Discovery-based
lessons are highly encouraged as often as
possible however, time does not permit every
lesson to be completely based on discovery.
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Institute
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Common Perceptions Skills lessons are never
appropriate. Skills are a crucial part of our
mathematics instruction. Skills lessons should
be embedded within tasks as often as possible.
When they are taught in isolation, skills should
brought back into a context as soon as
possible. Direct instruction is never
appropriate. Some information will need to be
presented in the form of direct instruction,
with lecture and notetaking. Think of this
time as a DIALOGUE as opposed to a
MONOLOGUE.
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Institute
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Common Perceptions All work must be done in
pairs or in groups. The standards-based
classroom should incorporate a mix of group
work, partner work, and individual
accountability. Closings must always include
formal student presentations.
While student presentations are one of the most
effective methods of solidifying student
learning, not every lesson lends itself to this
type of closing. Sometimes a whole group
discussion with strategic questioning is just
as effective.
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Institute
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Common Perceptions Every student must play a
major role in the closing every day. Our goal
should be to involve as many students as possible
each day (in meaningful ways). Using the status
of the class sheet allows teachers to make note
of students who either make formal presentations
or who contribute to the class discussions
through meaningful questions and comments. For
example, a closing may involve 1-4 students
giving formal presentations, with the remainder
of the class giving feedback and asking
questions.
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Institute
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Time on Task
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Institute
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• GEORGIA PERFORMANCE STANDARDS
• NUMBER AND OPERATIONS
• Students will further develop their understanding
  of the concept of whole numbers. They will also
  understand the meanings of multiplication and
  division of decimals and use decimals and common
  fractions in computation, as well as in problem
  solving situations.
• M5N4. Students will continue to develop their
  understanding of the
• meaning of common fractions and
  compute with them.
• Understand division of whole numbers can be
  represented as a fraction
• (a/b a b).
• b. Understand the value of a fraction is not
  changed when both its numerator and denominator
  are multiplied by or divided by the same number
  because it is the same as multiplying or dividing
  by one.
• c. Find equivalent fractions and simplify
  fractions.
• d. Model the multiplication and division of
  common fractions.
• e. Explore finding common denominators using
  concrete, pictorial, and computational models.

Northwest Georgia RESA Summer Mathematics
Institute
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M5P3. Students will communicate
mathematically. a. Organize and consolidate
their mathematical thinking through
communication. b. Communicate their
mathematical thinking coherently and
clearly to peers, teachers, and others. c.
Analyze and evaluate the mathematical thinking
and strategies of others. d. Use the
language of mathematics to express mathematical
ideas precisely. M5P4. 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. M3P5. Students will represent
mathematics in multiple ways. a. Create and use
representations to organize, record, and
communicate mathematical ideas.
Northwest Georgia RESA Summer Mathematics
Institute
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Opening

• Write a story problem about the following
  equation 3 x 5 15.
• Draw a picture illustrating your problem.
• In your own words explain what the factors 3 and
  5, along with the product 15 represent in the
  equation above.
• Be prepared to discuss this with the class.

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Institute
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Mini Task

• Use our opening problem to solve the following
  situation.
• There are 15 cars in Michaels toy car
  collection. Two thirds of the cars are red. How
  many red cars does Michael have?

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Mini Task

• Lets try one more with the area model.
• You have ¾ of a pizza left. If you give 1/3 of
  the leftover pizza to your sister, how much of
  the whole pizza will your brother get?
• Which would be best to illustrate this problem a
  circle or an array?

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Institute
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Northwest Georgia RESA Summer Mathematics
Institute
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My Multiplication and Division of Fractions Book
(Day 1)

• A major mathematics textbook company is asking
  for your help. They are looking for ideas on how
  to model multiplication and division of fractions
  using fraction circle and/or arrays.

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Institute
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Work Period

• You need to create a mini-book to model
  multiplication and division of fractions using
  circles and arrays.
• Include pictures, appropriate story problems and
  a brief statement of what your answer means.
• You need to draft one example of each operation
  on a scratch piece of paper to submit to your
  TTYP before printing it in your mini-book.

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Institute
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Work Period

• Discuss with your editor the following
• How many pages of your mini-book will be used for
  multiplication and division.
• Should you include the algorithm or not?
• Should the model come before the algorithm or the
  algorithm before the model?
• Also, any other items that you feel need to be
  finalized before sending your mini-book to the
  printing press.

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Closing

• Which should we teach first the model or the
  algorithm?
• Explain why you feel that way.

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Institute
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• GEORGIA PERFORMANCE STANDARDS
• NUMBER AND OPERATIONS
• Students will further develop their understanding
  of the concept of whole numbers. They will also
  understand the meanings of multiplication and
  division of decimals and use decimals and common
  fractions in computation, as well as in problem
  solving situations.
• M5N4. Students will continue to develop their
  understanding of the
• meaning of common fractions and
  compute with them.
• Understand division of whole numbers can be
  represented as a fraction
• (a/b a b).
• b. Understand the value of a fraction is not
  changed when both its numerator and denominator
  are multiplied by or divided by the same number
  because it is the same as multiplying or dividing
  by one.
• c. Find equivalent fractions and simplify
  fractions.
• d. Model the multiplication and division of
  common fractions.
• e. Explore finding common denominators using
  concrete, pictorial, and computational models.

Northwest Georgia RESA Summer Mathematics
Institute
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M5P3. Students will communicate
mathematically. a. Organize and consolidate
their mathematical thinking through
communication. b. Communicate their
mathematical thinking coherently and
clearly to peers, teachers, and others. c.
Analyze and evaluate the mathematical thinking
and strategies of others. d. Use the
language of mathematics to express mathematical
ideas precisely. M5P4. 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. M3P5. Students will represent
mathematics in multiple ways. a. Create and use
representations to organize, record, and
communicate mathematical ideas.
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Institute
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Opening

• Model the following multiplication problem
• 3/5 x 3/4
• How can we use our model to derive a way of
  solving this problem without having to draw it?
• P.S. Make sure it will always work.

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Institute
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My Multiplication and Division of Fractions Book
(Day 2)

• A major mathematics textbook company is asking
  for your help. They are looking for ideas on how
  to model multiplication and division of fractions
  using fraction circle and/or arrays.

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Institute
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Mini Task

• Before we tackle a division fraction problem for
  our mini-book we need to go back and discuss the
  meaning of division.
• James has 24 apples to be shared with between him
  and 3 friends. How many apples does each person
  get?

This is an example of a sharing or partition
division problem.
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Institute
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Mini Task

• Before we tackle a division fraction problem for
  our mini-book lets discuss one more option.
• James has 14 quarts of water, how many canteens
  holding 3 quarts each can he fill?

This is an example of a measurement division
problem which are used most when dealing with
division problems involving a fractional divisor
and dividend.
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Institute
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Work Period

• You need to create a mini-book to model
  multiplication and division of fractions using
  circles and arrays.
• Include pictures, appropriate story problems and
  a brief statement of what your answer means.
• You need to draft one example of each operation
  on a scratch piece of paper to submit to your
  TTYP before printing it in your mini-book.

Northwest Georgia RESA Summer Mathematics
Institute
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Work Period

• Discuss with your editor the following
• How many pages of your mini-book will be used for
  multiplication and division.
• Should you include the algorithm or not?
• Should the model come before the algorithm or the
  algorithm before the model?
• Also, any other items that you feel need to be
  finalized before sending your mini-book to the
  printing press.

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Institute
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Closing

• A group will discuss a multiplication section of
  their mini-book with the class.
• Are there any Questions or Connections ?
• How does your work meet the standard?
• Another group will discuss a division section of
  their mini-book with the class.
• Are there any Questions or Connections ?
• How does your work meet the standard?

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Institute
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• GEORGIA PERFORMANCE STANDARDS
• NUMBER AND OPERATIONS
• Students will further develop their understanding
  of the concept of whole numbers. They will also
  understand the meanings of multiplication and
  division of decimals and use decimals and common
  fractions in computation, as well as in problem
  solving situations.
• M5N4. Students will continue to develop their
  understanding of the
• meaning of common fractions and
  compute with them.
• Understand division of whole numbers can be
  represented as a fraction
• (a/b a b).
• b. Understand the value of a fraction is not
  changed when both its numerator and denominator
  are multiplied by or divided by the same number
  because it is the same as multiplying or dividing
  by one.
• c. Find equivalent fractions and simplify
  fractions.
• d. Model the multiplication and division of
  common fractions.
• e. Explore finding common denominators using
  concrete, pictorial, and computational models.

Northwest Georgia RESA Summer Mathematics
Institute
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GEORGIA PERFORMANCE STANDARDS (PROCESS
STANDARDS) M5P3. Students will communicate
mathematically. a. Organize and consolidate
their mathematical thinking through
communication. b. Communicate their
mathematical thinking coherently and
clearly to peers, teachers, and others. c.
Analyze and evaluate the mathematical thinking
and strategies of others. d. Use the
language of mathematics to express mathematical
ideas precisely. M5P4. 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. M3P5. Students will represent
mathematics in multiple ways. a. Create and use
representations to organize, record, and
communicate mathematical ideas.
Northwest Georgia RESA Summer Mathematics
Institute
65
Reflection
66
Multiplication Strategies

• Using the following strategies to solve 83 x 47.
• Estimation
• Traditional Algorithm
• Area Model
• Partial Products (Chunking)
• Lattice Multiplication

Northwest Georgia RESA Summer Mathematics
Institute
67
Questions, Comments, and Concerns

Northwest Georgia RESA Summer Mathematics
Institute
68
Contact Information
Danny Lowrance, Math Specialist W.L. Swain
Elementary 2505 Rome Rd SW Plainville, GA
30733 706-629-0141 dlowrance_at_gcbe.org
Northwest Georgia RESA Summer Mathematics
Institute