Steve Rioux
Shelley Shabenas
Current Issues/Trends in Mathematics (EDU 532)
Dr. Hari P. Koirala
June 9, 2004
Table of Contents
Content Page
Concept Map 2
Unifying Theme 3
Assumptions 3
Grade Level 3
Mathematical topics to be covered 3
Required resources 4
Unit Features 4
Tentative Timeline 5
Unit objectives and the standards
alignment 6
Introduction 7
Lesson Connections 7
Featured Lesson 12
Worksheets / Activities 14
Lesson Connections (Continued) 18
Appendix 21
Bibliography 25
The theme of this unit is to redesign their bedroom. The unit will encourage students to develop an understanding of the measurable attributes of objects, explore the processes of measurement, and solve realworld problems through organization and mathematical reasoning.
Assumptions
It is assumed students have used rulers and measured in the U.S. Customary system. They can measure objects to the nearest quarter inch, are able to find the perimeter of rectangles, and have been introduced to computer programs such as Word and Excel. However, it is not necessary that students have mastery of these skills to be successful in this unit.
Grade Level (s): 35
This unit is designed for
Mathematical topics to be covered
Estimation and rounding Ratios and Scales
Decimals and fractions Measurement
Designing blueprints  Area
Problem solving  Perimeter
Geometry  Time
Spatial / Proportional Reasoning 
Required Resources
Lesson 1: Television with VCR, Word Processor (optional)
Lesson 2: Rulers and Yardsticks
Lesson 3: Graph paper and Rulers
Lesson 4: Fraction Kits, Virtual Manipulatives (i.e. www.visualfractions.com)
Lesson 5, 6, & 7: Geoboards
Lesson 8: Graph paper and Rulers
Lesson 9: Calculators
Lesson 10: Computers with a spreadsheets program, such as Excel
Lesson 11: Computers and Internet access
Unit Features
Selfreflection of one’s character
Spatial Reasoning
Review of geometric shapes
Collecting and organizing data
Prioritizing one’s materialistic needs
Research the responsibilities of owning a
pet
Encourages problem solving
Combining measurements and using
fractions
Discussing the concept of area
Creating a personal schedule
Purchasing items while maintaining a
budget
Tentative timeline
This unit will take at least three weeks
to complete. However, it is likely to
take four weeks to complete. Each lesson
will be 40 to 50 minutes long. This unit
may be taught in conjunction with a language arts assessment and a science
assessment.
Lesson 1: Write a letter and include the
dimensions in your room.
Lesson 2:
Measure objects to the nearest quarterinch.
Lesson 3:
Read blueprints to find actual measurements of design.
Lesson 4:
Add fractions with unlike denominators of 2, 4, and 8.
Lesson 5: Perimeter
Lesson 6: Area
Lesson 7: Area (cont.)
Lesson 8: Create a blueprint
Lesson 9: Creating a budget (Featured
Lesson)
Lesson 10: Graphing
Lesson 11: Finding a pet
At the end of this unit the students will be able to:
Unit Objectives 
NCTM Standards 

1.
Determine reasonable estimates of lengths and areas and describe, in
writing, the strategy used to make the estimate. 
Measurement Reasoning and
Proof Numbers &
Operations Geometry 
Measurement Estimation
and Approximation Number Sense Operations Spatial Relations and Geometry 
2.
Measure lengths to the nearest quarterinch. 
Numbers &
Operations Measurement 
Number Sense Measurement 
3. Read a blueprint and convert a
scale size to its actual size (within the same system). 
Numbers &
Operations Geometry Measurement Problem
Solving Connections 
Number Sense Operations Spatial
Relations Measurement Discrete
Mathematics 
4.
Add fractions with like and unlike denominators (such as, 2, 4, and
8). 
Numbers &
Operations Measurement 
Number Sense Operations 
5.
Determine the perimeter of certain objects in a room. 
Numbers &
Operations Measurement 
Number Sense Operations 
6.
Solve multistep word problems involving area and purchasing from an
ordering catalog. 
Numbers &
Operations Problem
Solving Connections 
Number Sense Operations Discrete
Mathematics 
7. Find the area of composite figures. 
Numbers &
Operations Geometry Measurement Problem
Solving 
Number Sense Operations Spatial
Relationships and Geometry Measurement Discrete
Mathematics 
8.
Create a model representation of their room using an appropriate
scale. 
Representation Algebra 
Ratios,
Proportions, and Percents Algebra and
Functions 
Unit Objectives 
NCTM Standards 

9a.
Use estimation and logical reasoning to allocate and budget their
money appropriately. 9b. Create a budget and allocate
appropriate amount of monies to each category. 9c.
Perform all operations on decimals 
Number
& Operations Problem
Solving Reasoning and
Proof 
Number Sense Operations Estimation
and Approximation Discrete
Mathematics 
10. Students will create a bar graph
to represent the proportions in their budget. 
Data Analysis
& Probability Numbers &
Operations Communication 
Probability
and Statistics Ratios,
Proportions & Percents Estimation
and Approximation 
11. Add different measurements of
weight and determine appropriate amount of food needed to feed a pet for a different
period of time. 
Number &
Operations Measurements Problem
Solving 
Number Sense Operations Estimation
and Approximation Measurement Ratios,
Proportions & Percents Discrete
Mathematics 
National
Council of Teachers of Mathematics, (2000),
Connecticut State
Department of Education, (1999).
Introduction
Our
unit is designed to give students a purpose to use mathematical reasoning and
make connections with other disciplines.
We expect students to be able to communicate mathematically through
written language and through the use of visual aids. Our featured lesson in this unit will be
lesson nine. This lesson will also
illustrate possible modifications for the gifted and talented as well as those
with special needs.
Lesson Connections
In
our first lesson the students are shown the introduction portion of the hit ABC
series, Extreme Home Makeover.
The reality TV based program remodels the homes of deserving
families. The program begins by showing
the audience a video request that families submit to ABC in order to be considered
for a makeover. After the students see
the introduction part of the program, they will then create a letter describing
why they deserve an “Extreme Bedroom Makeover.”
First, students will be shown a sample letter to give them an idea of
what is expected from them. Students will then be given a writing prompt
(see Appendix A) to help organize their thoughts. Students must include a personal reflection
of their character and personality. They must also include a detailed
description of the dimensions of their room.
They need to be as accurate as possible and then justify how they
determined their estimates. The intent
of this activity to have students use items of known measurement, such as a
doorway (six feet) or their bed (six feet) and create spatial relations in
their room. Students will be asked, “How
will the reader visualize your room? How
can you estimate the dimensions of your room?
Do you know the length of any object, such as a bed or doorway, which
may be used as a point of reference? Do
you know any geometric vocabulary that will help specifically describes objects
in the room?”
Stimulating interest in student learning
is a major goal of this unit. Lesson 1
will directly relate to lessons 6, 7, and 8.
The essay will serve as a preassessment for understanding of area and
perimeter. It will be expected for
students to give the dimensions of their floor but not the square units of
their rug on the floor. As a homework
assignment, students will find all appropriate measurements of objects in their
room in order to create a blueprint of their room. After viewing the show at the beginning of
the unit, the students will also be shown sample blueprints (see Appendix B and
C) to aid how they may want their personal blueprint to be designed. Students however may have trouble rounding to
the nearest quarterinch.
Lesson 2 will focus on assessing
student’s ability to measure objects to the nearest eighth of an inch. However, they will only be assessed on
measuring to the nearest quarterinch.
After this lesson students will selfevaluate the accuracy of their
bedroom measurements from the night before.
Students will then discuss the strategies they used to determine the
estimates they made of their bedroom in their essay. Students will be encouraged to share their
frustrations by responding to these questions.
“Was there any object that was difficult to find an accurate measurement
for? How did you determine what was
important to measure?” These discussions
will encourage students to compare their actual measurements and their estimates
on their letter. Students may then make
any necessary adjustment to their actual bedroom measurements they made the
previous night.
Lesson 3 involves reading
blueprints. Students have had
experiences reading scales from a map.
We will build on this previous learned information to include its uses
in math class thus forming connections.
Students will need an understanding of adding fractions and experience
with working with area. These concepts
will explore in lessons 5, 6, 7, and 8.
In lesson 3, students will read a blueprint (see Appendix C) and discuss
how the designer represents doors, windows, closets, and the lengths of walls
on the scale model. Students will be
asked, “Does the design look realistic? Is it proportional? What does proportional mean? How did he make
the drawing proportional to the actual size?
What mathematical skills do you think the designer used?” These questions are intended to create a
purpose for learning new skills from the following lessons.
In lesson 4, students will begin to get
familiarized with fractions with unlike denominators. They will need this skill
in order to combine some of the measurements they collected from their
room. After given an introduction to
adding fractions with unlike detonators, students will then be asked questions
dealing with adding fractions that relate to their new bedroom. Some of the questions could be, “If onehalf
of your room was painted red, and oneeighth was painted blue, how much of your
room is painted?” Another question you could ask is, “If your closet is 6 1/8
feet wide and you make it 1 ½ foot wider, what will be the new width of your
renovated closet?” For added practice
you can have your students spend some time working with fractions kits for a
more hands on approach to see how fractions are added or even try visual
manipulatives on the World Wide Web. Web
sites like www.visualfractions.com
offer and interactive approach to working with fractions and offer a new
strategy to helping your students learn the important task of adding fractions.
Before students actually draw their
blueprints, they will investigate the concepts of perimeter and area in lessons
5, 6, and 7. In these lessons students
will use Geoboards to assist them in their explorations. Students will begin by discussing
perimeter. Students will be asked,
“Create a polygon that has a perimeter of twenty.” We will then display them by the board and
begin discussing designs. It is expected
that students will count twenty pegs, thus not having a perimeter of
twenty. We can review geometry concepts
and vocabulary by having students create objects with specific
characteristics. The instruction will
then lead students to try and communicate how one describes the area of an
object. Area and perimeter use two
different forms of units to describe their measurement. Students can take those experiences and begin
discussing the area of the floor of their bedroom. Students may then design their blueprints on
graph paper. The use of graph paper is
intended to bridge to the Geoboard activity to realworld applications,
therefore making the connections more probable.
To modify this for early grades or special needs students and to
incorporate technology into this lesson, the students can visit http://www.iknowthat.com/com/L3?Area=BluePrints&COOK= . Here they can click on interactive blueprints
that have the measurements marked out for them and they have to figure out the
area and perimeter. It’s a great site that presents area and perimeter in a way
that may help special needs students who are having trouble grasping this
concept.
In lesson 8 the students will design a
blueprint. They will discuss how they will choose an appropriate scale to make
the blueprint. This
is very challenging for many students. For example, if a student
chooses 1 ft = 1in, and the dimension of their actual room is 15' by
12' the blueprint design will not fit on a standard piece of paper. Some
students will choose a scale that will create a blueprint that is too
small. They will be asked questions such as, “How big should
our paper be? What estimations need to
be made in order to decide on an appropriate scale? Should we use the metric system or the U.S.
Customary system? Why?” Students will
then discuss their ideas with one another and justify their reasons
verbally. As an enrichment activity, this
lesson can be modified to discover different strategies that can be used to
solve ratios and determine if certain proportions are true. This enrichment can also include the use of
decimals within the proportions.
Students in the fourth grade typically do not see numbers with decimals
in the numerator and in the denominator of
Our featured lesson, lesson nine, teaches
students the mathematical concepts and operations shown in the table above by
means of another practical application: how to calculate a budget. From this point, students will focus on the
second phase of the unit, which deals with projecting costs and purchasing
materials for their bedroom. Our lesson
plan for “Creating
a Budget” begins on the following page. The next few lessons will cover important
mathematical topics such as currency, estimation, graphing, and problem
solving. Lesson connections will
continue on page 18.
Lesson 9
Creating a Budget
Grade 4
Standards Alignment: This lesson aligns with most of the NCTM
and
Required Resources: Calculator, “The Task” Activity Sheet,
“Specialty Designs For Less” Price List and Order
Form, and Mathematical Design Sheet (questions 110).
Lesson Assumptions: Students will have been working on this
unit already and will be involved in the last few lessons of the unit. The unit was introduced through the use of
the “Extreme Bedroom Makeover, Student Prompt” sheet. It is assumed that students will have a good
understanding of area and perimeter and how to measure them before starting the
lesson. Students should also have a
general knowledge of common
Objectives: At the end of this lesson, the students
will be able to:
a) Create a bedroom design on
b) Use the area and perimeter of the room to
purchase items in their bedroom design.
c) Use the “Specialty Designs For Less” Order Form to list purchases and the amount spent
(see attached).
Lesson Procedure: The teacher will initiate the lesson by
distributing and explaining “The Task” (see Activity Sheet) to students. Approximately 1520 minutes of lesson time
will be spent discussing the budget activity while permitting any student
questions. After that, each student will
receive the “Specialty Design for Less” Price List as well as the corresponding
“Order Form” (all activity sheets shown on the next few pages).
Students
will first select their bedroom’s design theme (ie. safari, cars, disco,
etc.). This will be the basis for all
items ordered. Students will use their
own personal experiences and imaginations to select the desired look for their
new bedroom. The teacher will direct
students’ attention to the price list in which he or she must carefully guide
students through their understanding.
Students will need to have a good understanding of area and perimeter to
be able to complete the order form.
At
this point in the lesson, students would use the price list to complete their
order. Students are reminded that their
price list must include a bed and their total should not exceed the $500
spending limit, including shipping charges.
Calculators will be made available for students in this activity. For this activity, students will be applying
many mathematical skills such as estimation, mental imagery, problem solving,
logical reasoning, numeration, and measurement.
It is expected that they will modify and adjust their price lists
accordingly in order to comply with the given budget.
Moreover, students will be making
applications to reallife situations.
This lesson will connect to science where students will be researching a
pet using various resources such as the Internet and nonfiction expository
texts.
Lesson Assessment: When the teacher is listening to student
discourse and observing students’ progression through the budgeting activity,
he or she will continuously monitor and evaluate the thinking processes of all
students. Furthermore, the teacher and
students will be evaluating themselves when they compare their work to the
scoring rubric. This assessment process involves both the teacher and students
engaging in reflection of the learning process.
Specialty Designs For Less
We
get what you want at a price you can afford!
**All items are custom
made, please specify colors and pattern on order form.
If you can dream it, we can
make it!
Wall Designs 
Border Specify
design choice. Each roll covers a
length of 5 yards. $12.50
per roll 
Paint Specify Color. $12.95 per gallon. 
Decals Your design choice, as
set of 10. SelfSticking. Specify Design. $14.95 per set. 
Beds 
Twin Bed Basic Bed $100.00 
Specialty Twin Bed Built the way you want
(Car shape, etc…) Please specify on order form. $150.00 
All twin beds are 5’6” x 3” 
Bedspreads/ Comforters 
Twin size bedspreads –
any color or design. $55.25 
Twin size comforter – any
color or design. $55.25 
Twin size dust ruffle –
any color. $25.00 
Furniture 
Chairs Small (2’ x 2’) – color
of your choice. $175.00 Desk Chair $75.00 
Desk (4’ x 2’) – 3
drawer, color of your choice. $75.00 Bookcase (1’ x 3’) $75.00 
Chest of drawers (3’ x 2’) – 4 drawers $125.00 Dresser (4’ x 4’) – 3 small drawers, 4 large $200.00 
Extras 
Color TV Sets 25”  $250.00 36” – 350.00 Stereos Basic – with AM/FM $100.00 With AM/FM & CD
Player $200.00 Deluxe – With AM/FM, CD,
& Large Speakers $350.00 
Lamps Lava Lamps Blue, red, or green $15.95 Specialty Lamp Your design. $50.00 Desk Lamp $25.00 Disco Ball –with lights $40.00 
Car Track $45.00 Train Track $45.00 Aquarium – Includes Everything! $75.00 Reptile Tank – with
heater and lamp. $50.00 
Extras 
Clock – Digital Specify design choice. $45.00 
Computer System $100.00 With Printer. $150.00 
Telephone Specify design choice. $50.00 
Specialty Designs For Less
Order Form
Name:
_____________________
Shipping Address:
____________________
____________________
Item 
Product
Description & Color/Design Specifications 
Price

Quantity

Total



$ 

$ 


$ 

$ 


$ 

$ 


$ 

$ 


$ 

$ 


$ 

$ 


$ 

$ 


$ 

$ 

*********** 
*********** 
SUBTOTAL 
$ 

*********** 
*********** 
SHIPPINGCHARGES 
$ 

*********** 
*********** 
TOTAL 
$ 
**Please use additional order forms if needed**
Shipping Charges:
$0.00  $49.99…….$2.99
$50.00  $199.99…….$5.99
$200.00  $399.99…….$8.99
$400.00 and up…….$10.99
Extreme Bedroom Makeover
Mathematical Designs Sheet
Designer’s Name___________________________________________
1. What are the dimensions of your dream bedroom?
________________________________________________________________
2. What is the AREA of your dream bedroom?
________________________________________________________________
3. What is the PERIMETER of your dream
bedroom? ________________________________________________________
4. How many feet of border would you need for your
dream bedroom?
________________________________________________________________
5. How many yards? (3ft in one yard)
________________________________________________________________
6. How much carpeting would you need for your
bedroom? ________________________________________________________
7. How many gallons of paint would you estimate
you would need for your dream bedroom?
________________________________________________________________
8. Assume your bedroom has 7ft. high ceilings.
What is the area of each wall?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
What is the total area of your walls?
________________________________________________________________
9. If one gallon of paint covers 300 sq. ft.,
how many gallons will you need for your room?
________________________________________________________________
10. The dimensions of a twin bed are 5'6 x 3', what is the
area?
________________________________________________________________
Extreme Bedroom Makeover
“Dream Room”
Scoring
Rubric

Outstanding 
Doing Good 
Needs Some Work 
Unsatisfactory 
Perimeter 
The
perimeter is correctly drawn for a room with dimensions of: ___________ 
The
perimeter is within one foot of the correct dimensions. 
The
perimeter is within 23 feet of the correct dimensions. 
The
perimeter is more than 3 feet off of the correct dimensions. 
Furniture 
Furniture
sizes are drawn correctly and labeled with item names. 
Furniture
sizes are drawn correctly, but some are labeled. 
Furniture
is only drawn, but not labeled, or vice versa. 
Drawings
are unclear, or the furniture is so packed it would be impossible to walk
through the room. 
Letter to Parent 
The
letter is written in proper format and follows the assignment. 
The
letter has 
The
letter has distracting errors in format. The letter does not stay on topic
for the assignment. 
The
letter does not follow letter format. The topic of the letter does not follow
the assignment. 
Spelling 
The
letter has no spelling errors. 
The
letter has 13 spelling errors. 
The
letter has 46 spelling errors. 
The
letter has more than 6 errors. 
Grammar 
The
letter has no grammar errors. 
The
letter has 13 grammar errors. 
The
letter has 46 grammar errors. 
The
letter has more than 6 errors. 
Sentence Structure 
The
letter has no errors in sentence structure. 
The
letter has 13 sentence structure errors. 
The
letter has 46 errors in sentence structure. 
The
letter has more than 6 errors in sentence structure. 
Name:
______________________________
Total Points: ________/24
Teacher Comments:
Students can be given a list of items that that they need to buy like a television, dresser, phone, alarm clock, etc. Next they will be given some weekly flyers, a catalog, or a couple websites and asked to purchase the items that are required to buy. The only drawback is that they are only allowed to spend a certain amount of money. This will introduce students in the early grades to the concept of budgeting. They can then be asked, “What did you consider before purchasing an item? Why did you spend more on one item and less on another? Were you able to get everything you wanted? Did you go over budget and why do you think you did? Have you ever had to budget before in real life?” When the students realize that they have had to budget before or think about if they have had enough money for anything they make a connection to how math like this is important and used in the real world, hence covering some of the connections sections under the national standards for mathematics. Also other national standards covered in lesson would be numbers and operations and problem solving. As an enrichment activity, technology could be brought in for higher grades. For example, students will first be told what they have to buy for their brand new bedroom and how much they have to spend. After getting an introduction to Microsoft Excel they will then enter in their estimated prices of what they estimate each item will cost or what they think they can afford. After entering their estimated prices they will graph it with Excel showing the percentages that make up their total amount they have to spend. They can then be asked questions such as, “Based on your estimations do you think you will be under budget, over, or right on?” “What considerations did you make when deciding on how much you wanted to spend on and item? By asking questions and bringing discussion into the classroom you will then be covering the communications section of the National Standards for Mathematics. Through the graphing you will cover the data analysis section.
Lesson ten will deal with incorporating
technology into the unit by having students use computers to graph their
budget. Through the use of Microsoft
Excel the students will enter in each item that they purchased (TV, paint, DVD
player, rugs, etc) and how much that item(s) cost them. After that is finished
the students will find the percentage each item represents out of the total
amount spent. The students will have already had a background on division and
finding percents before this unit is used.
However, a tutorial will be given to show how to convert their data into
bar graphs or pie charts in excel, it will be their choice on how they want to
present their budget visually.
Lesson eleven, which is the final lesson
of the unit, is a continuation of using computer and incorporating Internet
navigation. The student and or students
will have the opportunity to get a new pet for their brand new bedroom. Through the use of searching on the internet
the student will be required to not only find a pet but write a report on what
family it is part of, the things it eats, characteristics, how small or large
it grows to be, what type of climate or region is it mostly found in, how they
plan to take care of it and why they chose this pet. To incorporate mathematics
into this lesson you can have the students find out what the pet eats and how
much. Next, ask them to research how much the pet food costs and based on how
much the pet eats, what will they pay for pet food a
day, in a week, a month, and a year. They can even figure out how much visits
to a vet would cost and how much they would spend on vet visits in a month or
year. For special needs students or students in earlier grades (12) you can
incorporate math by making up world problems about the pet they chose. For
example, student A chooses to have a pet tiger. You can ask simplified
questions like, “If
your pet tiger got loose and met up with another pet tiger, how many legs would
there be total?” Answer: 4 tiger legs +
4 tiger legs = 8 legs or “How many tails would they have?”
Unit Assessment: Students’
assessment will be an ongoing process throughout the entire unit. Students will compile a collection of their
best work and place it in a portfolio.
Students will include their letter, blueprint, order form, graphs, and
pet choice. At any point in the unit a student may resubmit previously
corrected work. Students will then
present their new bedrooms to the class in a short fiveminute oral
report. The total score will be based on
a combination of completed work, presentation, participation, and their oral
report.
Appendix
A
“The Task”
Dream
– What kind of theme will your bedroom have?
Today is the day for you to get your
creative juices flowing! What kind of
bedroom design theme will you choose…Tye Dye…Cars…Safari? What colors will you choose…Blue…Red… Purple? The choices are endless, so you need to
decide on a theme for your “Extreme Bedroom Makeover.” You might want to make a list of your
ideas. Once you have decided on your
theme and have sharpened your math design skills, you will need to complete the
order form using the “Specialty Designs For Less”
Price List so you will be ready to go shopping tomorrow to purchase your
supplies. Using your mathematical
design abilities, you must come up with items needed to complete your dream
bedroom on a budget of $500. Your
purchase must include a bed. Don’t
forget to include shipping charges and do not exceed the $500 spending limit.
Appendix
B
Appendix
C
Scale: 1ft. = 3/4 inch
Appendix
D
Specialty
Designs For Less:
Sample Design
Order Form
Name: Student A
Shipping Address:
Item 
Product
Description & Color/Design Specifications 
Price

Quantity

Total

Paint 
Red 
$
12.95 
2 
$
25.90 
Beds 
Twin Bed 
$
100.00 
1 
$
100.00 
Bedspreads 
Twin Size 
$
55.25 
1 
$
55.25 
Furniture 
Bookcase 
$
75.00 
1 
$
75.00 
Extras 
StereoBasio 
$
100.00 
1 
$
100.00 
Extras 
Aquarium 
$
75.00 
1 
$
75.00 
Extras 
Telephone 
$
50.00 
1 
$
50.00 


$ 

$ 

*********** 
*********** 
SUBTOTAL 
$ 481.15 

*********** 
*********** 
SHIPPINGCHARGES 
$ 10.99 

*********** 
*********** 
TOTAL 
$ 492. 14 
**Please use additional order forms if needed**
Shipping Charges:
$0.00  $49.99…….$2.99
$50.00  $199.99…….$5.99
$200.00  $399.99…….$8.99
$400.00 and up…….$10.99
References
National
Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
Connecticut State
Department of Education. (1999). A guide to K12 program
development in mathematics.