E-Mail Address:kmurphy@hfhighschool.org
School:Homewood Flossmoor High School: Flossmoor , Ill.
School Home Page URL: http://www.hfhighschool.org
Author: Kathleen Murphy
E-Mail Address:kmurphy@hfhighschool.org
School:Homewood Flossmoor High School: Flossmoor , Ill.
School Home Page
URL: http://www.hfhighschool.org
THEME :Geometry is Real
BROAD CONCEPT:Team work,project building, presentation skills,transfer of school to real life
GRADES:7-9 geometry
INTEGRATED SUBJECTS: math, science, language arts,technology, art
UNIT GOALS AND
PURPOSE;
The purpose of this project is for the students to work as a team to
use internet resources in order to make connections between two- and
three dimensional shapes and the real world. They will be given
opportunities to explore their own world and the world of the
internet. The students will develop new ideas and understandings
while working with others. Students will analyze characteristics
and properties of two- and three-dimensional geometric shapes to
visualize and solve problems such as those involving surface area and
volume. Students will use a spreadsheet to display
information and KidPix Deluxe Studio to present their slide show
on geometric solids. In completing the house project on
home
improvement the students will have solved problems in, and gained
insights into, other disciplines and other areas of interest such as
art and architecture.
The unit will be evaluated in an ongoing manner by the teacher
since every class has an activity that allows the teacher to monitor
student work. In regards to evaluation, the unit is also
performance-based since the students will be completing many authentic
tasks. With the open-ended culminating project, the unit will
also be evaluated in a summative manner.
TIME FRAME:
10 school days
OBJECTIVES:
In this lesson, students will:
_x_Word Processing = MS Word _x_Spreadsheet =Ms Excel
_x_CD-ROM Encyclopedia = Encarta __ Database = MS Works
_x_
Multimedia=KidPix,Powerpoint,Hyperstudio
1.C.2d
Summarize and make generalizations from content and relate to purpose
of
material.
1.C.2f
Connect information presented in tables, maps and charts to printed or electronic
text.
1.C.4f Interpret tables, graphs and maps in
conjunction with related text.
.3.B.2a
Generate and organize ideas using
a variety of planning strategies (e.g., mapping, outlining, drafting).
3.C.1b
Create media compositions or productions which convey meaning visually
for a
variety of purposes.
3.C.3b
Using available technology, produce compositions and multimedia works
for
specified audiences.
3.C.4b
Using available technology, produce
compositions and multimedia works for specified audiences.
4.A.4a Apply listening skills
as individuals and members of a group in a variety of settings (e.g.,
lectures,
discussions, conversations, team projects, presentations, interviews).
4.B.4a Deliver planned informative and
persuasive oral
presentations using visual aids and contemporary
technology as
individuals and
members of a group; demonstrate organization, clarity, vocabulary,
credible and
accurate supporting evidence.
5.A.3a Identify appropriate resources to solve problems or answer questions through research.
5.A.3b Design a project related to contemporary issues (e.g., real-world math, career development, community service) using multiple sources.
5.A.4a Demonstrate a knowledge of strategies needed to prepare a credible research report (e.g., notes, planning sheets).
5.A.4b Design and present a project (e.g., research report, scientific study, career/higher education opportunities) using various formats from multiple sources.
5.C.5a Using contemporary technology, create a
research
presentation or prepare a documentary related to academic, technical or
occupational topics and present the findings in oral or multimedia
formats.
Mathematics
6.D.4 Solve problems involving geometric similarity using ratios
7.A.3a Measure length using sophisticated instruments
7.A.3b
Apply the
concepts and attributes of
length, capacity, weight/mass, perimeter, area, volume, time,
temperature and
angle measures in practical situations.
7.A.4a Apply units and scales to describe and compare numerical data and physical objects.
7.A.4b Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values.7.B.3 Select and apply instruments including rulers
7.B.5 Estimate perimeter, area, volume, and capacity of irregular shapes, regions and solids and explain the reasoning supporting the estimate.
7.C.2b Construct or draw figures with
given
perimeters and areas.
7.C.4b Interpret scale drawings and models using maps and blueprints.
7.C.4c Convert within and between measurement systems and monetary systems using technology where appropriate.9.B.4 Recognize and apply relationships within and among geometric figures
9.C.4a Construct logical arguments for geometrical situations using technology
9.C.4b Construct and communicate convincing arguments for geometric situations10.B.1b Collect, organize and describe data using pictures, tallies, tables, charts or bar graphs.
10.B.1c Analyze data, draw conclusions and communicate the results.|
• |
precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties; |
|
• |
understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects; |
Use
visualization, spatial reasoning, and geometric modeling to solve
problems
|
• |
draw geometric objects with specified properties, such as side lengths or angle measures; |
|
• |
use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume; |
|
• |
use visual tools such as networks to represent and solve problems; |
|
• |
use geometric models to represent and explain numerical and algebraic relationships; |
|
• |
recognize and apply
geometric ideas and relationships in areas outside the mathematics
classroom, such as art, science, and everyday life. |
STUDENT ACTIVITIES WHICH
WILL PROMOTE ENGAGED LEARNING
Lesson
1. Brainstorm
The class will open with a PowerPoint
presentation showing triangles, quadrilaterals,and circles and
their area formulas. Students will be introduced to the unit Geometry Around Us. We will
then brainstorm using Inspiration as an entire class on all the facts that
the students may know about three dimensional objects (e.g.,prisms,
pyramids, cones, cyllinders and spheres) and their surface area and
volume. We will use a KWL/KWLH Chart as a graphic organizer
to help students develop orgnizational skills for this and other
research projects. To relate this lesson to the real world,
students will be expected to find an example of each kind of
three-dimensional solid at home and be prepared to share their findings
with the class. These examples will include pictures,
photos(using a digital camera) or actual objects of each solid.
Lesson 2. Sharing and
research
After a discussion about the three-dimensional
solids students found at
home, the class will go to the computer and work in groups to discover
examples of three-dimensional solids in everyday life, science, nature,
business and art. Each group will use Inspiration
to organize their findings. The groups will supplement
their Inspiration
webs on three-dimensional solids, so that each solid has two or more
real world examples. Use internet sites such as Images/google.com.or
http://multimedia.lycos.com/
Lesson 3 & 4.
Research and Slide Show
Using the initial KWL Chart, internet sites, Websters Dictionary, MS Encarta, and World
Book Encyclopedia, each group will record definitions, surface
area and volume formulas for each three-dimensional solid using MS
Word. Further research will include finding graphics for
each
geometric solid. Use internet sites such as http://www.webmath.com/geo_cylinder.html
,and http://www.webmath.com/index5.html
.
Each group will produce a slide show presenting this information using KidPix Deluxe,
PowerPoint or Hyperstudio. The slide show will contain at
least two slides for each geometric solid with definitions,surface area
and volume formulas, illustrations and graphics of real world
occurrences of these geometric solids. Each group will
present their slide show to the class.
Lesson
5. Cereal box
This activity will provide a tangible example of deriving the formula
for the surface area of a rectangular solid. The students will be
assigned to cooperative groups. Each group will be equipped with
a cereal box, scissors,rulers, and colored markers. The students
will be
instructed to produce a net for the cereal box in scale using MS Excel, shade
congruent faces the same color, write the area on each face, then find
the total surface area. Each group will generalize how to find
the surface area(use variables instead of numbers). Groups will
share to see if their generalization works on the neighbor's box or on
any box. Each group will report to the class what they have
discovered about their cereal box, explaining how they came to their
conclusions. The connection of this formula to the House
project will be discussed.
Lesson 6. Volume
and Space
This lesson involves activities
using the volume and surface area
formulas for geometric solids. The students will work in
pairs. For activity one, the students are given the dimensions of
a swimming pool and asked to determine its volume, how much water it
contains and how much that amount of water weighs. Students will
use MS
Word
and MS Excel
to record results and computations
for each activity. For
activity two titled
We Have
Liftoff:Math and the Space
Program, the students, using
the
Manned Space Program Data Sheet
, will answer questions involving volume of the cone-shaped capsules
and how much space was allowed for each person on the Mercury, Gemini,
and Apollo missions. For activity three titled The Capacity of
the Planets,
the students, using a chart listing the planets and their diameters,
will answer questions about their volumes and surface areas. Data
sheets and suggested questions can be found at these sites http://www.pbs.org/teachersource/mathline/concepts/space2/activity3.shtm
and
http://www.pbs.org/teachersource/mathline/concepts/space/activity1.shtm
Lesson
7. Research for the
House Project.
Students will begin the house project in this lesson. Working in
pairs, the students
will visit internet sites like http://www.dreamhomesource.com/and
http://www.design-house.com/
The project requires a blueprint of a 3-bedroom house, ads for carpet,
tile, interior house paint , fertilizer and an airconditioner. If
ads cannot be found on the internet, they can be scanned from
newspapers or brochures. The students could also visit local
stores and take pictures with a digital camera of these items and their
prices. This data will be included in the final
presentation using KidPix,Hyperstudio or PowerPoint.
Lessons 8&9.
Dimensions and Cost
Students will use MS Excel
to determine areas, volumes and costs for the project. Students
will enter the dimensions of the 3 bedrooms and livingroom into MS Excel.
They will determine the area of each room in square feet and square
yards. Using the carpet ad, they will determine the cost of
carpet. Students will enter the dimensions of the kitchen and
bathroom(s) and find the area in square feet. Using the tile ad ,
they will determine the cost of tile (no partial tiles
purchased). Using the dimensions of the three bedrooms, the
students will determine the ceiling and wall areas in square feet
(assuming walls are 8 ft. high). Using the paint ad, the
students will determine the cost of paint (applying 3
coats). Assuming the lawn extends 50 feet from the house in each
direction, determine the lawn area in square feet. Using the
fertilizer ad, the students will determine the cost of
fertilizer. Using the dimensions of the recorded rooms, the
students will determine the volume in cubic feet and the cost of the
airconditioner indicating how many tons are needed.
Lesson
10. Total Costs
and Show
Students will complete their house projects. Students will use MS Excel
to determine and record the total cost for carpet, tile, paint,
fertilizer and airconditioner. The house project will be
presented in a slide show using KidPix,
PowerPoint or Hyperstudio.
The presentation will contain blueprints, ads, spreadsheets indicating
their results for
area,volume and costs as well as a written explanation of all
calculations and
costs using MS
Word. Additional activities would include preparing
a sign of
a brochure using Print Shop
advertizing their chosen house plan and illustrating their
materials for their home improvement.
SHARE YOUR IDEAS:
Students will present their final project to the class. The
culminating project for the unit will be a multimedia
presentation to the class as well as a written explanation of all
calculations in the project to the teacher. The rubric for the
activity is as follows:
Presentation includes:
Points
| blueprint of 3 bedroom
house |
10 |
| ads for carpet, tile, interior
house paint, fertilizer and airconditioner |
10 |
| accurate area in square feet for
the bedrooms, livingroom, kitchen and bathrooms |
10 |
| accurate area in square yards
for the livingroom and bedrooms |
4 |
| accurate dimensions and area of
the lawn |
2 |
| accurate volume in cubic feet
for the bedrooms, livingroom, kitchen and bathrooms |
4 |
| accurate costs for carpet, tile,
paint, fertilizer and airconditioner accurate total cost |
30 |
| set of slides are
organized,sequenced smoothly and show
creativity accurate spreadsheet and explanation of calculations |
15 15 |
STUDENT AND TEACHER
ROLES:
Students will lead much of their own work because they will be working
together. The tasks are authentic, challenging, and
multi-disciplinary. The students have the opportunity to be
explorers. The students become the teachers for their small
groups and the class as a whole. Students become producers in
that they develop products of use. The teacher is a facilitator
of learning by creating well-developed lessons that have a
problem-solving aspect to them. The teacher will also facilitate
group set-up by ensuring that groups are flexible and
heterogeneous. The teacher is a guide by modeling different
concepts for the students. The teacher supports the students'
journey through the unit by giving feedback based on student
need. Whole class discussions as well as group work facilitate
learning. The teacher focuses not controls student
learning. Finally, the teacher is a co-learner. Many
activities require the teacher to adapt and modify the unit to
meet students' needs.
ADDITIONAL REFERENCE PRINT RESOURCES STUDENTS MAY USE :
World Book Encyclopedia
Webster's Dictionary
THE FOLLOWING BOOKS CONTAIN INFORMATION ABOUT THIS TOPIC:
Exploratorium Guide to Scale and Structure by Barry Kluger-Bell and the School in the Exploratorium
FOR ADDITIONAL ONLINE INFORMATION AND MEDIA PERTAINING TO THIS UNIT, TEACHERS MAY WANT TO USE THE FOLLOWING INTERNET ARTICLES:
URL1: http://www.pbs.org/teachersource/mathline/concepts/space/activity1.shtm
Description1: Lesson plan and activities with data
sheet for finding volume related to the space program
Title2: The Capacity of the Planets
URL2: http://www.pbs.org/teachersource/mathline/concepts/space2/activity3.shtm
Description2: Lesson plan and activities
with charts and questions related to volume and surface area of spheres
as well as relative distances of the planets
Title3: Math in the Park or City
URL3:
http://www.pbs.org/teachersource/mathline/concepts/neighborhoodmath/activity2.shtm
Description3: Lesson plan and
activities for real life problems involving
ratio,proportion, length, area, volume, weight and patterns.
Title4: Baseball Geometry
URL4: http://www.pbs.org/kenburns/baseball/teachers/lesson4.html
Description4: Lesson plan and activities
relating the volume and surface area of a sphere to the construction of
the baseball
Title5: Glencoe Online:Web resources Mathematics
URL5: http://www.glencoe.com/sec/math/cool/index.htm
Description5: A Glencoe textbook link that
offers extended activities and web resources
Title6: ifigure.com
URL6: http://www.ifigure.com/math/geometry/geometry.htm
Description6: Provides links to sites for interactive
geometry
concepts , calculators and formulas
URL1: http://www.dreamhomesource.com/
Purpose of Use1: Finding a blueprint of a three-bedroom house
Description1: Provides printable house
plans
Title2: Design-house.com
URL2: http://www.design-house.com/
Purpose of Use2: Finding a blueprint of a three-bedroom house
Description2: Provides printable house
plans
Title3: Ask Dr. Math
URL3: http://mathforum.org/dr.math/faq/formulas/
Purpose of Use3: Research of formulas for 2- and 3-dimensional geometric shapes
Description3: Provides links to definitions and
formulas for geometric shapes
Title4: Bizrate.com
URL4: http://www.bizrate.com/buy/browse__cat_id--13000000.html
Purpose of Use4: Ads for carpet, tile, paint and fertilizer
Description4: Provides links to various
sources for ads and data on home improvement items
Title5: School.discovery.com
URL5: http://school.discovery.com/clipart/category/math1.html
Purpose of Use5: Graphics of the three-dimensional solids for the KidPix slide show on solids
Description5: Provides pictures of
the solids in real life depictions when a term is
typed .
Title6: Webmath.com
URL6: http://www.webmath.com/
Purpose of Use6: Investigation of geometric
shapes as well as their formulas for area and volume
Description6: Provides quick answers to
numerous math questions on a variety of topics with links to a math
expert