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Northwest Georgia RESA Summer Mathematics

Institute

- 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

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

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

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

Content Topic Numbers and Operations

(Fractions) Pedagogy Topic Questioning

Strategies and Techniques

Northwest Georgia RESA Summer Mathematics

Institute

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?

Northwest Georgia RESA Summer Mathematics

Institute

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

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

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

How close can you get to filling 8 containers?

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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

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

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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

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

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 Summer Mathematics

Institute

These seven survival skills for the world of work

can be directly correlated to Georgias

Standards-Based Classrooms Rubric.

Northwest Georgia RESA Summer Mathematics

Institute

- 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 Summer Mathematics

Institute

- 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

- 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

- 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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

- 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

- 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

- 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

What do all of these skills have in common? They

can all be directly correlated to good

questioning.

Northwest Georgia RESA Summer Mathematics

Institute

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 Summer Mathematics

Institute

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

Northwest Georgia RESA Summer Mathematics

Institute

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

Northwest Georgia RESA Summer Mathematics

Institute

(No Transcript)

(No Transcript)

Taking our temperature with respect to

establishing a standards-based

classroom

Northwest Georgia RESA Summer Mathematics

Institute

Perception vs. Reality

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

Time on Task

Northwest Georgia RESA Summer Mathematics

Institute

- 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

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

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.

Northwest Georgia RESA Summer Mathematics

Institute

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?

Northwest Georgia RESA Summer Mathematics

Institute

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?

Northwest Georgia RESA Summer Mathematics

Institute

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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

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.

Northwest Georgia RESA Summer Mathematics

Institute

Closing

- Which should we teach first the model or the

algorithm? - Explain why you feel that way.

Northwest Georgia RESA Summer Mathematics

Institute

- 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

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

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.

Northwest Georgia RESA Summer Mathematics

Institute

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

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.

Northwest Georgia RESA Summer Mathematics

Institute

Northwest Georgia RESA Summer Mathematics

Institute

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

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.

Northwest Georgia RESA Summer Mathematics

Institute

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?

Northwest Georgia RESA Summer Mathematics

Institute

- 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

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

Reflection

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

Questions, Comments, and Concerns

Northwest Georgia RESA Summer Mathematics

Institute

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