ETE 5017777777Jane Doe

This project features an assignment illustrating the usage of Microsoft Excel for a sixth grade mathematics project. The topic is calculations pertaining to the gear ratios, and measures of circular and linear distances. The project is to be worked on within a group of 3-4 students. Each student is to find out the specifications for a bicycle. This can be done by looking at the owner’s manual or looking up the bicycle on the internet. From this research they are to determine what the rear and front sprocket sizes are, diameters of the wheels, etc. Next they are to compile this information in the spreadsheet template that would be given to them after all of the formulas have been thoroughly explained. This project would cover two lessons, which are basic multiplication and basic division using Excel. Please see the actual project in the following pages.

11/8/201811:56:17 AMComprehensive ProjectPage 1 of 8

ETE 5017777777Jane Doe

The Sixth Grade Bicycle Project[1]

Teachers Using Technology in Mathematics Project

Bikes on a Spreadsheet

Purpose:

To use two bicycles as models for setting up the gear ratios as the "driving connection" for distance traveled in a particular gear during one pedal revolution, and to introduce the spreadsheet as a tool for recording and computing bicycle data.

Time Required:

2 days

Discussion of Purpose:

Students should be able to:

  • measure linear and circular distance
  • begin using correct terms for bicycle parts and understand their function
  • compute ratio and state as relationship using names and numbers
  • enter and format numbers in spreadsheet cells

Format:

  • Students work initially in large group setting with teacher questioning.
  • Students work in groups to compute and compare recording sheet.
  • Individuals enter spreadsheet data on large screen monitor.

Related Topics:

  • Continue individual work with Gears software, "Build Gear Factories"

Teacher Materials:

  • Microsoft Works 3.0, large screen monitor
  • trundle wheel (ft.)

Student Materials (per person unless otherwise noted):

  • measuring tapes, yardsticks (group)
  • handout: Appendix 2
  • calculator

Additional Preparation:

  • multiple copies of Appendix 2 and Appendix 6
  • For this lesson, arrange for a student to bring a BMX bike to school; another to bring a 10-speed (best) or 15-speed bicycle.

Assessment:

  • Completed Appendix 2 student recording sheet
  • Appendix 6

The most popular, and available, single-gear bicycle is a BMX (bicycle motocross) bicycle. BMX bikes are strong, durable, and light off-street bikes made to fly as well as ride. The front chainwheel may have from less than forty to more than fifty teeth. This is in contrast to the smaller rear sprocket, which may have thirteen to twenty-two teeth. The most common is 44-tooth chainwheel and 16-tooth freewheel, expressed as 44/16, or a gear ratio of 2.75. Of two different widths, BMX knobby-treaded tires are commonly on twenty-inch wheels.

(Note: students may bring up the length of the pedals' rotating cranks, often longer than on a standard street bike, for quicker acceleration and more power (torque) from the rider. This does not affect gear ratio, however. Good leg muscles are needed to get the longer cranks turning; short cranks demand faster pedaling.)

The suggestion of beginning with the ratio of distance traveled in a particular gear to tire circumference is based on our classroom experience. Turning the bike upside down and recording the revolutions of the back tire allows students to see the "turning relationship" of the pedals and the tire. This will later lead to better establishing the idea of gear ratios with students--ratios which determine the performance of the bicycle. This connection will happen at various times and in various stages throughout the project. To help students visualize how the ratios reflect the actual bike performance, two suggestions are offered:

  • Position the bike with front tire to their right. This helps match the left to right location of the parts as they will appear in the gear ratio. As in the BMX above, 2.75:1 is 2.75 turns of the rear wheel (cog) to 1 turn of the pedals (chainwheel).
  • State ratios with names of expressions and numbers of expression. "Rear wheel is to the pedal as 2:75 is to 1." or "Distance traveled in gear #1 is to circumference of the tire as...."

Procedure:

Day 1

  • By this date the class should be ready to apply what they know about gears, ratios, recording data about bicycles, and how a spreadsheet would appear and record this data. With the two bikes at hand, students in their groups, and Appendix 1 on the classroom monitor, begin by distributing copies of Appendix 2. Note the student spreadsheet is unlike the monitor spreadsheet (Appendix 1), but the column headings are the same. Three suggestions:
  • If the teacher works from the monitor and selects pairs or teams of students to rotate through the keyboard, better classroom management and quicker keyboard skills should result.
  • If the TV-ator has a "zoom", or a larger font is used, the text is clearer and they will not see gear inches at the top of Column L.
  • Demonstrate commands for the spreadsheet as data is recorded, not as a separate lesson at the end.
  • Begin with the question: "What do we need to know?" In any order suggested by students, follow with 2 more questions. "Why do we want to know that?" and "How might we find it out?" Again, in any order, student responses might be:
  • "What is the circumference of the tire?"Use the tape measure, convert fractions to decimals, and record. Some may suggest using diameter x pi... The "teacher reason" of why they need to know diameter is to compute gear inches, but this term has not been introduced yet and could be done when needed. Select the method they agree gives the best accuracy.
  • "How many teeth on the chainwheel? The cog?" Again, why and how?
  • "How many times will the rear wheel revolve as the pedal(s) goes around once?" Record as decimal estimation.
  • "How far in inches will the bike travel if the pedal(s) goes around once?"
  • Students enter the numbers in the correct cell. Here are good opportunities to demonstrate how to Format Cells by highlighting number, 1234.56, and setting decimal place value (see bottom row on student sheet).
  • Students are recording the data on their sheets before/as it are entered on the spreadsheet. Continue this exercise with the same questions concerning the ratio columns. Using calculators, compute the ratio for d/c and Tfront/Trear. Enter.
  • The reasoning here is more abstract and may be difficult for them to express; they may not yet know why. The ratios should be stated using the nouns and the numbers, as "The front chainwheel sprocket is to the rear cog sprocket as... is to one". If the bike is placed with the front tire pointed to their right, the ratio alignment matches the sprocket alignment.
  • Lastly, to introduce the idea of formulas, demonstrate the spreadsheet convention of speaking of numbers as their cell location. Set Options to Show Formulas. Teaching from the monitor, have a student enter these formulas as below, taken from Appendix 3. Return Options to Show Values. The ratios should be the same. If necessary, Format Cells to correct place value.

Day 2: Using a spreadsheet with a multi-gear bike.

  • Suggest the following question. Ask groups for an answer and the strategy used to solve it.

"When we go on our class trip, we will need to decide what biking attire to wear. Bikers are well known for their colorful outfits. Think about the following problem. Greg LeMond has two pairs of cycling shorts: black and dark blue. He has five colorful jerseys: rainbow, USA flag, official Unione Cycliste Internationale (UCI) colors, black/red checkerboard, and Shimano logo design. What are the possible number of shorts & jersey combinations he can wear? (15, organized list) Let's use this strategy to think about another problem. How might we determine the 10 gears on our 10-speed bicycle?"

  • There are multiple gears on both sprockets: two on the chainwheel, five on the cog. What are the possible combinations? First, we must determine the number of teeth on each gear (and confirm with second student). In groups, make an organized list of front-rear tooth combinations. The combos do not need to begin with first gear or end with last. A list on the board might be: (example)

AVERY'S 10-SPEED HUFFY BIKE
Chainwheel / cog / Combinations
39 / 14 / 50-14 / 39-14
50 / 17 / 50-17 / 39-17
20 / 50-20 / 39-29
24 / 50-24 / 39-24
28 / 50-28 / 39-28
  • Place Appendix 1--Gear Spreadsheet on class monitor again. Review procedure for compiling and recording data on bicycles: measuring diameter and circumference, distance traveled in each gear. revolutions of rear tire, etc. Each group should provide a member for the following tasks:
  • students to measure and record diameter and circumference of rear tire. Record on student sheets, the enter in Columns B & C, Row 3.
  • others to enter their list of gear combinations in Columns H & I. Begin with first gear listed (as above), not low gear. In the example above, 50-14 will actually become 5th gear. Ignore the gear no. # in first column until all data is gathered. Later we will Sort by gear ratio to match gear number.
  • students to measure the distance traveled in several or all gear combinations and enter distance in inches on recording sheet. They must match their distances with the tooth combinations group (not the gear number) when they enter their data.
  • As it is measured and recorded on their sheets, students may enter the data in appropriate columns on classroom monitor. Columns B, C, D, H, I, J, K should be filled in. There are not enough tasks here to engage every student. It is expected each student will complete their recording sheet with the data as it is compiled, and to compute the ratios on their calculators. So while classmates finish, others might work on Gears software, ratio homework sheet, or help with keyboard commands. Urge students to move cell box with arrow keys, not the mouse. Later in the lab this practice will save them many problems, and you many headaches!
  • TEACHER NOTE: Many new bikes have a shifting mechanism on the handlegrips which displays the gear number. Some elementary biking students will not be aware of any connection between this number and what goes on between their feet. This is the time to circulate, to check for understanding, and insure a member of each group is competent at measuring and entering data on their recording sheet and on the spreadsheet.
  • Gather class together for computer command instruction.First, model how to pull down Window, Show Header and enter name of student, number of gears, and brand name. Since spreadsheet is template, it is critical to File, Save As... and give it title with student or bike name. Model this again, and note file title at top of window.
  • To illustrate the Edit, Fill Down command procedure, first use the diameter and circumference columns. Next, quickly set the Options to Show Formulas.
  • "How might we enter a formula for computing the ratio of chainwheel to cog on our top gear listed here? This may or may not be first gear."
  • Engage students to state formula (=H3/I3) in Column J, then go to Edit, Fill Down. The formulas should appear sequentially by letter and number (see Appendix 4). If **** appears, you will need to slide the column wider to display the longer formulas at the bottom. Go slowly; this is an important moment for students to see this progression. Now Options, Show Values. If displayed with many decimals, go to Format Cells to number, highlight 1234.56, 2 decimals. For review, go to Column F.
  • "How might I enter a formula for computing the ratio of distance to circumference?" (=D3/C3) Repeat formula to value displays. Continue stating ratio in terms of nouns and numbers.
  • "How do I fill in the rest of the column? (Edit, Fill Down)
  • "How do I format the numbers so they have just 2 decimal places, to hundredths? (Format Cells to number, highlight 1234.56, 2 decimals)
  • Note again the file title. Do not close without checking this. Review using Options, Show FormulasShow Values and using arrow keys to move cell box.
  • Last, groups plan for tomorrow, and report on following questions:
  • "What is the name of your research group?"
  • "Who will provide disk to copy template for spreadsheet?"
  • "Who will bring multi-speed bicycle?"
  • Collect student recording sheets for checking.

Appendix 6

Student name______Student Group ______

Write in your own words what gear ratio means and how you might find it on a bicycle. What could you say about other ratios you might find when studying a bicycle.

Homework! Read the following story to someone older than you who might be able to explain Ronnie's misunderstanding. Record their comments below and bring back to class for discussion. You may want to use a drawing to help explain.

Ronnie Racer bought oversized drag "slicks" tires for the rear wheels on his Pontiac Trans Am. During the summer months he wanted a "raked" look, with the rear bumper raised. After having them mounted at the tire shop, he was driving west to Indianola on Interstate-80 at the speed limit of 65 MPH. Looking in his rear view mirror, he noticed the blinking red light of the Iowa Highway Patrol. Checking his speedometer, he confirmed to himself he was not speeding. He pulled off onto the shoulder, convinced he had done nothing wrong. The officer stated Ronnie was clocked by radar going 73 MPH. Radar is extremely accurate to within 1 MPH. Despite his objections, Ronnie got a speeding ticket.

Question: What sixth grade math idea did Ronnie ignore which ended in his speeding fine?Explain.

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