# Geometry-Proportions-Shapes

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```					Names: __________________
Subject: Math
Date: March 12, 2007

Lesson Plan Introduction

The following five-day lesson plan is designed to demonstrate to students

the pervasive nature of math and math concepts that are already present in their

world. In other words, math does not exist in a vacuum---these concepts extend

far beyond their textbooks and far beyond the walls of their school.

Each of the lesson plans herein are introduced to the students with an

image retrieved from the Library of Congress, an important resource that children

should be aware of. Each image is drawn from the Chicago archives with a view

toward helping kids make clearer connections to their community, from Chicago

City Hall to Soldier Field; and from The Chicago Stock Exchange to the Chicago

History Museum.

The lessons and the activities embedded in them should help kids develop

a sense of, and interest in, the world of math that exists and surrounds them in

their everyday lives.

Lesson Plan Outline – MONDAY
Math/Science Learning
skills
Names: ____________                                              _*_Investigations
_*_Recording Data
Subject: Math                                                    _*_ Interpreting/Analyzing
Date: March 12, 2007                                             __Designing questions
_*_Listening
_*_Designing
Tables/Charts
_*_ Number Fluency
_*_Computational
Fluency
_*_Algebraic Reasoning

Process Skills
_*_Analyzing
__Guess & Check
_*_Developing
Metacognition
_*_Measuring
_*_Classifying
_*_Predicting
_*_Generalizing
_*_Justifying solutions
_*_Organizing/comparing
_*_Communicating
_*_Investigating
_*_Describing
_*_Comparing
_*_Looking for patterns

Problem Solving Skills
_*_Identifying problem
_*_Designing
Implementation plan
Geometry/Proportions/Shapes (45 minutes)                                 _*_Collect information
_*_Organization data
_*_Representation
_*_Analyze data
_*_Present Data
National/State/District Alignment:                                         _*_Check sensibility of
STATE GOAL 7: Estimate, make and use measurements of                    solution
__Evaluation plan
objects, quantities and relationships and determine                        _*_Communicating
acceptable levels                                                          _*_Estimating
of accuracy.                                         Strategies
A. Measure and compare quantities using appropriate units,              __KWL
_*_Cooperative Learning
instruments and methods.                                           _*_Demonstrations
7.A.2a Calculate, compare and convert length, perimeter, area,     __Drill & Practice
weight/mass and volume within the customary and metric systems.        _*_Games
B. Estimate measurements and determine acceptable levels of            __Field Trips
__Journals
accuracy.                                                                  __Drama
7.B.2a Determine and communicate possible methods for              _*_Reading/Writing
estimating a given measure, selecting proper units in both customary and   _*_Discussion
_*_Groups/individuals
metric                                                                     projects
systems.                                                    _*_Brainstorming
C. Select and use appropriate technology, instruments and
Equity
formulas to solve problems, interpret results and communicate              _*_Heterogeneous
findings.                                                                  grouping
7.C.2a Describe relationships in a simple scale drawing.            _*_Meaningful problems
_*_Decode rules & codes
_*_Wait time
STATE GOAL 8: Use algebraic and analytical methods to                      _*_Discipline
identify and describe patterns and relationships in data, solve            _*_Teacher/student
interactions
problems                                                                   _*_Quality of feedback
and predict results.                                      _*_Knows student culture
_*_Knows students
A. Describe numerical relationships using variables and                strengths
patterns.                                                                  _*_Inquiry-based

8.A.2a Identify, describe, extend and create geometric and          Technology
numeric patterns                                                           __Films
__Laser disc
__Computer software
__VCR/DVD
Instructional Objective(s):                                         __Calculators
_*_Digital
Objectives for this lesson: Students will be able               Camera/Scanner
to…                                                                 _*_Web-based
Resources
1. Identify geometric shapes and patterns as
they are applied to architectural building design.
2. List different geometric shapes and patterns
used by architects and builders.
3. Understand how geometry, measurement,
pattern,      and    symmetry        influence
architecture.
4. Examine uses of geometry and patterns in
architecture.

Vocabulary:
Various geometric shapes, including square, rectangle,
circle, oval, arch, diamond, triangle. Also discuss architecture,
design, pattern, symmetrical and asymmetrical, proportion.

Materials:
1. LCD projector, screen, and laptop.
2. Black and white image of the New City Hall Building,
(LOV.GOV), cited as
DN-0008404, Chicago Daily News negative collection,
Chicago Historical Society.
3. Two- and three-dimensional geometric manipulatives.

Teaching Strategies:
Anticipatory Set: What is the Library of Congress?
[Briefly describe LOC as the world’s largest library and our
country’s oldest
cultural center. Easy access is made possible to it
through the use of the internet.]

Display image on LCD; ask if anyone has been to
downtown Chicago and been in or has seen City Hall. Ask
them to describe
other buildings that might have a similar appearance.

Practice

Guided
Ask students to identify all the various geometric
shapes and patterns they can find in the City Hall image.

Independent practice
Have students work in pairs to draw and label as many
of the individual geometric shapes as they can that comprise
City Hall.

Have students pretend they are architects hired by the
City of Chicago to design and draw an addition to City Hall
that is consistent with the existing building. They will focus on
proportion and pattern. Each drawing will be approved by the
teacher. This activity can accommodate various skill levels
and modalities. For example, not as much detail will be

Closure
Have students present their drawings to the class with
a brief (1-2 minutes) explanation of their design.

Assessments(Teacher made tests, journals, project report,
observations, portfolios, written report, oral response,
drawing, project)
Collect student drawings as part of the unit
assessment.

Lesson Evaluation
 Personal reflection (How did I feel about my delivery?
Have I used student’s assessment data to develop
next steps? Have I been able to engage all students in
a meaningful way?)

   Professional development needs (Common planning
time,. Consultant, in-service workshop, conference,
study group, individual study).

Lesson Plan Outline – TUESDAY
Math/Science Learning
skills
_*_Investigations
_*_Evaluating
_*_Recording Data
_*_
Interpreting/Analyzing
__Designing questions
_*_Listening
_*_Designing
Tables/Charts
_*_ Number Fluency
_*_Computational
Fluency
_*_Algebraic Reasoning

Process Skills
_*_Analyzing
__Guess & Check
_*_Developing
Metacognition
_*_Measuring
_*_Classifying
_*_Predicting
_*_Generalizing
__Justifying solutions
_*_Organizing/comparin
g
_*_Communicating
_*_Investigating
_*_Describing
_*_Comparing
_*_Looking for patterns

Problem Solving Skills
_*_Identifying problem
_*_Designing
Implementation plan
_*_Collect information
_*_Organization data
_*_Representation
_*_Analyze data
_*_Present Data
_*_Check sensibility of
Field Trip (1/2 day field trip, plus 45 minutes                 solution
_*_Evaluation plan
in class)                                    _*_Communicating
_*_Estimating

Strategies
__KWL
National/State/District Alignment:                               _*_Cooperative Learning
See Monday’s ISBE Goals and Standards.                        _*_Demonstrations
__Drill & Practice
_*_Games
Instructional Objective(s):                                      _*_Field Trips
__Journals
RATIONALE FOR FIELD TRIP:                                   __Drama
1. Enrich student learning and curricular                  _*_Reading/Writing
_*_Discussion
objectives; expand related vocabulary.                 _*_Groups/individuals
2. Extend      classroom    activities to  gain            projects
_*_Brainstorming
perspective of real world in language arts,
social studies, math, and science.                     Equity
_*_Heterogeneous
3. Develop student appreciation, application,              grouping
_*_Meaningful problems
and higher-level understanding of arts and             _*_Decode rules &
sciences.                                              codes
_*_Wait time
4. Develop an understanding of, and make                   _*_Discipline
connections to, the history surrounding                _*_Teacher/student
interactions
Chicago.                                               _*_Quality of feedback
_*_Knows student
culture
Activity:                                                       _*_Knows students
strengths
Each student shall photograph or sketch his or her favorite   _*_Inquiry-based
Technology
each student will be given a square of construction paper in     __Films
varying colors on which to draw their item. All the squares will    __Laser disc
__Computer software
be combined on our class bulletin board to form our “Field Trip     __VCR/DVD
Quilt”.                                                             __Calculators
_*_Digital
Camera/Scanner
Materials:                                                          _*_Web-based
Resources
1. LCD projector, screen, and laptop.
Congress (LOV.GOV) digital collection ID: afcqltle
le002, call number AFC 1997/011: folder 8933 P1.
3. Request for bus transportation.
4. Parental permission slips.
5. Personal cameras or sketch paper and pencil.
6. 6” X 6” construction paper of varying colors.
7. Markers.

Teaching Strategies:
Anticipatory Set
Talk about historical significance of quilts and quilting.
This quilt won 2nd place in the national competition in 1992; it
currently resides in River Forest, Illinois, just outside of
Chicago. The title of the quilt is Adwiniasa, a Ghana
translation meaning “my skill is exhausted”.
Remind students to be on the look-out for geometric
shapes and patterns as discussed in class yesterday and that
would be suitable for their quilt patch as part of the class
project.

Practice

Guided
Field trip to Chicago History Museum (formerly Chicago
Historical Society).

Independent practice
Students are to choose and design a square patch for
the class field trip quilt.

Each student is to complete a square for the field trip
quilt to the best of his or her ability.

Closure
In class, have students draw their square patch for the
class quilt. As the students finish their work, pin or staple the
squares to the
bulletin board to form the quilt.
Assessments(Teacher made tests, journals, project report,
observations, portfolios, written report, oral response, drawing,
project)
Upon returning from the field trip, have students work
on their quilt square and write in their math journals a
description of their quilt square and a rationale for the design
they each chose.

Lesson Evaluation
 Personal reflection (How did I feel about my delivery?
Have I used student’s assessment data to develop next
steps? Have I been able to engage all students in a
meaningful way?)

   Professional development needs (Common planning
time,. Consultant, in-service workshop, conference,
study group, individual study).

Lesson Plan Outline – WEDNESDAY
Math/Science Learning
skills
_*_Investigations
_*_Evaluating
_*_Recording Data
_*_
Interpreting/Analyzing
__Designing questions
_*_Listening
_*_Designing
Tables/Charts
_*_ Number Fluency
_*_Computational
Fluency
_*_Algebraic Reasoning

Process Skills
_*_Analyzing
_*_Guess & Check
_*_Developing
Metacognition
__Measuring
_*_Classifying
Chicago Board of Trade/Money (45 minutes)                          _*_Predicting
_*_Generalizing
_*_Justifying solutions
_*_Organizing/comparin
g
National/State/District Alignment:                                  _*_Communicating
STATE GOAL 7: Estimate, make and use measurements of            _*_Investigating
_*_Describing
objects, quantities and relationships and determine acceptable      _*_Comparing
levels                                                              _*_Looking for patterns

of accuracy.                                   Problem Solving Skills
A. Measure and compare quantities using appropriate units,       __Identifying problem
_*_Designing
instruments and methods.                                          Implementation plan
_*_Collect information
7.A.2b Solve addition, subtraction, multiplication and division   _*_Organization data
problems using currency.                                                 _*_Representation
_*_Analyze data
_*_Present Data
STATE GOAL 8: Use algebraic and analytical methods to                _*_Check sensibility of
identify and describe patterns and relationships in data, solve          solution
__Evaluation plan
problems                                                                 _*_Communicating
and predict results.                               _*_Estimating
A. Describe numerical relationships using variables               Strategies
and patterns.                                                            __KWL
_*_Cooperative Learning
8.A.2b Construct and solve number sentences using        _*_Demonstrations
a variable to represent an unknown quantity.                             __Drill & Practice
_*_Games
__Field Trips
Instructional Objective(s):                                              _*_Journals
__Drama
Objectives for this lesson: Students will be able                    _*_Reading/Writing
to…                                                                      _*_Discussion
_*_Groups/individuals
1. Understand that “how many” and “how                             projects
much” are important aspects of business and                    _*_Brainstorming

other aspects of daily life.                                   Equity
2. Identify the appropriate means to measure                       _*_Heterogeneous
grouping
and answer questions involving quantity in                     _*_Meaningful problems
__Decode rules & codes
general and money in particular.                               _*_Wait time
3. Participate in solving problems involving                       _*_Discipline
_*_Teacher/student
money and currency.                                            interactions
_*_Quality of feedback
_*_Knows student
Vocabulary:                                                              culture
Invest, interest, stock, stock market, company, shares,             _*_Knows students
strengths
shareholder, stock broker, return, profit, stock price, Wall             _*_Inquiry-based
Street.                                                                  Technology
__Films
Materials:                                                               __Laser disc
__Computer software
1. Image of Chicago Stock Exchange (1926). Retrieved                  __VCR/DVD
from Library of Congress (LOV.GOV), DN-0080464,                   _*_Calculators
_*_Digital
Chicago Daily News negative collection, Chicago                   Camera/Scanner
Historical Society.                                               _*_Web-based
Resources
2. LCD projector, screen, and laptop. Overhead projector
and markers.
3. Business section of Chicago Tribune or Chicago Sun-
Times. Highlight certain recognizable companies of
interest such as Disney, Starbucks, Walgreen’s, and
McDonald’s: transfer to transparency.
4. Calculators.

Teaching Strategies:
Anticipatory Set
Explain that the picture is of the Chicago Stock
Exchange. This, and other such places, is where the buying
and selling of shares of stock in all kinds of different
businesses takes place. (This project could continue for
several months as the students track the individual stocks they
choose in their “mock-stock” market.)

Practice

Guided
Describe process of investing in a company through the
purchase of shares of stock. Show transparency with familiar
companies
highlighted.

Independent practice
Have students look at newspaper to see all the different
companies; explain the numbers following the names and
what the
fractions represent.

Have students first estimate the amount it would cost to
purchase 10 shares of a given stock, and then compute the
actual cost.
More advanced students can create an extensive
“portfolio” of stocks. Calculators may be used.

Closure
Have the students write a paragraph on how the stock
market works and why math is important in understanding it.

Assessments(Teacher made tests, journals, project report,
observations, portfolios, written report, oral response, drawing,
project)
Assessment will be ongoing as the stock market project
will last several months. Students will be assessed not on the
performance of their stocks but on their understanding of the
application of math sense to participating in the market.

Lesson Evaluation
 Personal reflection (How did I feel about my delivery?
Have I used student’s assessment data to develop next
steps? Have I been able to engage all students in a
meaningful way?)

   Professional development needs (Common planning
time,. Consultant, in-service workshop, conference,
study group, individual study).

Lesson Plan Outline – THURSDAY
Math/Science Learning
skills
_*_Investigations
_*_Evaluating
_*_Recording Data
_*_
Interpreting/Analyzing
_*_Designing questions
_*_Listening
_*_Designing
Tables/Charts
_*_ Number Fluency
_*_Computational
Fluency
_*_Algebraic Reasoning

Process Skills
_*_Analyzing
__Guess & Check
_*_Developing
Metacognition
_*_Measuring
_*_Classifying
_*_Predicting
_*_Generalizing
__Justifying solutions
_*_Organizing/comparin
g
_*_Communicating
_*_Investigating
_*_Describing
_*_Comparing

Sports or Hobbies/Statistics/Percentages (45
_*_Looking for patterns

minutes)                                                    Problem Solving Skills
_*_Identifying problem
_*_Designing
Implementation plan
_*_Collect information
National/State/District Alignment:                                            _*_Organization data
_*_Representation
STATE GOAL 10: Collect, organize and analyze data using                   _*_Analyze data
statistical methods; predict results; and interpret uncertainty               _*_Present Data
_*_Check sensibility of
using                                                                         solution
concepts of probability.                               _*_Evaluation plan
_*_Communicating
A. Organize, describe and make predictions from existing data.             _*_Estimating
10.A.2a Organize and display data using pictures, tallies, tables,
charts, bar graphs, line graphs, line plots and stem-and-leaf graphs          Strategies
__KWL
10.A.2b Using a data set, determine mean, median, mode and           _*_Cooperative Learning
range, with and without the use of technology.                                _*_Demonstrations
10.A.2c Make predictions and decisions based on data and             __Drill & Practice
communicate their reasoning.                                                  _*_Games
__Field Trips
_*_Journals
Instructional Objective(s):                                                   __Drama
Objectives for this lesson: Students will be able to…                         _*_Discussion
1 Understand and interpret data.                                        _*_Groups/individuals
2. Tell how to organize data and make sense of                projects
_*_Brainstorming
variables     and    patterns   for  real-world
Equity
applications.                                                 _*_Heterogeneous
3.    State or communicate their findings to                  grouping
_*_Meaningful problems
answer specific questions.                                    _*_Decode rules &
4. Recognize the role probability plays in data               codes
_*_Wait time
collection and decision making.                               _*_Discipline
_*_Teacher/student
interactions
Vocabulary:                                                          _*_Quality of feedback
_*_Knows student
Writing in math; real-life math; sports; hobbies; integrate;     culture
applications; probability; percentages.                              _*_Knows students
strengths
_*_Inquiry-based
Materials:
Technology
1. LCD projector, screen, and laptop.                              __Films
2. Image of Soldier Field, Chicago (Armistice Day peace            __Laser disc
__Computer software
(LOV.GOV), DN-0090037, Chicago Daily News                      _*_Calculators
_*_Digital
negative collection, Chicago Historical Society.               Camera/Scanner
3. Whiteboard and markers.                                         _*_Web-based
Resources
4. Calculators.

Teaching Strategies:
Anticipatory Set
this stuff for?” Point out that statistics and percentages are
used in all sports and hobbies. For example, at Soldier Field
(shown in the image), football players use percentages like
passes made/passes attempted or how many yards per carry
on a running play. Baseball players rely on their batting
averages and the manager “plays the percentages” when
deciding whether to use a left-handed or right-handed pitcher.
Likewise, most hobbies rely on math in one way or another,
such as measuring cloth, string, or lumber.

Practice
Guided
Demonstrate a baseball player’s batting average based
on 10 at bats (e.g. 3 hits would be .333), and then show the
probability of
that player getting a hit if he goes to bat 3 times the next
game.

Independent practice
Have students write in their math journals what their
favorite sport or hobby is. Then have them list three ways in
which math is used
or related to their sport or hobby. They should give
specific examples.

Have the students write two math word problems
involving their sport or hobby and relating it to math. The
complexity of the
problems will be commensurate with the level of
competency each student has demonstrated. Students should
Calculators may be used.

Closure
Remind students that math is found everywhere, and
that they will need “this stuff” in everything they do.

Assessments(Teacher made tests, journals, project report,
observations, portfolios, written report, oral response, drawing,
project)
Journal paragraphs will be graded pursuant to a rubric
which will include 1 point for hobby or sport, 3 points each for
the examples of math usage, and 3 points each for word
problems (a total of 10 points).

Lesson Evaluation
 Personal reflection (How did I feel about my delivery?
Have I used student’s assessment data to develop next
steps? Have I been able to engage all students in a
meaningful way?)

   Professional development needs (Common planning
time, Consultant, in-service workshop, conference,
study group, individual study).

Lesson Plan Outline – FRIDAY
Math/Science Learning
skills
_*_Investigations
_*_Evaluating
_*_Recording Data
_*_
Interpreting/Analyzing
_*_Designing questions
_*_Listening
__Designing
Tables/Charts
_*_ Number Fluency
_*_Computational
Fluency
_*_Algebraic Reasoning
Process Skills
_*_Analyzing
_*_Guess & Check
_*_Developing
Metacognition
_*_Measuring
_*_Classifying
_*_Predicting
_*_Generalizing
__Justifying solutions
_*_Organizing/comparin
g
_*_Communicating
_*_Investigating
_*_Describing
_*_Comparing
_*_Looking for patterns

Problem Solving Skills
_*_Identifying problem
__Designing
Implementation plan
_*_Collect information
_*_Organization data
_*_Representation
_*_Analyze data
_*_Present Data
_*_Check sensibility of
solution
__Evaluation plan
_*_Communicating
_*_Estimating

Music/Rhythm/Pattern (45 minutes)                               Strategies
__KWL
_*_Cooperative Learning
_*_Demonstrations
__Drill & Practice
National/State/District Alignment:                                     _*_Games
__Field Trips
STATE GOAL 6: Demonstrate and apply a knowledge and                __Journals
sense of numbers, including numeration and operations                  __Drama
subtraction, multiplication, and division),      __Groups/individuals
projects
patterns, ratios and proportions.                                      _*_Brainstorming
A. Demonstrate knowledge and use of numbers and their
Equity
representations in a broad range of theoretical and practical   _*_Heterogeneous
settings.                                                       grouping
6.A.2 Compare and order whole numbers, fractions and decimals   _*_Meaningful problems
using concrete materials, drawings and mathematical symbols         _*_Decode rules &
codes
_*_Wait time
_*_Discipline
_*_Teacher/student
Instructional Objective(s):                                            interactions
Objectives for this lesson: Students will be able to…                  _*_Quality of feedback
_*_Knows student
1. Understand how the concepts of fractions                      culture
relate to music notation.                                              _*_Knows students
strengths
2. Apply the concepts of fractions to music                      _*_Inquiry-based
notation.                                                        Technology
3. Recognize patterns in musical notation.                       __Films
__Laser disc
__Computer software
Vocabulary:                                                          _*_VCR/DVD/CD
__Calculators
Musical notes, rests, whole notes, half notes, quarter           _*_Digital
notes, measures.                                                     Camera/Scanner
_*_Web-based
Resources
Materials:
1. LCD projector, screen, and laptop.
2. Image of All Aboard for Dixie Land / words by Jack
Yellen; music by George L. Cobb (c.1913). Retrieved
from Library of Congress (LOV.GOV), cited as rpbaasm
0265 http://hdl.loc.gov/loc.award/rpbaasm.0265.
3. Several sets of connecting manipulative math blocks
(fraction strips or Cuisenaire rods).
4. CD and player with a popular song of choice to
demonstrate rhythm, beat, and pattern. (E.g., Kid’s
Rock or Now That’s What I Call Music).

Teaching Strategies:
Anticipatory Set
Review basic musical notes, rests, and their values
(focusing on fractions). Use image to demonstrate how all
measures have an equal value, but can be made up of
different combinations of note values.

Practice

Guided
Play CD several times, clapping with rhythm, stomping
feet with beat, and stopping during rest. Emphasize that the
pattern is
embedded in the music.

Independent practice
Using the fraction strips, have students work in pairs to
visually represent their favorite part of the song on their desks.

Working in pairs, have one student arrange a measure,
and then have the other student attempt to tap it out on the
desk.

Closure
Play some more music while the kids put the
manipulatives away.

Assessments(Teacher made tests, journals, project report,
observations, portfolios, written report, oral response, drawing,
project)
Assessment for this day will be teacher observation based
on participation and oral response to determine understanding
and emergent fluency of applying fraction sense to music.

Lesson Evaluation
 Personal reflection (How did I feel about my delivery?
Have I used student’s assessment data to develop next
steps? Have I been able to engage all students in a
meaningful way?)

   Professional development needs (Common planning
time,. Consultant, in-service workshop, conference,
study group, individual study).

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