Mathematical Cross Country Trip

Unit Plan

 

 

By

Eileen Laramie

Sister Mary Grace, SCMC

Susan DuBois

EDU 546

Dr. Hari Koirala


Table of Contents

 

 

Concept Map.. 3

Assumptions.. 4

Topics to Be Covered.. 4

Required Resources.. 4

Unit Features.. 4

Unit Objectives and the Standards Alignment.. 5

Tentative Timeline. 7

Lesson #1 - Introduction.. 7

Lesson #2: Plan Trip.. 7

Lesson #3 - Food and Lodging Lesson.. 8

Lesson #4 Amish Country.. 8

Lesson #5 Great Lakes Get rid of Pollution.. 8

Lesson #6 Indiana - Logic Puzzle. 8

Lesson #7 St. Louis, Missouri - Arches and Arcs.. 8

Lesson #8 The FBI Needs Our Help.. 9

Lesson #9 Climb that Mountain - Colorado.. 9

Lesson #10 Mt. Rushmore, Montana.. 9

Lesson #11 Seattle, WA - Its Raining, Its Pouring.. 9

Lesson #12 Viva Las Vegas, Here We Come!! 9

Lesson #13 Nevada - Oh no, We Left Someone Behind.. 10

Lesson #14 California, Here We Come. 10

Lesson #15 We Made It!! Class Presentations.. 10

Lesson #9 - Colorado.. 11

Unit Extension and Modification.. 14

Unit Assessment.. 16

Appendix A.. 17

Appendix B.. 19

Appendix C.. 21

Appendix D.. 24

Appendix E. 25

Appendix F. 27

Appendix G.. 29

Bibliography.. 31


Concept Map

 

 

 


Unifying Theme

The theme for this unit is to explore mathematics using a trip across the United States. The unit is designed to engage students in mathematics topics as they plan their own small group trips across the U.S.

Assumptions

It is assumed that students have some previous knowledge of algebra and measurement as well as practice using the Internet as a resource. It is also assumed that students are familiar with Microsoft Excel. This is a mid-semester unit, so it is likely that many concepts have already been taught, namely, the four quadrants of a coordinate plane, x and y coordinates, and plotting points on a graph. It is also assumed that the students are proficient in addition, subtraction, multiplication, division, fractions and percents.

 

Grade Level: 9

This unit is designed for 9th grade students. However, it could be used with advanced 7th and 8th grade students as well. Grades 10-12 could also benefit from using this unit for review of concepts, extra practice, motivation, etc. It could be modified by adjusting the math topics to fit any grade level.

Topics to Be Covered

      Estimation and rounding

      Decimals, fractions, and percentage

      Slope

      Variables and equations

      Probability

      Circumference, diameter

      Ratios

 

Required Resources

US Map, Calculator, Atlas or map books, several computers with Internet access, Popsicle sticks, straws, matchbox cars.

Unit Features

      A realistic application

      Involves problem solving and planning

      Links to geography and demography

      Use of calculators and mental estimation

      Use of computers

      Cooperative learning

      Encourages the use of students personal experience

      Active assessment

      Use of technology

      Links to Science

      Use of presentation skills

      Logging information and reflections into a math journal

Unit Objectives and the Standards Alignment

Unit Objectives

Alignment

 

NCTM Standards

Connecticut Standards

By the end of the unit students will:

 

 

1. Budget time and money for a long trip.

Number and Operations

 

Representation

 

Connections

Number sense

Operations

 

2. Estimate distance, mileage and cost.

Number and Operations

 

Geometry

 

Estimation and Approximation

 

Spatial Relationships and Geometry

3. Work cooperatively in groups.

Communication

 

4. Determine the best route and probability of reaching destination on time and within budget.

Data Analysis and Probability

Probability and Statistics

5. Determine the slope of a line.

Geometry

 

Measurement

 

Problem Solving

Spatial Relationships and Geometry

Measurement

6. Find the boiling point of water at a high altitude.

Algebra

 

Problem Solving

Algebra and Functions

7. Find the circumference, diameter and radius of a circle.

Geometry

 

Problem Solving

 

Connections

Spatial Relationships and Geometry

8. Find Mean of rainfall and temperature of 2 states. Graph results.

 

Data Analysis & Probability

 

Algebra

 

Connections

Representation

Probability & Statistics

 

 

Algebra and Functions


 




9. Find the number of revolutions of a wheel.

Geometry

 

Numbers and Operations

Spatial Relationships and Geometry

 

Number Sense

 

Operations

Ratios, Proportions, and Percent

10. Design an Excel Spreadsheet.

Algebra

 

Data Analysis & Probability

Algebra and Functions

 

Probability & Statistics

 

11. Monitor bacterial populations growth as function of time.

Numbers & Operations

 

Algebra

 

Data Analysis & Probability

 

Problem Solving

 

Connections

Number Sense

 

Operations

 

Ratios, Proportions, and Percent

 

Algebra and Functions

 

Probability & Statistics

 

12. Calculate duration of medicine effects given half life.

Numbers & Operations

 

Algebra

 

Problem Solving

 

Connections

Number Sense

 

Operations

 

Ratios, Proportions, and Percent

 

Algebra and Functions

13. Solve Logic Puzzle.

Numbers & Operations

 

Data Analysis & Probability

 

Problem Solving

Reasoning & Proof

Number Sense

 

 

Probability & Statistics

 

 

Patterns

14. Design bridge and ski slope.

Algebra

Geometry

Measurement

Problem Solving

Connections

Representation

Algebra and Functions

 

Spatial Relationships and Geometry

Measurement


Tentative Timeline

This unit will span 3- 4 weeks with 15 lesson plans of 45-50 minutes each. Much of the work will be collaborative with a culminating presentation at the end of the unit. If possible, this unit will be taught with the Social Studies, Computer, and Science classes.

 

 

Lessons

Number of Days

Description

1

1

Introduction of a Cross Country road trip

2

2

Planning the trip

3

1

Food and Lodging Lesson

4

1

Amish Country

5

1

Great Lakes Get Rid of Pollution

6

1

Indiana Logic Puzzle

7

1

St. Louis, MO Arches and Arcs

8

1

Dodge City, KS - The FBI Needs our help

9

1

Colorado Slope Activity (Expanded lesson)

10

1

Montana

11

1

Seattle. WA - Its Raining, Its Pouring

12

1

Viva Las Vegas

13

1

Nevada - Oh no, we left someone behind

14

2

California, Here we come

15

1

We Made It!! Class Presentations

 

Lesson #1 - Introduction

Students will work in groups of 3 to plan a virtual trip cross country. They will be given a budget of $2,000.00 to make this trip and they will be tracking their money with an Excel Spreadsheet that they will create and update and keep on the school server. They will need to use Mapquest to map out their trip and maps to decide on their stops along the way. They will need to keep track of miles driven and roads taken as they will need to purchase gas along the way and know what speeds they will be able to travel. For example: In Washington D.C. the speed limit is still 55, Colorado is 75. On the last day of this unit they will present their trip, including destinations selected and why, miles driven, route taken, and money spent. They will also be responsible for an independent portfolio, which will include all the math challenges along the way as well as their group presentation. They will reflect on their lessons daily in a math journal. Get your suitcases out its time to go!!

 

Lesson #2: Plan Trip

Students will begin by working in pre-selected groups. Student will work together and pick out at least 5 destinations. They will then use Mapquest to map out their trip deciding on routes to go. They will need to calculate roughly how many miles they plan on traveling a day.

Lesson #3 - Food and Lodging Lesson

For each location that your group decides to stop you will need to look up at least five 3-star hotels/motels that you will stay overnight at. Take the nightly rate of these hotels and compute the mean. Deduct that amount from your budget spreadsheet dont forget to calculate state tax!!

 

Food You must calculate how many meals your group has eaten during your trip. Figure on spending (per person) $5.00 for breakfast, $7.00 for lunch and $10.00 for dinner. Again, remember to calculate your tax.

 

Lesson #4 Amish Country

Your group has made it to Amish country. The farmer has inadvertently left 2 rickshaws in the middle of the road. Your group decides to have a race. If one rickshaw has 3 foot diameter wheels and the other has wheels with a diameter of 3.5 feet, how many rotations would the wheels of each rickshaw take to get to the farmhouse mile away?

 

Lesson #5 Great Lakes Get rid of Pollution

Your group has visited Lake Erie. The local EPA has asked for your help in getting rid of the pollution that dirties their waters. Back in 1969, the lakes were so polluted, that one of the rivers that feed the lakes (Cuyahoga River) caught fire. That's right, the river was on fire. Bacteria are growing in the lake at a rate of 3000 cultures per hour.

Make a graphical analysis to monitor the bacterial population as a function of time, volume of effluent, external temperature, etc.

Use resource: http://www.great-lakes.net/teach/pollution/water/water6.html

Lesson #6 Indiana - Logic Puzzle

One of your group members woke up with a terrible headache. Hes the driver. You rush to the local pharmacy and buy him/her Excedrin (pay $5.00). He/she quickly takes 2. Then you all realize you bought Excedrin PM with a half-life of 2 hours. How long will you need to wait for your driver to wake up?

 

After group finishes with Excedrin PM problem have students do a logic problem worksheet. (Appendix A) After 15 minutes have them pair up and continue to work on it. Have them complete this for homework if needed and be sure to add it to final portfolio.

 

Lesson #7 St. Louis, Missouri - Arches and Arcs

In St. Louis, your group has learned that your architectural knowledge is required. The mayor at St. Louis wants to build another arch to accompany the Gateway Arch. The Gateway Arch is 630 feet across and 630 feet high. However, the current mayor prefers circles to arches. What would the new circumference be for a full circle, and what would the length of the semi-circle arc be?

Use resource: http://go.hrw.com/math/cnn/course3/3_7_Arch/3_7_Arch.htm

Lesson #8 The FBI Needs Our Help

Dodge City, Kansas: While visiting, Marshal Matt Dillion and his deputies Chester Goode and Festus Haggen come to you needing your help. Billy the Kid has wandered into the peaceful city and Marshal Dillion needs you to find the way from his office on Front Street to Billy the Kids hideout south of the tacks, somewhere on Juneau Avenue. Use your knowledge of the coordinate plane to determine how far Billy the Kids hideout is and what the shortest route is.

See Dodge City Map Appendix H.

 

Lesson #9 Climb that Mountain - Colorado

See expanded lesson further down.

 

Lesson #10 Mt. Rushmore, Montana

You climb Mt. Rushmore and you realize that Teddys nose is in need of repair. Design his nose in proportion to the rest of the sculpture. See resource listed for width of eyes and face. Find the area and volume of Teddys new nose. Use graph paper and a net diagram to properly show dimensions.

Also, use the listed resources to answer the following questions.

How does the boiling temperature of water change with altitude?

Examine temperatures on top of Mt. Rushmore. If it is 70 at sea level, what is the temperature at the top of the sculpture? (For this exercise look up what dry adiabatic lapse rate is and use this rate to calculate your answer)

Use resource: http://www.enchantedlearning.com/history/us/monuments/mtrushmore/

Use resource: http://www.fact-index.com/d/dr/dry_adiabatic_lapse_rate.html

Use resource: http://geography.about.com/library/faq/blqzbiolingwater.htm

 

 

Lesson #11 Seattle, WA - Its Raining, Its Pouring

Have students look up the average temperature and rainfall of Seattle and your home state Connecticut. Have them graph their results by season. Then have them choose and write about which destination they would rather live and why.

Extension: Graph your data on at least two other types of graphs. Use your graphs and your statistics knowledge to decide which graph best represents the data. Explain your answer in your journal.

 

Lesson #12 Viva Las Vegas, Here We Come!!

While visiting Las Vegas, you come across a recovering gambling addict. He explains that no matter what you do, the casino will always win money. You ask why. He explains that in roulette, you have a 1 in 36 chance of getting a win that will give you $17 for every $1 you put down. How much money would the casino have to give out in order for the casino to loose money?

 

Lesson #13 Nevada - Oh no, We Left Someone Behind

Your group has left you behind they didnt see you take a restroom break. They begin to pull out and are traveling 15 mph through the parking lot. You begin to run at a rate of 8mph. Unfortunately, they travel two miles before they see you running and finally stop. How long will it be before you get to their car?

 

Lesson #14 California, Here We Come

Looks like the Golden Gate Bridge is in need of repair. Students can use the internet to look up some design ideas of building bridges. They will design and build their own bridge utilizing materials such as Popsicle sticks, straws, etc. Bridge will be added to portfolio. During presentation students will test their bridges by loading matchbox cars. Bridge must be able to hold 10 matchbox cars.

 

Lesson #15 We Made It!! Class Presentations

Students will do a 10 minute presentation of their trip to their class for a grade. Their presentation/portfolio must include all completed activities along the way, as well as information about each of their destinations. At this point, the bridge is displayed and tested.


Lesson #9 - Colorado

Colorado Slope Activity

Grade 9

Lesson objectives: At the end of this lesson, the students will be able to:

  • Find the slope of a mountain.
  • Compare slopes.
  • Discover patterns in slopes.

 

Standards Alignment: This lesson aligns as follows.

 

NCTM standards:

      Number and Operations

      Geometry

      Measurement

      Algebra

      Data Analysis

      Connections

      Communication and Representation

 

Connecticut standards:

      Number Sense

      Operations

      Estimation and Approximation

      Spatial Relationships and Geometry

      Algebra and Functions

      Measurement

 

Required Resources:

Cardboard, marbles, rulers, protractors, graph paper, US map, Colorado map, worksheet

 

Lesson Procedure:

The students will be working in the groups they made at the start of the unit. If their plan includes Colorado they will do this lesson. The students will pretend to go skiing in Colorado each taking a different angle: ski faster down steeper hills, or go slower down the bunny hill. During this virtual ski trip, the students will do the following activities:

  • Create a steep ski slope and a bunny slope with cardboard.
  • Roll a marble down each incline and ask the students if they can describe the rate of the marble rolling for each.
  • Measure the angles of the two ski slopes using protractors.
  • Compare the rise/run for the first and second ski slopes using a coordinate plane.
  • Ask the students to come up with a standard for comparing slopes, for example: upward or to the left-positive slope, downward or to the right-negative slope.
  • Have the students investigate these two cases:

(i) Horizontal line (slope=0)
(ii) Vertical line (slope=undefined)

Students will be given the worksheet found in Appendix B.

 

Lesson Connections:

 

This lesson will be preceded by lessons 6 or 7 which both deal with the measurement and circumference. The student will gain an understanding of measurement as they find the diameters and this lesson goes a step further in requiring the students to measure the slopes of lines. This lesson is followed by lesson 10 which also deal with angles and the measurement of sides of triangles.

 

This lesson could lead to analyzing data using scatter plots and relating graphs to events. Rate of change could be further developed and the students could find the rate of change in their typing speed, in shopping (quantity per unit), renting fees that change by number of days rented, etc. Students could make small parachutes and measure the rate the parachute descends.

 

Students should be introduced to the use of graphing calculators. A simple exercise for becoming familiar with the calculator interface could be used (See Appendix G). Another activity that could be used would be to have students create a display on their calculators that resembles the Jamaican flag or the Tanzanian flag.

 

 

                                             Jamaican Flag

 

 

The Jamaican Flag design can be made with values for k in the equation y = kx.

 

Another activity to extend the concept of slope would be to suppose the students are given a job in which they receive a salary plus a 20% commission. They could come up with an equation that expressed their earnings and then rewrite the equation in slope-intercept form. They could then graph their equations.

 

The important idea in this whole unit is that the students will see practical applications for the mathematical topics covered. They will understand the meaning of the formulas and in fact, come up with their own formulas based on an in-depth understanding of the concepts. The mathematics learned can be a basis for learning the more advanced concepts of statistics, geometry, trigonometry and calculus.

 

Lesson Extensions and Modifications:

 

For students who need a review of problem solving, we have a problem solving worksheet in Appendix A. We believe that all students can learn problem solving skills. If they are struggling we plan to give guidance, but expect students to use the information given as a jumping board to develop their own personal style for solving problems. All students should be empowered with a positive expectation from teachers that they can solve problems.

 

For an extension of the slope formula, we have an activity to use a ladder in Appendix C.

 

Lesson Assessment:

 

The teacher will observe the ongoing process of student thinking as well as the worksheet that will be handed in at the end of the project.

While doing active assessment, the teacher will answer these questions:

         Did the student understand the concept of slope with regards to rise/run?

         Can the student use the slope formula?

         Was the student engaged all of the time?

         Does the student recognize special cases such as 0 slope or no slope?

         What methods did the student use to determine a standard for comparing slope?

The formal assessment of this lesson will be a test on the meaning, application and calculation of slope, the worksheet and journal entries.

 

 


Unit Extension and Modification

All of these lessons are well connected to each other in that they are all stops along the way in a trip across the United States. The mathematics involved in each lesson builds upon previous lessons. This unit could also be easily related to various other disciplines such as:

o       Geography the study of the United States

o       History the historical background of the sites we visit

o       Science the boiling point of water at a high altitude, architecture, rainfall, bacteria growth

o       Art American artists

 

This unit can help teachers to accomplish most of the standards set forth by the National Council of Teachers of Mathematics (NCTM) and the Connecticut State Department of Education (CSDE).

 

We chose lessons in this unit that will be engaging for all of the students regardless of their proficiency. The slower learners as well as the advanced students will be engaged in these lessons because of their appealing and unique quality. Having an imaginary race in a rickshaw, helping the FBI to catch a criminal, rebuilding the Golden Gate Bridge, all of these will be motivating to all students.

 

To further ensure the success of the unit, we will choose students of different levels to make up each of the small groups. Each small group will include at least one advanced student and one student who is struggling. This way the slower learners will be helped along by the more advanced students. We will also monitor the activity of each of the groups to ensure that there is a mutual sharing of ideas and that everyone is included in the discussions and decisions.

 

To facilitate the learning of the slower learners, we have also included a worksheet on problem solving in Appendix A and a re-teaching sheet for Lesson 2 in Appendix D. Various other aids could be implanted depending on the need of the students. The availability of the Internet is a valuable aid for reinforcing any topic in which a student is weak. Teacher prodding is also an important tool for guiding the struggling learner during these activities.

 

For the advanced student we have an additional slope project to follow our detailed lesson. It involves breaking into your hotel room using a ladder and can be found in Appendix C. This and the original slope activity can both be further extended by the use of graphing calculators. We will definitely have these available to the students throughout the unit and the advanced students will be encouraged to use them as an extension of each lesson. For example, in the slope activity, they could investigate various slopes using the calculator to better enable them to explore the meaning of slope. Questions that could be asked include:

 

        Can you make a line that lies in the first, second and third quadrants?

        How steep a hill can your car drive?

        How does the slope of an advanced ski slope compare to the slope of a beginner ski slope?

        How does the slope of a mountain affect the construction of a building?

        How does slope affect the runoff of mountains?

        Why do rockets launch at a slope and not in a straight line?

 

One group lesson could be to use the graphing calculator simulation found at http://www.coolmath.com/graphit/.

Other graphing calculator activities for this unit include:

         Investigating the distance formula. Perhaps the students could be encouraged to create a formula for finding distance after lesson 2, 3, or 4 which all deal with distances.

         Evaluating and graphing functions. During lesson 5 the students are studying the bacterial population of Lake Erie as a function of time.

         Working with matrices. In lesson 6 the students study the half-life of Excedrin PM. The lesson could be extended by including another pill with a different half-life.

         The study of curves which comes up in the arches and arcs lesson (lesson 7).

         Probability which is included in the Las Vegas lesson (lesson 12).

 

As you can see, nearly all of the lessons in this unit lend themselves to the use of graphing calculators and can easily be extended to the most advanced students in the class.

 

The unit can be used to teach all of the mathematics standards in an entertaining way. It also, as we have seen, can easily be implemented in many of the other disciplines especially social studies and science.


Unit Assessment

The entire unit will be actively assessed and students will present their final projects to the class. Their presentation/portfolio must include all completed activities along the way, as well as information about each of their destinations. Their bridges are displayed and tested. The mathematical concepts will also be assessed by traditional testing. Math journals will be regularly monitored as these journals are reflective.

Rubrics for grading the unit are posted below.

 

 

Target (5)

Acceptable (3-4)

Unacceptable (0-2)

 

 

 

 

Presentation of Research and work completed

Excellent description of the group trip. All destinations highlighted and key areas of interest were noted. Included all encountered issues and how they were solved.

 

Good description of the group trip. Most destinations highlighted and key areas of interest were noted. Issues were not given enough time in presentation.

 

Weak description of group trip. Many destinations left out or barely mentioned. Issues were not addressed.

 

Presentation

Presentation flowed smoothly. Title page and table of contents were included and accurate. Graphs and other problems were presented in a very eye-catching format

Presentation flowed well. Table of contents slight. Graphs and other problems from the trip were presented.

Presentation was very weak, missing several pieces and did not flow smoothly.

Mathematical Computation

Accurate Balance of budget. Each problem was correct and all work was shown clearly and easy to follow.

Most items were accurate and problems done out properly OR items were accurate but work was not properly shown.

Problems were inaccurate or work was missing.


Appendix A

SETTING A FOUNDATION FOR PROBLEM SOLVING

GRADES 3-12

The beginning of the school year is a crucial time to begin the problem solving process--a process that is a central component of all new Math texts adopted today. The following are a number of stages, approaches and steps for problem. They should be discussed with the students, and if possible, put onto charts for display throughout the year. Examples should be chosen in accordance with the age and level of your students.

 

6 STAGES OF THE PROBLEM SOLVING PROCESS
  1. Define the problem
  2. Brainstorm possible solutions
  3. Evaluate and prioritize the possible solutions
  4. Choose the best solution
  5. Determine how to implement the solution
  6. Assess how well solution solved the problem
7 APPROACHES TO PROBLEM SOLVING
  1. Guess and check
  2. Find a pattern
  3. Use a systematic list (charts & tables)
  4. Use a drawing or a model
  5. Eliminate possibilities
  6. Work backwards
  7. Use a similar, simpler problem
5 STEPS TO PROBLEM SOLVING
  1. Read and understand the problem
  2. Organize the information
  3. Determine the operations needed, establish equation
  4. Solve and check answer
  5. State and label your answer

Submitted by

ROB SCHUCK
PACOIMA MIDDLE SCHOOL

LOS ANGELES, CA
rschuck@pacificnet.net


Appendix B

Colorado Worksheet for Finding Slope

 

Draw lines on the coordinate plane to show your two ski slopes. Find any two points on each line and determine the slope of each.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note: Remember, when calculating slope, order is important. For any points (x1, y1) and (x2, y2), slope can be found through the following:

 

 

Critical thinking:

Why does the formula for slope include the statement where x2-x1 0?

 

 

When would two lines be parallel? Or perpendicular? Try making parallel or perpendicular lines on the graph and see how their slopes compare.

 

True or False:

  1. All horizontal lines have the same slope.
  2. Two lines may have the same slope.
  3. A line with slope 1 passes through the origin.
  4. The slope of a line in Quadrant III must be negative.

 

Extension:

Draw another ski slope different from the first two. Find its slope. Explain what that slope means and compare it with the other slopes. Which is steeper? Why? How does this number relate to an equation?

 


Appendix C

Breaking Into Your Hotel Room

Overview of Topics:

  1. Finding the x and y intercepts.
  2. Finding the slope of a graph from two points.

Student Required Materials:

  • Graph paper
  • Straight-edge
  • Mathematics: Principles and Process (10). Frank Ebos et al. Scarborough, ON: Nelson Canada, 1990



Procedures/Activities:

  1. Present the following problem to the class: When you arrive at your hotel, you realize that you do not have your room key, however, you can get into the garage where there is an extension ladder stored. You notice that your window is open, so despite your fear of heights, you proceed to get the ladder.

    What are some of the factors that become important when you set up the ladder?


Look for ideas about the angle at which you place the ladder, where on the ground it should start, where it needs to end, etc.

  1. Next ask the students how the ladder situation is like the graph of a linear equation. Have them sketch different possible placements of the ladder (line).

    Make sure the students remember that lines are continuous, so the question of length becomes irrelevant. If they are ignoring the lengths of the ladder, you can discuss what is causing the steepness of the ladder to change in each situation. They should come up with the idea that the amount of vertical distance covered with respect to that covered by the horizontal distance is changing. This will head into the conclusion that the measure of steepness, slope, is actually a measurement of how fast height changes as length changes. At this point the following formula can be presented:


    Go over an example such as the one below:


  2. Next, ask how we might distinguish between two lines that have the same steepness, but different direction. Look at two lines with the same steepness, but opposite direction and calculate the slope, stressing the importance of reading changes from left to right or right to left, but not to mix and match.

    This should lead the students to conclude that for / lines, both the rise and the run, working left to right are positive changes (or from right to left both are negative changes), so
    rise over run will be positive overall.

    Such a line is called an increasing line.

    Similarly, for \ lines, one change will be positive and the other will be negative, so the overall result will be negative. Such a line is called a decreasing line.
  3. Brainstorm for places where slopes are important. Ask how the value of the slope of a particular line, say a ski slope, tells how steep it really is. Sketch various lines and ask the students to indicate which line has the greatest slope and which has the least slope. A quick calculation of the slopes will confirm their hypotheses.
  4. Now, return to the ladder scenario. Ask the students what other than the slope must be fixed to give the specific placement of the ladder. Their conclusion should be either where you place the bottom or the top of the ladder.

    Discuss where, if the ladder were in fact a line on a coordinate grid, these points would occur on the graph. The students should be able to identify them as being the points where the graph crosses the x and y axes. Some discussion can be had on the number of x and y- intercepts that a linear equation might have. If they decide that any linear equation must have one x and one y-intercept, you may wish to have them consider a vertical or horizontal line (eg. y = 3, or x = 5, etc.)
  5. Have each student sketch a line and identify the coordinates of the x- and y- intercepts of their line. Their results should be recorded as ordered pairs on a class chart.

Analysis of this chart should lead the students to conclude that an x-intercept occurs when y = 0 and that a y-intercept occurs when x = 0. Do a few examples of calculating these values from an equation.

CELs: 
  • Creative and Critical Thinking
  • Communication


Evaluation:

  • Rating scale on positive participation 0 - 5
  • Homework completion rating scale 0 - 2
  • Slope and intercepts quiz 6


Time Line:

  • 1 - 2 hours

Appendix D

Re-teaching Worksheet -Lesson 2

1.  My first stop is __________________________.

2.  I will stay at the _______________________________ hotel.

    The address of my hotel is

________________________________________________________

________________________________________________________

3.  Find out how many miles from your home to your motel. I will be traveling _________ miles.

4.  What size car do you have? Do an Internet search on that make to find out mileage per gallon. My car gets _______________ miles to a gallon of gas.

5.  To determine the amount of money you will need to get to your motel follow the steps below.

# of miles traveled      ____________

Divided by # of miles your car can travel on one gallon of gas   ____________

Multiplied by the cost of one gallon of gas  _______________

 


Appendix E

 

Bridges to Math Comprehension

by Jan Rottner

Objectives:

Students will collect bridge statistics to use for geometry identification and measurement calculations.

Grade level: 4 (appropriate for 4-6)

Materials:

  1. Student Worksheets
  2. Computer and Internet Access
  3. Calculators

Internet Resources:

Procedures:

  1. Have students do Worksheet #1 Part 1: Collecting Data (html) / (pdf). This can be done at a one computer station as a Math Center activity.
  2. Have students follow the directions on this student page while on-line.
  3. Have the students find length and width facts about 2-4 famous bridges. (Teachers Choice)
  4. Students calculate the requested items on Worksheet 2 Part 2: Comparing Data (html) / (pdf) based on the decisions they made on the web site.

Evaluation:

Data collection and accurate computation will be evaluated using a 3 or 4 point rubric.

Extensions:

Write about any interesting facts you learned about Famous Bridges of the world while participating in this project. Explore Related Web Sites see the Extension Worksheet (html) / (pdf).

 


SCORE Mathematics | | SCORE Mathematics Lessons Index | |  SCORE Mathematics Search

California's Mathematics Academic Standards:

Grade 4:
Measurement and Geometry
1.0 Students understand perimeter and area.

1.1 measure the area of rectangular shapes by using appropriate units, square centimeter2, square meter2, square kilometer2, square inches2, square yard2, square mile2
1.4 understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use these formulas to find the areas of more complex figures by dividing the figures into basic shapes

3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.

3.1 identify lines that are parallel and perpendicular

Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, sequencing and prioritizing information, and observing patterns
1.2 determine when and how to break a problem into simpler parts

Copyright Kings County Office of Education
December 1998/Revised
August 26, 1999
SCORE Webmaster

 


Appendix F


 

 

Appendix G

First Graphing Calculator Activity

 

This activity will help you to learn all the different keys available on your calculator.

 

 

  1. Make five drawing of your Ti 89 calculator. On the first put the keys in regular mode.

 

  1. Make a heading for the second drawing: 2nd. On this drawing, put the 2nd mode keys only. Color them blue.

 

  1. Make a heading for the third drawing: diamond. On this drawing, put the diamond mode keys only. Color them yellow.

 

  1. Make a heading for the fourth drawing: Shift. On this drawing, put the shift mode keys only. Color them gray.

 

  1. Make a heading for the fifth drawing: Alpha. On this drawing, put the Alpha mode keys only. Color them white.

 


Appendix H

 

For the Dodge City map:


Bibliography

 

About. (2004). How does the boiling temperature of water change with altitude? Retrieved October 2, 2004, from http://geography.about.com/library/faq/blqzbiolingwater.htm

 

Annenberg/CPB. (2004). Play your bets: cashing in on probability. Retrieved October 4, 2004, from http://www.learner.org/exhibits/dailymath/placebets.html

 

Building Big. (2001) Bridges. Retrieved October 1, 2004, from http://www.pbs.org/wgbh/buildingbig/bridge/index.html

 

The Class A Truckstop. Speed limits for each state. Retrieved October 3, 2004, from http://www.geocities.com/TheTropics/1608/speedlimits.htm

 

CNN Student News. The Gateway Arch. Retrieved September 21, 2004, from http://go.hrw.com/math/cnn/course3/3_7_Arch/3_7_Arch.htm

 

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA. Retrieved September 3, 2004, from http://standards.nctm.org/document/index.htm

 

Sparknotes, LLC. (2004). The new SAT. Retrieved September 21, 2004, from http://www.sparknotes.com/testprep/books/newsat/chapter20section6.html

 

Spector, L. (2004). The Math Page Trigonometry. Retrieved October 5, 2004, from http://www.themathpage.com/aTrig/arc-length.htm

 

State of Connecticut State Board of Education. (1999). A guide to K-12 program development in mathematics. Hartford, CT. Retrieved September 3, 2004, from http://www.state.ct.us/sde/dtl/curriculum/currmath_publ_guide1.htm

 

Teach. (2002). Water pollution in the Great Lakes. Retrieved October 5, 2004, from http://www.great-lakes.net/teach/pollution/water/water6.html

 

United States Geological Survey. (2002). Elevations and distances in the United States. Retrieved October 3, 2004, from http://mac.usgs.gov/isb/pubs/booklets/elvadist/elvadist.html

 

Wildernet, your guide to outdoor recreation. (2003). National Park Service. Retrieved October 1, 2004 from http://areas.wildernet.com/pages/area.cfm?areaID=US0075&CU_ID=1