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Northwest Georgia RESA Mathematics Academy

- 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

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

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

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

Content Topic Algebra Pedagogy Topic

Writing and Using Commentary Effectively

Northwest Georgia RESA Mathematics Academy

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 teachers and

students write and use commentary effectively?

Northwest Georgia RESA Mathematics Academy

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A task

Northwest Georgia RESA Mathematics Academy

SIXTH GRADE

GPS ALGEBRA M6A1. Students will understand the

concept of ratio and use it to represent

quantitative relationships. M6A2. Students

will consider relationships between varying

quantities. a. Analyze and describe

patterns arising from mathematical rules,

table, and graphs. b. Use

manipulatives or draw pictures to solve problems

involving proportional

relationships. c. Use proportions to

describe relationships and to solve

problems, including percents. d.

Describe proportional relationships

mathematically using y kx, where k

is the constant of proportionality.

e. Graph proportional relationships in the form y

kx and describe characteristics of

the graph. f. In a proportional

relationship expressed as y kx, solve for one

quantity given values of the other

two... Solve problems using the

relationship y kx. g.Use

proportional reasoning (a/b c/d and y kx) to

solve problems. M6A3. Students will evaluate

algebraic expressions, including those

with exponents, and solve simple one-step

equations using each of the four

basic operations.

Algebra Standards

Northwest Georgia RESA Mathematics Academy

Opening

- Which class has more girls?
- Class A

Class B - 20 students 25

students - 10 girls

12 girls - How do you know?

Northwest Georgia RESA Mathematics Academy

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

Work Period

- Redrawing Bucky the Blockhead
- 1. Get with a partner and redraw Bucky according

to the directions on the page. - 2. Complete the tables that show how each line

segment changes. - 3. Write an equation to represent each new

drawing. - 4. Graph the equation and discuss

proportionality.

Northwest Georgia RESA Mathematics Academy

Closing

- What is a ratio?
- What is a proportion?
- What does it mean to think proportionally?
- What does a proportional equation look like?
- What does a proportional graph look like?
- What is the constant of
- proportionality?

Northwest Georgia RESA Mathematics Academy

SIXTH GRADE GPS ALGEBRA M6A1. Students will

understand the concept of ratio and use it to

represent quantitative relationships. M6A2.

Students will consider relationships between

varying quantities. a. Analyze and

describe patterns arising from mathematical

rules, table, and graphs. b.

Use manipulatives or draw pictures to solve

problems involving proportional

relationships. c. Use proportions to

describe relationships and to solve

problems, including percents. d. Describe

proportional relationships mathematically

using y kx, where k is the constant of

proportionality. e. Graph proportional

relationships in the form y kx and describe

characteristics of the graph. f.

In a proportional relationship expressed as y

kx, solve for one quantity given

values of the other two... Solve problems using

the relationship y kx. g.

Use proportional reasoning (a/b c/d and y kx)

to solve problems. M6A3. Students will evaluate

algebraic expressions, including those

with exponents, and solve simple one-step

equations using each of the four

basic operations.

Northwest Georgia RESA Mathematics Academy

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

Writing and Using Commentary

- Poster of Proportionality
- Split your chart paper into 2 sections.
- 2. Use the drawings, tables, equations, and

graphs from todays lesson to illustrate what

proportionality is and what it is not. - 3. Post your work on the wall in the classroom.
- 4. After discussing what it means to write

commentary you will need to write a piece of

commentary on one of the posters in the

classroom.

Northwest Georgia RESA Mathematics Academy

The parts of a performance standard

- STANDARDS AND ELEMENTS ADDRESSED
- THE TASK
- STUDENT WORK
- COMMENTARY
- Teacher-written
- Student-written

Northwest Georgia RESA Mathematics Academy

A feedback system depends on

Vision

and

Reality.

Feedback exists between the two. Grant Wiggins

Northwest Georgia RESA Mathematics Academy

Good commentary provides evidence that

shows the level of proficiency of the work as

measured against the standard, cites

specific strategies used, and uses the

language of the standards.

Why are these things important?

Northwest Georgia RESA Mathematics Academy

Feedback is specific, and descriptive

information you can use.

Feedback is not advice, praise, or

blame. Grant Wiggins

Northwest Georgia RESA Mathematics Academy

Time to Look at Student Work with Commentary

Take a look at the work and commentary provided.

Make notes about what you notice.

Northwest Georgia RESA Mathematics Academy

What did you notice about the samples of

commentary?

Northwest Georgia RESA Mathematics Academy

Time to Write

Using the standards and the student work sample

provided, write commentary you could use as a

teaching tool for your students.

Northwest Georgia RESA Mathematics Academy

a sculptor chips away at a block of marble for

days and daysand a horse or a man emerges.

But an ordinary person could chip away at

the same block of marble for months and nothing

at all might emerge. The difference is in the

quality of attention. Its the intention

The difference between assessment that is

busywork and assessment that reflects the essence

of our teaching is what we and our students make

of what we collect (Calkins, p. 325).

Northwest Georgia RESA Mathematics Academy

Taking our temperature with respect to

establishing a standards-based

classroom

Northwest Georgia RESA Mathematics Academy

Perception vs. Reality

Northwest Georgia RESA Mathematics Academy

Common Perceptions Perception Openings, work

periods, and closings must meet exact time

constraints. Reality While there

are time suggestions for each portion of the

instructional framework, times will vary

depending on the type of lesson and the

content. Perception Every concept must be

completely discovered by students.

Reality 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 Mathematics Academy

Common Perceptions Perception Skills lessons

are never appropriate.

Reality 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

be brought back into a context as soon as

possible. Perception Direct instruction is never

appropriate. Reality Some

information will need to be presented in the

form of direct instruction, with lecture and

note taking. Think of this time as a

DIALOGUE as opposed to a MONOLOGUE.

Northwest Georgia RESA Mathematics Academy

Common Perceptions Perception All work must be

done in pairs or in groups.

Reality The standards-based classroom should

incorporate a mix of group work, partner work,

and individual accountability. Perception Closi

ngs must always include formal student

presentations. Reality 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 Mathematics Academy

Common Perceptions Perception Every student

must play a major role in the closing every

day. Reality 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 Mathematics Academy

Common Perceptions Perception Commentary should

be lengthy. Reality Commentary

can be of varying lengths, depending on the

purpose and the scope of the work. The length

also depends on the number of standards being

addressed. Perception Commentary should always

be written for every student on a particular task

or assignment. Reality While our

goal should be to have multiple pieces of

commentary for each student over the course of

the year to show growth, it is not necessary

to write commentary for each student on every

task!

Northwest Georgia RESA Mathematics Academy

Common Perceptions Perception All commentary

should be written by the teacher.

Reality The ultimate goal with commentary is

to give specific ways that students have met or

exceeded the standard, or next steps to use in

order to make the work better. It should also

be our goal to teach students how to evaluate

their own work. Consequently, we should begin

to train our students how to write commentary

for their work on the work of others. Perception

Commentary is mainly used for student work

displays. Reality It is

important that student work and commentary be

displayed but only if it is being used as a

teaching tool. Commentary may be public or

private. Some commentary may only be used by the

teacher and an individual student. Some of

this commentary may be verbal. Ultimately, it

is a tool to improve student achievement by

giving students a true understanding of how

their work stacks up with respect to the

standards.

Northwest Georgia RESA Mathematics Academy

Questions, Comments, and Concerns

Northwest Georgia RESA Mathematics Academy

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