finding geometry in small business
A TechMath Module
Carol Arnold, Teacher
Rebecca Arnold, Student
Southern Nash High School, School
Michael Parker, Business Partner
Carolina Shooting Sports
July 2008
Preface
This module is designed to transfer basic skills learned in Technical Mathematics I into a useable real world setting. Student knowledge of collecting data, measuring and constructing angles, and creating circle graphs will be expanded to creating circle graphs and spreadsheets of real world business data. This module is intended to be the closure for the chapter involving angle measure, using a protractor and a compass. Students will use survey data of ten products, proportional reasoning, and Excel to present data and create an appropriate t-shirt order based on the survey results. The module can be completed in seven, ninety-minute class days. Students have had a basic overview of Excel during the eighth grade. Though prior knowledge of Excel is beneficial, it is not required for the success of this module. The teacher should be proficient in creating a basic spreadsheet, inserting simple formulas, and the ability to access and create graphs within Excel (directions are included in the appendix). Most of these students will not go on to Geometry or a four-year college. This unit is designed to foster their knowledge of angles in the real world setting and apply them to spreadsheet creation. Students will also be exposed to how spreadsheets can be useful to the students in a business setting. The students will be able to analyze and interpret various graphs from the real world. It should also be noted that the final project for this unit does not have to be as stated. Teachers can be flexible and allow students to choose another topic such as cost of building a deck, or a deer stand, or ingredients in recipe. The spreadsheet portion can be expanded to cover any student interest which involves multiple parts for construction. Teachers are not limited to T-shirt samples or ice cream choices within a classroom. One expansion I used was with the measurements for countertops in a kitchen. It is important to convey to the students the real world potential of spreadsheets in their future and the extensive use of pie graphs today.
This module was developed with the assistance of Michael Parker co-owner and operator of Carolina Shooting Sports in Rocky Mount, NC and Rebecca Arnold, student at Southern Nash High School. The context of the module deals with survey data for ten products and the visual representation of demand for these products. Basic circle graph presentation is transferred to an Excel spreadsheet to incorporate technology into a standard Technical Mathematics I project. The module also leads students to explore projecting product inventory based on current survey results. Utilizing the product data, students will also create an interactive spreadsheet to aid their making the connection between classroom and the small business setting.
Carolina Shooting Sports is a small two-person business. It supplies the outdoorsman with all his/her needs. The store is open year round with fluctuating stock based on the season, as well as, a line of year round stock. Hunting and fishing licenses are also available. The store carries a wide variety of guns and ammunition. Saturdays are often used for educational and certification classes. Carolina Shooting Sports is located on North Church Street in Rocky Mount. It is a one story approximately 3000 square foot building.
This module was developed during the spring and summer of 2008. During the fall of 2008, initial piloting within five classrooms began. The module was further edited and then piloted in additional classrooms in the spring of 2009.
Table of Contents
Lesson 1 Market Survey...... 4
Lesson 2 Targeting the Data...... 9
Lesson 3 Examining the Data……………………………………………………..16
Lesson 4 Aiming the Data Computer Lab………………………………….….….18
Lesson 5 Interpreting Real World Graphs…………….……………………….….21
Lesson 6 Research, Plan and Score ~ Bulls eye ………..……………...…….…...26
Lesson 7 Taking it to the Board of Directors………………………………….….27
Appendix Excel Anyone?………………………………………………………....29
Key Question
How can a simple survey paired with a spreadsheet, equip you for owning your own business?
Student Prior Knowledge:
Students should be able to: ~ use a protractor to measure angles
~ construct a given angle with compass and straightedge
~ understand the basics or be minimally familiar with Excel
Required Student Collection
Students will need access to a collection of 5-10 business related graphs from the internet, magazines or newspapers for use within this module.
Module Goals:
Students will be able to independently:
~ calculate frequency distributions for business product data
~ calculate relative frequencies, percentages, and degree measures which correspond to the data
~ using Excel, compare data in various graph formats to determine which, if any, method of data presentation is more useful when generating a visual representation of the survey results
~ create a basic spreadsheet to display business information product name, and survey results which includes formulas enabling future generic usage
Technical Mathematics I NCSCOS OBJECTIVES
1.01 Apply various techniques and strategies to solve problems.
a. Select or create an appropriate graphical display for a given set of data
2.01 Select and use appropriate tools to measure two- and three-dimensional figures; interpret and communicate results with regard to precision
Lesson Plan One
Market Survey
Lesson Abstract: The class will create a frequency distribution from classroom data to assist our business partner in ordering Mossy Oak t-shits. As a class, students will also calculate relative frequencies and derive angle measures for each category. The class will create a circle graph representing the Mossy Oak T-shirt Market Survey Class Data. Students will complete a Mossy Oak T-shirt Market Survey Homework Data survey of their family and friends on the topic and create a frequency table and a circle graph of their findings for homework. This lesson will take two days to complete.
NCSCOS Technical Mathematics I
Objective 1.01 Apply various techniques and strategies to solve problems.
a. Select or create an appropriate graphical display for a given set of data
Materials Needed:
Straightedge, protractor, compass, pencil, colored pencils, calculator, white paper, student handout #1, student handout #2, T-Shirt power point, teacher overhead #1
Lesson Goals:
~ to create a frequency table
~ to calculate relative frequencies
~ to calculate percentages
~ to calculate angle measures
~ to conduct a survey
~ to present two separate data sets in two individual pie graphs
Activity Description of Activities and Setting Materials
1. Introduction / Whole groupTeacher Questioning: How many of you have ever had to make a decision about something? What kind of decisions do you think retail businesses make?
2. Statement of Objective: Students will be able to assemble survey data into a frequency chart and a pie chart (circle graph).
NCOS 1.01, 2.01 NCTM Geometry, Data Analysis, Measurement / Whole group
Teacher Input: “Today we are going to start a project which will help you if you ever decide to have a business of your own. We will collect data from our class and create an appropriate graphical presentation of our class data.”
3. Major instructional sequence
A. Teacher input –
Utilizing the PowerPoint display of the t-shirt choices, teacher explains that if a student had a business that sold these t-shirts, it would help their business to predict an appropriate number of each kind to order.
B. Guided Practice -
Take class survey, recording tallies on teacher overhead transparency #1. Pass out student worksheet #2. Lead students in filling in frequencies, relative frequencies, percentages, and degree measures. Lead students to decide what makes comparison of data easy to compare?
Suggest a uniform color code and a circle or pie graph since they have just completed a chapter on angles
C. Independent practice –
For homework students will survey a minimum of 10 people. They will create a frequency table and a color-coded pie graph of their homework data during warm-up time the following day. / Activity #1 Gathering Data: Display Mossy Oak T-Shirt Selections
1. Teacher will display a visual of Mossy Oak T-shirt (located http://store.mossyoak.com) or T-Shirt PowerPoint or Teacher Overhead Transparency #1 and a list of the available colors for the upcoming season.
2. Survey students for preferred color and place a tally next to appropriate color on the Teacher Overhead Transparency #1. During the survey, explain to students that businesses need to survey their potential customers to order appropriately.
3. Students will tally number of males and females surveyed at the bottom of each survey table. This data is purely for discussion about data collecting and enables the teacher to indirectly draw student attention to factors which can affect data results. Students should be aware that if the order they are preparing is based on 90% female data and their store is patronized by an 80% male population, their stocking could result in a poor selection for the clientele. Some other factors could be age, race, and location. When compiling the final survey numbers, it can also be used as a double check for accuracy. / T-Shirt PowerPoint
Teacher Overhead Transparency #1
Activity #2 Create a frequency table
1. Convert tallies to frequencies (count tally marks and record as numeral
2. Calculate relative frequencies (divide frequency by total number of students surveyed)
3. Calculate percentages (multiply relative frequency decimal by 100)
4. Calculate degree measures ( multiply relative frequency by 360)
Suggest to the students that they record the means to finding each number at the top each column for future reference because they will need to be able to do this independently in the future). / Teacher Overhead Transparency #1
Calculators
Student Worksheet #2
Activity #3 Deciding on a graphical display
Instruct students to utilize a uniform color code for all circle graph data during this unit. Create a pie graph and color coded key as a class. IMPORTANT remember that the accuracy displayed here will affect the student products you receive at the end of this unit. Students will record color code on worksheet #2.
Students will use compasses and protractors to create a pie graph of the classroom data. / Teacher Overhead Transparency #1
Colored transparency markers
Overhead Compass
Overhead Protractor
Colored pencils
Student worksheet #2
Color Code Key
Activity #4 Individual Student Surveys, frequency tables and pie graphs.
Homework: Each student is to expand the classes’ market survey data. Students are to survey a minimum of 10 people to collect data. Their findings need to be recorded in a frequency table that includes: tallies, frequencies. / White paper
Colored pencils
Compass
Straightedge
Worksheets #1(a colored copy of the shirt samples) and #2.
Second day Warm-up activity: During warm-up students will calculate relative frequencies, percentages, and degree measures to complete their homework frequency table. They will also construct a circle graph of their homework data and a color according to the uniform color code already established. / Student Handout #2
6. Closure and/or Evaluation / Teacher should scroll through visuals representing each topic covered. Today we surveyed our class for t-shirt choices and learned to calculate relative frequency, percentage and degree measures. For our survey data, tomorrow we will display everyone’s homework survey pie graphs. Be considering what will make your data findings different and/or alike. Remember your pie graph must have title and a color-coded key. / Mossy Oak T-Shirt Selections
Teacher Overhead Transparency #1
Color Code Key
Lesson Essential questions:
1. Can students conduct a survey and create a data set?
2. Can students convert survey data into easily useable information?
3. Can survey data be used to influence a business product order?
4. Can students determine causes of differences/likenesses in their individual data sets?
Teacher reflection on lesson:
Students will mimic what they have seen and learned. Have I, as a teacher, demonstrated the importance of careful data calculation, careful angle creation? Are students able to calculate relative frequency, percentage and degree measures based on my instruction? Students will learn to apply what they have learned about angles to create a pie graph of the survey data. It is important for the teacher to demonstrate and then allow the students to mimic. Calculation of formulas should be clearly printed and left on display for students for reference.
Student Handout # 1
Student Handout #2 Name______
Mossy Oak Survey Class Sample
Color of T-Shirt/lettering / Tallies / Frequency / Relative Frequency / Percentage / Degree MeasureBrush Camouflage
Obsession Camouflage
Pink w/White
Brown w/ White
Black w/ Pink
Green w/ Yellow
Yellow w/ Pink
Gray w/ Black
Total:
Gender totals: Males______Females______
Mossy Oak Survey Homework Sample
Color of T-Shirt/ Lettering / Tallies / Frequency / Relative Frequency / Percentage / Degree MeasureSamples / ııı / number / Frequency/total sampled / RF x 100 / RF x 360°
Brush Camouflage
Obsession Camouflage
Pink w/ White
Brown w/ White
Black w/ Pink
Green w/ Yellow
Yellow w/ Pink
Gray w/ Black
Total:
Gender totals: Males______Females______
Homework: Using student handout #1 collect sample data from your friends and family. Record tallies of their answers and convert tallies to numerals.
Warm-up Day 2: Compute relative frequencies, percentages and degree measures. On a clean sheet of paper create a pie graph of your homework sample. Label it Mossy Oak Market Survey Homework Sample label shirt categories, percentages, and degree measures on the actual pie graph. Remember to include a key.
Teacher Overhead #1
Mossy Oak Survey Classroom Sample
Color of T-Shirt / Tallies / Frequency / Relative Frequency / Percentage / Degree MeasureBrush Camouflage
Obsession Camouflage
Pink w/ White
Brown w/ White
Black w/ Pink
Green w/ Yellow
Yellow w/ Pink
Gray w/ Black
Totals:
Gender totals: Males______Females______
Lesson Plan Two
Targeting the Data
Lesson Abstract: The class will compute the relative frequency, percentage and degree measures for their homework sample. They will also construct a pie graph for their homework data. Coloring can be completed for homework. Students will begin recording their homework survey data on the board during this time. Teachers will record frequencies for each t-shirt on Teacher Overhead #2 for the Community Survey Data (this is a compilation of all the student homework #s, as well as class data from day one.).