Pennies, Pennies, Pennies, and More Pennies

Pennies, Pennies, Pennies, and More Pennies

Objective: Ms Hornby’s Unified Geometry Students have been selected by Ms Penny Saver to determine the cost of covering the floor with pennies. Penny has been saving pennies for a long time. Your task today is to help her decide just how much it will cost to cover the floor next to the baseboard, cover the entire floor with pennies, and fill the room with layers of pennies. Ms. Saver wonders if there will be white space between the pennies. If she were to drop a head of a pin on the floor what is the probability that the pin would bounce first on the penny and not on the white space?

Geometry students will work in cooperative groups. Each group member will select a role and perform the task. You will complete your activity today by , and complete your individual report to be turned by .

Title / Role / Responsibility
Recorder / Collects and Records Data. / Records and Posts Group Data
Gatekeeper / Makes sure all members participate. / Obtains and Returns Materials
Advocate / Makes sure that all members are appreciated. / Presents group answer. Makes sure all members have information.
Administrator / Keeps group on task / Calculations.

If your group has only three members the Gatekeeper and Advocate will be the same person.

Assignment:

1. You must work cooperatively.

2. Discuss a plan for determining the number of pennies to line the base board, cover the floor and fill this room. How much do you estimate?

3. Write a short plan and then collect materials from the table. Do not horde. You will probably need to share. How will you arrange the pennies?Draw a diagram.

4. Determine the number of pennies for the baseboard.How many dollars?

5. Determine the number of pennies to cover the floor. How many dollars?

6. Determine the number of layers of pennies to reach the ceiling.

7. Determine the number of pennies to fill this room. How many dollars?

8. What is the probability the head of a pin will land on penny

9. Report your results on the chart.

10. Prepare a discussion of your method. Please include any ideas that you have concerning the accuracy of your results.

11. Be sure that all group members have your results.

Some formulas that might help you.

Turn in your individual reports with your group report on. Use a stapler or paper clip to keep your group’s work together. If your answers differ from the group assignment (1-11), turn them in with an explanation of why you differ from the group

Answer the following questions on your own paper. Please be neat and organize your work.

Individual Report

1. Briefly explain the problem in your own words.

2. Who were your group members? What roles and responsibility did each member have? Write your name first and then write their names with roles.

3. Discuss your group plan for determining the answer to Penny Saver’s questions. Did you modify your plan? How would you complete this assignment differently if you were to do it again? Do you feel your answers were accurate? Discuss possible sources of error. What if any were the differences in the answers from the other Groups? How could you help your group function more efficiently?How well did your group get a long?

4. Show the calculations your group used to determine your answers.Can you suggest another method?

5. How did the formulas help you?

6. Suppose Penny Saver does not have enough pennies to cover the floor. Suggest other dimensions for a room with the same perimeter but has less area.

7. What are the dimensions of this room(perimeter)? Floor area? Volume of this Room?

8. What grade do you believe you deserve? Why?

Your grade will be determined using this outline.

Group grade5I will decide if you worked cooperatively.

Group Plan5One copy for the group

Answers to Penny10Posted on chart

Presentation5Group discussed method with class.

Individual Report20Include all answers and calculations

Self evaluation5What grade do you deserve and why?

Total50

Late work accepted with a 15 point penalty.

Objective: Students will work cooperatively to solve a simulated real world problem. Students will use and develop formulas or and apply to solve problems. Students will use measurements to determine solutions. Students will analyze their procedures to determine accuracy of their work and possible sources of error.

Background: Beginning Geometry students must work cooperatively to complete tasks. This lesson correlates to the opening chapter in most student geometry texts and meets state and national standards. Pennies are quite interesting. Do not tell your students that 16 pennies stack to make one inch and that it takes 16 pennies to line up for one foot. Student will eventually find a scale factor that will work for them. Even if they use metric measurements their cost answer will be close. Using English measurements is the most efficient and provides opportunities for discussions on the minting of pennies. Opportunities exist to extend lesson to geometric probability and data analysis. Students enjoy the opportunity to use problem solving skills to answer questions whose answers are not in the back of the book. If students do not have a group you can select groups randomly using playing cards.

National Standards:

State Standards:

Alabama Course of Study:

5.) Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

11.) Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

17.) Analyze sets of data from geometric contexts to determine what, if any, relationships exist.
•Calculating probabilities arising in geometric contexts

Materials:

Pennies, (about 20 per group), rulers, yard stick, tape measure, any other tool to measure diameter, chart paper, markers, and copy of student sheet

Rubric for Grading Individual Report

Questions 1-7

0no answers

1answer unexplained

2answer explained

Total14

Whole Report

0no paper

3attempted some questions with some attempt at analysis

6attempted all questions, answers correct and explanations were thoughtful

Self Evaluation

0no evaluation

3evaluation without valid reason

5evaluation supported

Rubric for Group Grade

Group grade

0no work

3some attempt made to work cooperatively.

5group worked well, all members participated.

Plan

0no plan

3written plan

5written plan with diagram

Class Chart

0no posted results

5some results posted

8results posted late

10results posted on time

Presentation

0no presentation

3presented results only

5presented a method or analysis of data

Example of Chart

Group
Number and Names / Room Dimmensions / Number of Pennies to line the baseboard.
Show calculations / Cost / Number of Pennies needed to cover the floor.
Show calculations / Cost / Number of Pennies needed to fill this room.
Show calculations / Cost / Probability of hitting the penny
Show calculations
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II
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IV
V
VI
VII
VIII
Group / Write any comments or questions your group has in this space
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V
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VII
VIII