The Legend of Paul Bunyan

Unit Plan for a

Mathematical Journey

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Karen L. Beard

Lynda Lombardi

Course: EDU 464

Theme-Based Unit Plan

Prof. Hari Koirala

October 8, 2003

The Legend of Paul Bunyan

Unit Plan for a Mathematical Journey

 

Table of Contents

 

 

Unit Plan Overview

 

1.  Unifying Theme................................................................................................ 2

2.  Unit Assumptions............................................................................................. 2

3.  Grade Level(s)................................................................................................. 2

4.  Unit Topics....................................................................................................... 2

5.  Classroom Resources.................................................................................... 2

6.  Unit Features................................................................................................... 3

7.  Unit Objectives................................................................................................. 3

8.  Tentative Unit Timeline.................................................................................... 4

9.  Concept Map.................................................................................................... 5

10.  Unit Plan Connections and Extension

a. Lessons within the math unit.................................................................... 6

b. Unit in the context of other math concepts and units................................ 8

c. Unit extension into other subject areas..................................................... 9

11.  Unit Alignment with State and National Standards

a. Content...................................................................................................... 9

b. Process................................................................................................... 10

12.  Assessment................................................................................................. 11

 

 

Lesson Plan

..... 13.  Lesson Plan #3.......................................................................................... 13

..... 14.  Lesson Plan #3 Activity Sheet.................................................................... 16

..... 15.  Lesson Plan #3 Homework Sheet............................................................. 17

..... 16.  Lesson Plan #3 Quiz.................................................................................. 18

                                 

 

Appendix

A.  The Legend of Paul Bunyan Key Facts............................................................ 19

  1. Unit Resources................................................................................................ 19

 

 

The Legend of Paul Bunyan

A Mathematical Journey

 

1.  Unifying Theme

The theme for this unit is the tall tale The Legend of Paul Bunyan.  The unit will be introduced to the students by reading them a book of Paul Bunyan’s adventures, and the lessons within the unit will explore mathematical concepts based on the facts and inferences from the book, as well as other sources on Paul Bunyan tales. 

 

 

2.  Unit Assumptions:

It is assumed that the students will have a general, and not an in-depth, understanding of the following concepts: 

·         Scale, ratio, and proportion

·         Measurement in two and three dimensions (area and volume)

·         Decimal, fractions, and percentages

 

The unit is designed to provide a deeper understanding of these concepts, as well as to introduce other topics through hands-on activities, independent and group work, thought provoking questions and problems, and the usage of multiple mediums, including literary works, reference books, maps, modeling clay, and the internet.

 

 

3.  Grades Level(s):

This unit has been designed for grade 7 or 8 audiences, although it can be modified to teach grades 2 – 12.   (See Section # 10, page 8-9, for potential adaptations for lower or higher level audiences).

 

 

4.  Unit Topics

 Topics to be covered in The Legend of Paul Bunyan unit are as follows:

  • Measurement
    • Estimation
    • Standard and non-standard units of measure
    • One, two, and three dimensional measurement (length, area, volume)
  • Decimals, Fractions and Percentages
  • Data presentation and Graphing
    • Tables
    • Bar diagrams
    • Pie charts
    • Linear graphs
  • Scale, Ratio, and Proportion
  • Variables and Linear equations
  • Probability and Statistics
  • Data Analysis and Problem Solving

 

 

5.  Classroom Resources

 

The following resources are needed to teach this unit:  The Legend of Paul Bunyan book for unit introduction and reference, calculator with graphing ability, U.S. Map, modeling clay, rulers, yard sticks, graph paper, atlas, and computer with access to the internet.

 

6. Unit Features 

Important features of this unit include:   

·         Mental visualization and estimation

·         Modeling for exploring mathematical concepts

·         Cooperative learning

·         Use of technology, including calculators, computers, and internet

·         Data analysis and problem solving

·         Multiple modes of assessment, including independent work, group work, group projects, student assessment of other student/groups assignments, homework assignments, teacher observation, quizzes, and unit test.

·         Linkages to other concepts, topics, and subject areas (See Section 10, pages 6-9)

 

 

7.  Unit Objectives

 

At the end of this unit the student will be able to:

  1. Estimate and explore using standard and nonstandard units of measure.
  2. Build a cardboard replica of Paul Bunyan’s ‘axe handle’ to use as a unit of measure.
  3. Identify the advantages and disadvantages of using nonstandard units of measure
  4. Create 3-dimensional clay models for Paul Bunyan’s ox, Paul Bunyan’s frying pan, and Lake Superior to extend understanding of the concepts of length, area, and volume.
  5. Determine scale factors for two-dimensional and three-dimensional models.
  6. Set-up and solve ratio and proportion equations, based on their models’ attributes, to determine actual dimensional qualities (height, width, area, volume, etc) of objects and places from the Paul Bunyan tall tale.
  7. Demonstrate and explain how square units of measure can be used to measure objects that are not “square”.
  8. Conduct research using atlases, books, and the internet to gather data on lakes within Minnesota (including surface area, volume, and location) and other states in the U.S.
  9. Represent data pictorially through the creation of bar graphs, pie charts, and tables.
  10. Convert data from decimals to fractions and percentages.
  11. Analyze data to solve related word problems.
  12. Color-code a map of the United States to express ranges of water-land ratio percentages for each state.   Report observations.
  13. Utilize data and maps to identify patterns and consistencies with the legend of Paul Bunyan and U.S. topography to prove or disprove the validity of the legend’s tales.
  14. Create line graphs from numerical data tables 
  15. Convert line graphs to linear equations. (Students will be introduced to both the point-slope equation and the slope-intercept form.)
  16. Calculate the specific slope of the line.
  17.  Find the mean, mode, median of data from the folk tale and data they have researched, including data from Minnesota lake survey data on fish.
  18. Calculate the probability of catching certain types of fish in certain lakes and compare the data across other lakes.
  19. Complete a cooperative team project in which students must identify the most effective means of graphically representing data and create word problems related to their data.

 

8.  Tentative Timeline

 

The Legend of Paul Bunyan unit is comprised of 12 math lessons, some of which may take two days to complete.  The unit will take between 3 and 4 weeks to teach, assuming a school class length of 40-50 minutes.  Cross-curriculum topic planning and execution by teachers within the grade is encouraged; it would be ideal to have English/Literature and Social Studies teachers incorporate topics pertaining to story telling, folk tales, U.S. geography and/or U.S topographical points of interest into their lessons while the math unit is being taught. 

 

The following is a breakdown of the unit’s lessons.  More detailed lesson descriptions can be found in Section 10, pages 6-7.

 

    Lesson      Instructional

    Number          Days        Lesson

        1                  1           Standard and Non-Standard Unit of Measure

        2                  2           One dimensional Measurement and application of scale modeling and proportions

        3                  2           Two dimensional Measurement and application of scale modeling and proportions

        4                  2           Three dimensional Measurement and application of scale modeling and proportions

        5                  1           Graphing (bar graphs and pie charts)

        6                  1           Percentages

        7                  1           Decimals, fractions, and percentages

        8                  1           Graphing points and introduction of linear equations

        9                  2           Continued introduction of Linear equations, variables, slope

       10                 2           Mean, mode, and median

       11                 1           Probability

       12                 2           Problem Solving (and group presentations)

9. Concept Map of

      Unit Mathematics Content     


10.  Unit Plan Connections and Extensions

 

A.  Math lesson sequence within The Legend of Paul Bunyan math unit

 

This unit is comprised of 12 lessons, some of which will require 2 days of instructional time.  The unit will be introduced by reading a book of Paul Bunyan’s adventures.  The book and numerous tales of Paul’s adventures are a source of storytelling exaggerations and numerical references.  Each lesson will begin with a reference to a Paul Bunyan tale which will lead to the exploration of a mathematical concept.  (Note:  Appendix A, Page 19, contains a listing of Paul Bunyan facts which can be used for this unit.)   The following is a brief description of the lessons within this unit: 

 

Lesson #1.  Standard and Non-Standard Unit of Measure.

Lesson involves estimation and exploring standard and non standard units of measure.  In Paul Bunyan’s tales, Paul is reported to be a height of 63 ax handles tall, and his blue ox Babe is 42 ax handles wide from the tip of one horn tip to the other.  Student groups create replicas of axe handles from cardboard and ‘measure’ the room, desks, etc.  Have groups compare findings.  As the lesson progresses, interject that some accounts in another Paul Bunyan legend reference Babe’s width between his horns as 7 axe handles.  Discuss with the class; perhaps this is due to 1 of Paul’s ax handles being equal to the length of 6 ordinary ax handles.   Students will identify advantages and disadvantages of nonstandard unit of measure

 

Lesson #2 – 4.  Measurement and the application of scale modeling and proportions. 

These lessons involve the usage of models for investigating one dimensional (length), two-dimensional (area), and three dimensional (volume) measurements through three-dimensional models and the utilization of scale factors and proportionality.  In these lessons, students will create clay models for Paul Bunyan’s ox (Lesson #2), Paul Bunyan’s frying pan (Lesson #3), and Lake Superior (Lesson #4) where Paul Bunyan is said to have herded whales.  Measurements of the models will be used to set up proportions to identify attributes of things mentioned in Paul Bunyan’s tales.  Note:  A lesson plan for Lesson #3 is included in Section 13, pages 13 – 16.

 

Lesson #5.  Graphing (bar graphs and pie charts). 

This lesson involves having the students use bar graphs and pie charges to represent the volume of various lakes in Minnesota.  Paul Bunyan and Babe are said to have create the 10,000 lakes of Minnesota while they trotted around the state.  Their footprints made impressions in the land, and these indents filled up with water to form the many lakes in the state.  Students will use atlases, books, or the internet to identify lakes for their analysis.  Of the lakes they selected, they would represent the lake volume in a single pie chart and bar graphs.

 

Lesson #6.  Percentages

As a continuation of the looking at how Paul and Babe may have altered the topography of the land, students will be given a map of the United States.  They are instructed to identify states that Paul Bunyan is said to have visited and mark them on the map of the United States. (Some of the “documented” places in the Paul Bunyan tales include Minnesota, Wisconsin, Arizona, Washington, Maine), and mark them on the map of the United States.  Students will also identify states where there is no indication that Paul Bunyan visited.  Students will research what the ratio of land and water is for those states, and then calculate the percentages of water versus land.  Data, such as statistics on acreage of land and acreage of water, can be found in atlases or the internet.  The data the students will be recorded in a table with multiple columns.  The first several columns are labeled Name of State, Did Paul Bunyan Visit?,  Total acreage of the state, Acreage of Water, Acreage of Land, % of Water, % of Land.  There will be additional columns on the sheet which will be used in the next lesson.

Lesson #7.  Decimals, fractions, and percentages

This lesson involves the using the data from the Lesson #6.  Students will add labels to the additional columns from the worksheet in Lesson #6 for converting the percentages of land and water to decimals and fractions.   Students will begin to analyze the data to draw conclusions.  Do the states that Paul Bunyan and Babe visited appear to have higher ratios of water?  How does Minnesota’s ratio of water versus land compare to other states he visited?  (After all, Paul and Babe spent most of their time in Minnesota and, in their travels, “created” 10,000 lakes in the state.)   The teacher will then lead the class in a discussion on how could we modify a map of the United States to help with analyzing our water versus land ratios?  For example, color code different colors or shades of colors by ranges of land or water percentages. Shading states with low %’s of brown, students are given a new map and a complete list of water versus land percentages of all states.  They are asked to color code their maps (or modify by other means they’d like) and asked to report 5-10 facts on their analysis of water/land trends.

 

Lesson #8.  Graphing points and introduction of linear equations

These lessons involve the creation of data tables based on the “factual information’ from Paul Bunyan’s tales. Ideally the class will be divided into groups.   A few ‘facts’ include:  “Saw filers called ‘saw dentists’ could usually file one saw in 30 minutes, and sharpened approximately 20 files a day”,  “Babe the blue ox could eat 30 bales of hay – wires and all – a in a single day”,  “Paul trained giant ants that weighed 2,000 pounds each.  The ants could each do the work of 50 ordinary men.”  In the “ant” fact example, the data in a table would be 1 ant = 50 men, 2 ants = 100 men, 3 ants = 150 men, and so on.  This data would be translated into coordinates, and then plotted on a table with the # men on one axis of a graph and the # of ants on another axis.  The teacher will lead a class discussion to identify similarities and differences between the graphs, asking the students such questions as were they able to use the same unit of measure for each graph?  How did they have to adjust the interval of the X-axis and Y-axis data to suit the data they were graphically displaying?

 

Lesson #9.  Continued exploration of linear equations and slope

The data and graphs produced in Lesson #8 will be used for introducing the idea of representing linear equations as equations with X and Y values.  Similarly, the teacher will use this data to introduce the concept of slope. The teacher will show the students how to graphically display this data and equations on a graphing calculator.   Each group of students will be asked to create one tall tale of their own that involves rate of change. They should then represent data from their tale in a table format and graphing coordinates, and then graph the data.

 

Lesson #10.  Mean, mode, and median

This lesson involves exploring the mean, mode and median.  Students will research the fish-life found in the lakes of Minnesota through lake surveys which include data on number of fish netted, type of fish netted, length of fish netted, weight of fish netted, etc.  This information can be supplied to the students in hand-outs or they may research their own data on the internet.  The Minnesota Department of Natural Resources has a website that provides detailed lake survey for many of Minnesota’s lakes. (http://www.dnr.state.mn.us/lakefind/index.html)  The information will be used to explore the mean, mode and median.  For example, what is the mean length of a white perch netted?  What is the median weight of a smallmouth bass netted?  What is the modal number of fish netted?

 

Lesson #11.  Probability

This lesson involves using the data gathered in Lesson #10 to explore probability.  The data may be used to explore probabilities within one particular lake, or comparing the data across multiple lakes.  For example, what is the probability of catching a brown bullhead in Red Lake?  What is the probability of catching a fish greater than 5 pounds in Round Lake?  Would we have a higher probability of catching a fish greater than 20 inches in length in Leech Lake or Lake Vermilion?

 

Lesson #12.  Data Representation and Problem Solving (and group project and presentations)

This lesson involves having the students, in groups, working to identify the best way to graphically display the data they collected on one lake.  For example, they may choose to display data through pie-charts, bar graphs, line graphs, etc.  The goal of their graphical representation is to allow the audience to quickly discern information regarding their data.  Students will then create 5 word problems based on their data and graphs.  The teacher will collect the problem solving projects from each group and make copies of all projects to re-distribute to the class in a “Problem-Solving Packet”.  The students will solve the word problems of their peers based on the data and graphical displays and then assess the methods of displaying the data and the ease with which the data display assisted with solving the problems. 

 

 

B.  The Legend of Paul Bunyan Unit in the context of other Mathematical Concepts and Units

 

This mathematical unit can easily be extended to other math concepts and also used as the basis to introduce or cover topics not already included in the unit.  Here are a few examples:

 

  1. Geometry:  Lesson #3 on creating a model of Paul Bunyan’s frying pan can easily be extended into the area of geometry and covering in depth topics such as radius, diameter, perimeter, areas of cylinders, etc.  What is the perimeter of Paul Bunyan’s frying pan?  How much pancake batter could the pan hold if it was filled to the top?

 

  1. Calculus and Slope Concept:  Lessons #8 and #9 can easily be used to deeply explore the concepts of linear equations, variables, slope.  Concepts can be taught using graphing paper and simultaneously taught on a graphing calculator.  For example, students can create a line graph describing the number of bales of hay that Babe could eat in one week.  Select two points on the graph, and express as points and .  How do you find slope?  .  Create a linear equation to describe the line on your graph in  format.

 

  1. Exponential, Scientific, and Calculator notation:  Lessons on ways to represent very small or very large numbers.  In terms of the Paul Bunyan unit, students can use lake survey data, which includes lake volume estimates, the number of fish in a lake, etc.  and express in terms of scientific notation.

 

  1. Trigonometry:  Paul Bunyan is said to have created a number of mountains as he created lakes and inlets along the west coast, including Mt. Rainer and Mt. Baker when he created the Puget Sound in Washington.  If you were standing one mile from Mt. Baker measures 10,775 feet in height.  You estimate that the angle from you to the top of the mountain is 30%.  Approximately how far are you standing from the tip of the mountain?

 

  1. Discrete Math:  Students can look for patterns in objects in the Paul Bunyan tales. For example, logs from the trees were stacked as shown below.  How could the students identify how many logs are in the stack without counting?  Is there a pattern?  Can we create a formula to represent the pattern?  How many logs will be in a pile if the stacks are 10 logs high?

 

 

Note on Unit Adaptations for Diverse Learners:   The Legend of Paul Bunyan unit can be adapted for the full range of grade levels and for a wide range of student abilities.  As described above, the unit can easily be extended into other mathematical concepts and topics including as the study of Geometry, Calculus, Trigonometry and Discrete Math.

 

Additionally, The Legend of Paul Bunyan unit can be adapted to suite curriculum standards starting as early as Grade 2.  For example, the lessons could be planned around simple counting, mathematical operations (addition, subtraction, multiplication and division), estimation of measurements, estimation of numbers in the context of the Paul Bunyan legend, basics of Geometry though study of shapes, representing and interpreting data in simple tables or graphs.  For classes at Grade 4 - 6 levels, lessons and projects may be planned with lessons that require higher order mathematical skills, knowledge, and more refined execution of process skills (i.e. problem solving, communication, representation). For example, according to the tales, Paul Bunyan’s dinner menu consisted of seventy pounds of fried potatoes, forty-five pounds of T-bone steak, sixty pounds of ham, sixteen large loaves of bread, thirteen dozen eggs, six hundred and seventy-two pancakes topped with two gallons of maple syrup, and ten gallons of strong black coffee.  Students can plan a similar meal for Paul Bunyan based on proportions or estimate the cost of preparing a dinner for Paul Bunyan based on the prices of a local grocery store. 

 

For an example of how specific lessons may be adapted for usage, see the sample lesson plan on pages 13 – 16.   Page 15 contains a myriad of ideas on how the particular lesson may be adapted for diverse learners.  

 

 

C. The Legend of Paul Bunyan Unit extension into other subject areas

 

·         Social Studies

ü      Ecology and the Environment:  The unit can be extended to the studying the impacts of man on our environment (i.e. logging, pollution), conservation ‘limited’ resources such as forests, and the history and practices of the logging industry such as clear cutting and the regeneration of forest groves.

 

ü      U.S. Geography:  The unit can be extended to the studying natural points of interest, particularly including those 'created' by Paul Bunyan such as Puget Sound, Round Lake in Minnesota, Great Lakes, Grand Titon, Grand Canyon, Mt. Baker, and Mt. Rainer.

 

ü      Culture:  The unit can be extended to the studying the origins and cultural aspects of folktales in the U.S. and other countries throughout the world.

 

·         Science

ü      Geology:  The unit can be extended to the studying the creation of the natural points of interest in the U.S., such as the impacts of glaciers, volcanoes, flooding. 

 

·         English

ü      Students can write their own tall tales and explore the folktales associated with Connecticut (Connecticut Yankee) and regionally (Ethan Allen, Legend of Sleepy Hollow, etc.)

 

·         Music:  The unit can be extended to the study of folk music and historical significance of folk music stories, lyrics, colloquial use of language, etc.

 

 

 

 

11.  Unit Alignment with State and National Standards

The Legend of Paul Bunyan unit addresses and encourages the exploration of many aspects of the National and State content and process standard areas.

 

 

Content Standards

The mathematical concepts within The Legend of Paul Bunyan unit, as outlined in the lesson plan descriptions in Section 10, cover a number of topics outlined within the Connecticut and the NCTM national standards.  Alignment of the unit lessons is as follows:

 

        

Lesson #

Lesson Name

NCTM National Standard