*>@*L$Hl Dh _ (Cover should have a picture of the Applied Math Logo with the following title: )  *C$Hl Dh BStudent Success Through Problem Solving Investigations   7 Applied Mathematics Lab Development Project  *L$Hl Dh 7 credit to the powers that be..... on page 1  = Curriculum Development Team Members.....on page 2  + Laurie Norris, Project Director  " Steilacoom High School  1 Steilacoom Historical School District   Chuck Boyd  & Lake Roosevelt High School  , Grand Coulee Dam School District   Sandy Christie  " Eisenhower High School  " Yakima School District   Larry Lester   South Kitsap High  ( South Kitsap School District   Ana Miller   Renton High  " Renton School District   Dee Dee Olmer  ' Edmonds-Woodway High School  # Edmonds School District   Tim Phelan   Ingraham High School  # Seattle School District   Emil Rosenberg   Colville High School  $ Colville School District   Bud Rupe  # Clallum Bay High School  ) Cape Flattery School District   Eric Sorensen   Lakewood High School  $ Lakewood School District   Richard Tinder   Hoquiam High School  # Hoquiam School District  *C$Hl Dh  Table of Content *L$Hl Dh  Applied Mathematics Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4   Introduction of Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5   Standard Lab Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5    Estimation Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 *F$Hl Dh   Writing Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5    Problem Solving Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6    Cooperative Learning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6    Career and Life Skills. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  s  Applied Mathematics Lab Forms and How to Use Them . . . . . . . . . . . . . . . . 7  {  Teacher Information Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . 8  {  Team Information Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . 8  z  Individual Specifications Sheet . . . . . . . . . . . . . . . . . . . . . . . . 9  {  Team Specifications Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . 9   Software Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10   Grading Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10  8 Labs by Applied Mathematics Educators     Unit B: Remodeling Wall Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-12  {  Unit C: Pipe fitting/ Plumbing, A temporary cold water line . . . . . . . . . . . . . . 13-15     Unit 1: Designing a time-measuring device . . . . . . . . . . . . . . . . . . . . . . 16-20    Unit 3: Guess what it is? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-24  w  Unit 3: Comparison between Metric and English Bolt Sizes . . . . . . . . . . . . . . 25-26  z  Unit 4: Graphing Diameter and Circumference Values . . . . . . . . . . . . . . . . . 27-28     Unit 4: Comparing Breakfast Cereal . . . . . . . . . . . . . . . . . . . . . . . . . 29-32    Unit 6: Balloon Climb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-34    Unit 8: The Cubit Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-36    Unit 10: Dr. John's Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37-40   5 Blank Applied Mathematics Lab Forms     Teacher Information Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41    Team Information Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42    Individual Specifications Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43    Team Specifications Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44  }  Generic Lab/Problem Solving Worksheet . . . . . . . . . . . . . . . . . . . . . . 45   Grading Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46  *L$Hl Dh *C$Hl Dh ( Applied Mathematics Overview *L$Hl Dh *F$Hl Dh  Applied Mathematics follows an approach to learning used in other applied learning materials, which means, mathematics is made relevant by showing how the skills are used in the workplace, and by teaching problem-solving through hands-on, activity-centered environments. It conforms to the latest recommendations of the National Council of Teachers of Mathematics, as reflected in the NCTM Standards. CORD recommends six activity sessions, as a guide for the teacher. These sessions are as follows:   (F$$Hl Dh  Session 1 - Overviewing the unit, viewing and discussion the video and working - as a class - a problem posed in the video.   Sessions 2 and 3 - Reading through the text and doing the text activities, class activities, class discussion, and working through examples.   Sessions 4 and 5 - Students get involved in lab activities and problem solving exercises that involve extensive use of calculators. Cooperative learning is encouraged. Students work in groups, collect data, make calculations, and discuss their results. An emphasis is placed on "hands-on" experiential learning, with students helping one another discussing approaches to problem solving, and consulting with the teacher in a "team spirit" atmosphere.   Session 6 - activities include reviewing the unit objects, watching the video again for a more in-depth understanding, and recapping the ideas presented in the summary. An end-of-unit test can be used at this time to evaluate student progress. *F$Hl Dh c  Applied Mathematics is best suited for students who have at least an eighth grade reading level and has reached an eight grade competency level in mathematics. The Applied Mathematics materials are especially beneficial for students who learn mathematics best in "applied settings," and for students heading for vocational-technical careers.  *C$Hl Dh   * CORD Applied Mathematics Units  *L$Hl Dh e A. Getting to Know Your Calculator 16. Solving Problems That Involve Linear Equations  E B. Naming Numbers in Different Ways 17. Graphing Data  m C. Finding Answers with Your Calculator 18. Solving Problems that Involve Nonlinear Equations  R 1. Learning Problem-Solving Techniques 19. Working with Statistics  F 2. Estimating Answers 20. Working with Probabilities  _ 3. Measuring in English and Metric Units 21. Using Right-triangle Relationships  V 4. Using Graphs, Charts, and Tables 22. Using Trigonometrics Functions  4 5. Dealing with Data 23. Factoring  L 6. Working with Lines and Angles 24. Patterns and Functions  F 7. Working with shapes in Two Dimensions 25. Quadratics  S 8. Working with Shapes in Three Dimensions 26. Systems of Equations   A 9. Using Ratios and Proportions 27. Inequalities  O 10. Working with Scale Drawings 28. Geometry in the Workplace 1  T 11. Using signed Numbers and Vectors 29. Geometry in the Workplace 2  _ 12. Using Scientific Notations 30. Solving Problems with Computer Spreadsheets  b 13. Precision, Accuracy, and Tolerance 31. Solving Problems with Computer Graphics  e 14. Solving Problems with Powers and Roots 32. Quality Assurance and Process Control 1  ` 15. Using Formulas to Solve Problems 33. Quality Assurance and Process Control 2 *F$Hl Dh   *C$Hl Dh # Introduction of Purpose *L$Hl Dh *F$Hl Dh  In the State of Washington, an Applied Mathematics Steering Committee facilitates the coordination and development of Applied Math educators and provides support for curriculum needs. Applied Mathematics educators receive many continuing inservice opportunities. Each year, one day inservices are offered in the fall, winter, and spring, and week long training sessions are available in the summer, for Applied Mathematics I, Applied Mathematics II, and Curriculum Development. Over the years, a wealth W of curriculum, including labs, video worksheets, and reading worksheets, has been developed and compiled by the Washington State Applied Math Community. This curriculum currently exists in many different forms, formats, and fonts. To facilitate widespread dissemination of this curriculum, a Curriculum Development Team was assembled.    During the 1995 Washington State Applied Mathematics summer training, the Curriculum Development Team met to produce a manual to assist in the standardization of Applied Mathematics Lab Development. First, the team developed a format for labs. Secondly, the team identified areas of importance and the supporting information needed for lab development. Finally, the team developed or adapted labs from a variety of Applied Math Units, putting them in the newly developed format.  *C$Hl Dh  Standard Lab Format *F$Hl Dh   It is the goal of the Curriculum Development Team to standardize the format for writing and rewriting labs and to eliminate those that are confusing or redundant. The included format will be used to write all new labs and to rewrite the existing labs. Labs that are currently in the CORD Applied Math series A-33 or those that have been developed by or are being used by Applied Math Educators in the State of Washington will be targeted. At the Fall Inservice, Applied Math teachers will be given thi os format, with instructions and copies of the labs that have been rewritten. Every teacher will be expected to write or rewrite a lab and bring at least one to Winter and one to Spring inservice. All labs must be written in the given format. During the summer training, participants will be given this format, with instructions, for use in developing labs.    Five main areas identified as focus points for lab development by the Curriculum Development Team, include: encouraging the use of estimation skills, emphasizing writing skills, reinforcing the use of problem solving strategies, developing a team/group concept (cooperative learning), and impacting career and/or life skills. In writing or rewriting labs, emphasis should be given to these five focus points. Information sheets written for the Teacher, Team and/or Individual will be written to support  these five main areas.    Estimation Skills    Applied Mathematics is just that, math that is applied to situations faced in careers and everyday life. It is important for people, when faced with a problem, to have an idea, an estimation, of the solution to the problem. Estimation skills can be used in every problem requiring mathematics and estimation strategies are taught early in the Applied Mathematics series. It is important to include estimation in each lab, so the students are able to practice and internalize estimation strategies.    Writing Skills     Since in Applied Math, the focus is on "the process" rather than just 'the answer", it necessary to teach reading and writing in the content area so that students are able to communicate what they are doing and how or why they did it. Technical writing skills need to be included so that the students are able to communicate the mathematics needed to solve problems on the job or in life. Writing should be included in each lab to emphasize its importance. Included in each lab should be a summary of wh kat the student learned. Other writing exercises could include: lab reports, letters to employers or customers of the lab, likes and dislikes of the lab, suggested changes to the lab, and extensions/additions for the lab. Having students write their own labs is a great way to get the students involved and energized, while expanding teacher lab resources.    As a guideline for writing requirements, if the student can learn from writing the information, have all the students write that information, otherwise, having one student record the information would be sufficient.  & Problem Solving Strategies  *L$Hl Dh   The four step problem solving method used in Applied Mathematics is outlined below. When a student, or a student group has been given a problem to solve, these four steps, that include problem solving strategies, have been used as a guide to solve problems.   & 1) Understand the problem  $  a) picture the problem  !  b) what do you know?  )  c) what do you need to know?   2) Develop a plan  8  a) how are you going to find the solution?    i) draw a diagram    ii) make a model  %  iii) look for a pattern  )  iv) solve a similar problem  $  v) use a known formula  #  vi) write an equation  "  vii) guess and check  ! 3) Carry out the plan  #  a) estimate the answer  #  b) do the calculations  a  c) use the diagram, model, pattern, similar problem, formula, solve the equation,...   4) Check the results  ,  a) is it close to the estimate?  $  b) does it makes sense?  ,  c) does it answer the question?  !  d) is it reasonable?    e) does it work?  *F$Hl Dh  Cooperative Learning    Developing a team/group concept and equipping each student with the interpersonal skills needed to compete in today's job market is essential for success in Applied Mathematics. Cooperative learning labs help provide students with an opportunity to learn and practice those skills. When labs are written cooperatively, students need to find ways to work together toward a common goal. Labs can be written for groups of 2, 3, 4, or more, depending on the requirements of the particular problem. As a gu dideline, the Curriculum Development Team encourages the following three cooperative formats:   (F$$Hl Dh d  Format 1 - different tasks for each team member which when brought together support a team solution. Example: Each member of a team figures out the volume of the frosting for a cake. One is given a rectangular pan, one a circular pan, and one a square pan. The team is to figure out what size container the frosting should be marketed in.  k  Format 2 - different jobs for each team member while working on a team solution. Example: Each member of a team takes a job that will support the problem's solution. One may be assigned to read directions, one may be assigned to record the measurements, and two may be asked to perform the measurements. Together they work to solve the problem.    Format 3 - different jobs for each team which when brought together forms a class solution. Example: The class is to discover the amount of paint needed to paint the school's main office. Each team can be given their own wall or room to measure. When complete, the teams get together and figure the total amount of square footage and the amount of paint needed to paint the office. *F$Hl Dh   It is important to teach skills that encourage communication, tolerance, fairness, cooperation, and team building so the students may apply these skills in their future.      " Career and Life Skills    In the creation of labs, careers need to be a constant focus. The tasks addressed in the labs need to be similar to tasks in various real world occupations and/or situations. The students will begin to see the need for mathematics in their future. Daily discussion of various math applications is useful. Students actually know about some careers and are able to come up with examples of how math is used within those careers. During the introduction of a lab or a new unit is a good time to emphasiz e the various math applications. Reiteration of problem solving, estimation, data gathering, organization of data, and quality solutions is useful for math in the real world and helps the student develop successful math habits.    Guest speakers, work experiences of the students, and problem solving experiences of the students and/or teacher are great discussion topics. Second hand experiences from students' friends, parents, and relatives are also useful in discussion.    A survey on the first day of class asking "What do you want to do when you grow up?" can really help direct the focus of the instruction. Some direction for student job searches are W.O.I.S. (Washington Occupational Industrial Services) from the Department of Labor and Industry or Job Services; Discovery and/or other software career exploration programs; Job shadowing in the local industries; the Career Center with School to Work program; the Career counselor; and Military recruiters/ASVAB test s.   a  Student research on careers can require research papers, reports, or interviews with someone working in a career of interest. Upon completion of a research paper, report or interview, the student will know whether or not they might enjoy that career. The more the student knows, the more likely they are to successfully choose a career.   = Applied Mathematics Lab Forms and How to Use Them    Examples of the Teacher Information Sheet, Team Information Sheet, Individual Specifications Sheet, and Team Specifications Sheet are outlined on the following pages. All labs, at the minimum, should include a Teacher Information Sheet and a Team Information Sheet. These two sheets will provide the teacher and the student groups with all the necessary information to perform the lab. It allows for the student groups to explore the lab situation on their own. This approach is used when the students are able to proceed without assistance or when it is necessary to challenge individual students or groups. Students can follow the problem solving format outlined in the Problem Solving Strategies section. When Individual and Team Specifications sheets are used, in addition to the Teacher Information Sheet and the Team Information Sheet, the students are guided through a series of steps or questions, to assist them in problem solving. This approach is used when students are learning how to problem solve  through labs, or when it is necessary to assist students with special needs. When the range of student needs is great, a combination of guided and unguided lab formats may be used to assist the teacher in adapting the curriculum to the students' needs.    The following Teacher Information, Team Information, Individual Specifications, and Team Specifications Sheets are annotated to describe what is required in each section. Parentheses have been placed around words or symbols that need to be replaced with information from the lab being written. Blank forms have been placed in the appendix for assistance in writing labs.  *L$Hl Dh 2 Applied Mathematics Lab #_____  : Unit (#) - (Title of the Applied Math Unit)   V Teacher Information Sheet   this is information for the teacher only  A Lab Title:  ( DESCRIPTION OF LAB )   Goals and Career Applications:   this section should describe the goals and importance of the lab, and justify the lab by listing the work related benefits and career applications     Materials needed: list all materials and resources needed, including alternative materials that could be substituted in parenthesis, the number per team  i Team Formation: describe the number of students per team, and each student's responsibility   Suggested Timeline: give a general indication of the time line, in minutes, for the entire project, or for each section, subject to change depending on student level, if unsure, leave blank or write 'varies depending on student level'  m Lab Preparation: give step by step instructions for the teacher to follow, include needed set up   Helpful hints: list things to watch for, other Applied Math Units needed or math prerequisites that are not apparent through reading the lab, examples of work, when needed, and additional resources  j Optional Activities: OPTIONAL, list activities that extending the lab or supplement the lab  J  Submitted by: (Teacher Name), (School Name), (school phone)  T <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<  , Applied Math Lab #_____  : Unit (#) - (Title of the Applied Math Unit)   K Team Information Sheet this is information for the team only  / Lab Title: (DESCRIPTION OF LAB)   Goals and Career Applications: this section should describe the goals and importance of the lab, and justify the lab by listing the work related benefits and career applications   Materials needed: list all materials and resources needed, including alternative materials that could be substituted in parenthesis, and the number per team  B Statement of problem and procedures: write the problem to be solved and an overview of the procedures so that this can be a stand alone sheet for a student generated solution, without teacher guidance. Team and individual teacher guided specification sheets developed will lead students through the problem.    Individual Worksheet - this can be the same worksheet for each team member, or written as different worksheet for each team member  0 Applied Math Lab #___________  P Unit (#) - (Title of the Applied Math Unit) Team Name___________  F Individual Specification Sheet Member (#)___________  ( Start Date:__________   & Due Date: __________   / Lab Title: (DESCRIPTION OF LAB)  l Procedure: this section is a series of procedures for the students to follow and respond to       encouraging the use of estimation skills, reinforcing the use of problem solving strategies, developing a team/group concept (cooperative learning), emphasizing writing skills, and impacting career and/or life skills.   T <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<       Team Worksheet heading - blanks for team member names will vary depending on the number of members per team, this worksheet should summarize the lab  + Applied Math Lab #______  P Unit (#) - (Title of the Applied Math Unit) Team Name___________  @ Team Specification Sheet Member 1 ___________  = Start Date:__________ Member 2 ___________  < Due Date: __________ Member 3 ___________  +  Member 4 ___________  / Lab Title: (DESCRIPTION OF LAB)  h Procedure: this section is a series of procedures for the team to follow and respond to       encouraging the use of estimation skills, reinforcing the use of problem solving strategies, developing a team/group concept (cooperative learning), emphasizing writing skills, and impacting career and/or life skills.      *F$Hl Dh *C$Hl Dh  Software Guidelines *F$Hl Dh   The following software guidelines will provide continuity and facilitate compiling labs into easily accessible formats.  *L$Hl Dh J Macintosh software requirements: Microsoft Word 5.1/Works 3.0  T IBM software requirements: Microsoft Word for Windows/Works for Windows  " Macintosh font: TIMES  & IBM font: TIMES NEW ROMAN   Font size: 12 point  ) Section headings: Bold print  $ Title of lab: Bold Caps  1 Top, Bottom and Right Margins: .5"   Left margin: 1"  2 Applied Mathematics Lab #______  7 Unit #B - Naming Numbers in Different Ways    Teacher Information *C$Hl Dh *L$Hl Dh - Lab Title: REMODELING WALL SPACE  . Goals and /or Career Applications:  F  Recognize standards of measurements used in construction.  F  Recognize how to make a reasonable estimate of materials.  M  Able to research construction resources for prices of materials.  4  Able to make a proposal to send to bid.  E  Able to research construction resources for labor costs.  >  Able to express the problem in a readable sketch.  S  Recognize various ways to make measurements without measuring devices.   Materials needed:  &  Tape measures 1 per group    25' x 1" spring retractable ($5-15)(These get broken easily but are easy to use and available anywhere) or 200' fiberglass wind-up tape measure ($25- 75) (Fred Meyers or Paxton / Patterson) or 8' folding rule ($15-30) (available from Paxton Patterson),   2  calculator as needed for individuals  ,  graph paper 6 sheets per group  ?  (Everett Wholesale Paper, $53/case of 1/4" grid)  2 Team Formation: Suggest groups of 3-4  . Suggested Timeline: 45-95 minutes   Lab Preparation:    Have a room/s available for measuring and be sure access to ceiling is easy or pre measured. Could use a long story stick (pre-measured stick).   Helpful Hints:  :  Be certain you can measure to ceiling easily.  %  Round to the nearest 1".  V  Be certain the student answers each include Fraction / Decimal / Percent.   Optional Activities:  W  Calculate wall paper for trim at top of wall, wainscot, or paint required.  H Submitted By: Eric Sorensen, Lakewood High, (360) 652-7511   , Applied Math Lab #_____  7 Unit #B - Naming Numbers in Different Ways   % Team Information Sheet   - Lab Title: REMODELING WALL SPACE  / Goals and / or Career Applications:    Carpenter, Concrete Masons, Heating/Cooling specialists (HVAC), Painter, Finish Carpenters, Dry Wall / Sheet rockers, Interior Decorators, Insurance Adjusters   Materials needed:  2  Tape measure, calculator, graph paper  " Statement of Problem::  c  Find the percentage of wall space and window space for walls of a given room/building.   .   Procedure:  c  1. State 'Job Site'. List all surfaces to be calculated. Do rough estimate of sizes.  _  2. Measures sizes to nearest inch. Double check. Sketch and label on graph paper.  ]  3. Identify and label each wall with doors/vents/window/etc.... on your sketch.  ]  4. Measure all sizes of items in procedure #3. Write down and label on sketch.  =  5. Compute total wall space and non-wall space.  8  Write Fraction / Decimal / Percent (F/D/P)    6. Write summary.  V  Pick an occupation from list above and describe why this lab might apply    to that career.   [  7. Student comments: Include at least a complete sentence for the following.  ,  a. What you liked / disliked.  9  b. What career you might consider and why.  Q  c. Suggestions to increase accuracy / efficiency / communications.   Helpful Hints:  `  Standard residential ceiling heights are 6'-8". Widths 30-36". Tops of doors and   &  windows usually line up.  S  Make sketch large enough to write labels and measurements near object.  B  Use leaders/arrows for notes / labels / measurements.  T  Always double check for complete set of ACCURATE measurements and data.  Q  Keep all data neat / organized / simple so it makes sense to anyone.  E SUBMIT THIS SHEET WITH YOUR DATA AND SKETCHES FOR GRADING *Ld$Hl Dh 2 Applied Mathematics Lab #______  Q Unit C- Finding answers with your calculator    Teacher Information  K Lab title: PIPE FITTING/PLUMBING. A TEMPORARY COLD WATER LINE.  - Goals and/or career applications:  ,  Recognize standards of measure.  1  Recognize how to estimate materials.  (  Research cost of materials.  L  Show problem in a sketch or schematic with specific dimensions.  &  Make a list of materials.   Materials needed:  \  Tape measures, calculator, graph paper, 3/4" PVC pipe in 10' sections, 3/4" PVC  \  unions, 3/4" PVC 90 elbows, price list for PVC components, hack saw, knife or  *L$Hl Dh d  small half round file for deburring the end of PVC pipe after it is cut, and duct tape. *Ld$Hl Dh Y  OPTIONS: Steel or copper pipe may be used instead of PVC, (Not recommended).  S  SOURCES: Local hardware store will have PVC components and price list.  ] Team Formation: Based on teams of 3-4 students each. Each team may decide on the   Y  role for individuals. The teacher may want to assign students to record (1),  T  measure (2), and read directions (1). If the teams have only 3 members   N  recording and reading directions may be done by the same student.  4 Suggested timeline: 100 - 150 minutes.   o Lab preparation: The teacher must tell each group what routing their piping will take. Each group   l  should be different. Each group will do the measurements for the piping and write instructions  o  and give the information to another group to construct the actual piping run. As the teacher, it   f  will be your task to see that each group follows the specific instructions given to them.  f Helpful hints: All sketches of pipe are drawn as a center line schematic very similar to   n  electrical schematics. If a pipe is to be 5' long with a 90 elbow on each end the center  h  of each 90 turn will be exactly 5'. If you use steel pipe you will need to have some means  e  of threading the pipe. Pipe run should be longer than 30' and shorter than 40' with at   b  least four 90's and one union. Duct tape may used to hold pipe in place on the wall,  p  counter or the table once it is put together. Student must be able to measure to the nearest 1/16"   _  or nearest millimeter. Student must know how to use a hack saw safely.      S Submitted by: Emil Rosenberg, Colville High School, 1-509-684-7800.   g Applied Mathematics Lab #_______  8 Unit C- Finding answers with your calculator  " Team Information Sheet  K Lab title: PIPE FITTING/PLUMBING. A TEMPORARY COLD WATER LINE.  h Goals and work related career applications: The goals of this lab is to write clear concise  h  instructions, complete enough so that another team can follow them. Measuring and cutting   l  must be precise. These skills and principles are the same as plumbing a house or installing an  7  underground sprinkler system in your yard.  m Materials needed: Tape measure, calculator, graph paper, 3/4" PVC pipe in 10' lengths, 3/4" PVC   r  unions, 3/4" PVC 90 elbows, price list for PVC components, hack saw, knife or small half   a  round file for deburring the end of pipe after it is cut, and duct tape.   k Statement of Problem: You need to run a temporary water line. Your teacher will give you the   g  specific route where the plastic pipe is to be installed. You will determine how many 10'  e  lengths of plastic pipe, how many 90 elbows(curved fittings for making turns), and how   r  many unions(fittings that join straight pipes together) are needed. A sketch of the piping   h  with specific dimensions must be drawn. Instructions of what is to be done and the sketch   l  will be given to another team. The information that you give to them will have to be complete   m  so that they can construct the piping run without any problems. You will also have to construct  h  a piping system from the instructions and sketch that another team gives to your team. You   j  must follow the exact directions, even if you know that they are wrong. If the instructions   l  are wrong or incomplete rewrite them and give a copy to your instructor. You will give an oral   h  presentation to class to explain any problems you might have had and what should be changed  f  so that the instructions and sketch would have been correct. If the directions you were   -  given were perfect explain why.   f Applied Mathematics Lab #______  S Unit C- Finding answers with your calculator Team Name________________  k Team Specifications Sheet Name 1___________________   -  Name 2___________________  -  Name 3___________________  -  Name 4___________________  K Lab title: PIPE FITTING/PLUMBING. A TEMPORARY COLD WATER LINE.   Procedures:  I 1. Obtain the routing for your piping run from your teacher.  s 2. Use the tape measure to determine the lengths of the straight pipes and where the 90's and union(s)  6 will be located. Record the measurements.  U 3. Draw a sketch with specific dimensions to the nearest 1/16 of an inch.  V 4. Write directions to give to another team to construct your piping run.  W 5. Trade directions and sketches with the team that the teacher indicates.  q 6. Read and study the directions that you received from another team. Follow the directions exactly  3 even if you know that they are wrong.   q 7. Get the tools, piping, and fittings that you need to construct the piping run. (From the teacher)  u 8. Measure and cut the pipe accurately. Assemble all the pieces according to the directions and sketch.  J Use the duct tape to hold the constructed piping run in place.  u 9. Have your teacher check to if the piping is correct and if your team followed the directions you had    correctly.  t 10. Rewrite the directions or sketch if they need to have changes to make them correct. Use a separate  . sheet(s) of paper for the rewrite.  x 11. Using the piping run you actually constructed, the directions and sketch you used to construct it, and   t if necessary the new sketch and directions you had to rewrite to make an oral presentation to the class.  o Explain what you did, why it did or did not work, and if you had to make changes so the plans would  X work. Explain what problems might have occurred if this had been a real job.     *L$Hl Dh 0 Applied Mathematics Lab#______  8 Unit 1 - Learning Problem-Solving Techniques  % Teacher Information Sheet  8 Lab Title: DESIGNING A TIME-MEASURING DEVICE  * Goals and Career Applications:  L  Read a problem and decide what is given and what is to be found  3  Develop a plan for solving the problem  5  Carry out your plan to solve the problem  <  Check the answer and decide if it is reasonable  4  Problem solving is a daily part of life   Materials needed:  /  Each team: 2 feet of strong thread    tape measure    stopwatch  Q  small lead fishing weight w/ eyelet, or large washer, or plumb-bob    calculator  Q  dowel/yardstick/meter stick/or some other item to hang pendulum on   Team Formation:  M  Teams of at least three will be needed to perform the experiment   Suggested Time Line:    50+ minutes   Lab Preparation:  _  Gather materials in advance, shop/tech teachers may have large washers/nuts to use  K  Handout only the Team Information sheet for an exploratory lab    For a more guided lab, hand out the Team Information Sheet and the Individual Planning Sheet first for completion through Developing the Plan, then hand out the Team Specification and Individual Specification Sheets   Helpful Hints:  R  Cut notches in yardstick or meter stick to keep pendulum from sliding   Optional Activities:  N  Find the length needed to measure time intervals of three seconds  Q  Find the optimal angle for each swing (try 15, 30, 45, & 60 degrees)  P Submitted by: Sandy Christie, Eisenhower High School, (509) 575-3270  0 Applied Mathematics Lab #_____  8 Unit 1 - Learning Problem-Solving Techniques  " Team Information Sheet  8 Lab Title: DESIGNING A TIME-MEASURING DEVICE  * Goals and Career Applications:  L  Read a problem and decide what is given and what is to be found  3  Develop a plan for solving the problem  5  Carry out your plan to solve the problem  <  Check the answer and decide if it is reasonable  4  Problem solving is a daily part of life  & Statement of the Problem:     You would like to design a simple device for measuring short periods of time. The device is to be rugged, portable, and inexpensive. You learn from your friend, who is taking a physics course, that a pendulum of a fixed length always takes the SAME time for a complete back-and-forth swing. What length of line will give you a complete swing lasting approximately 1 second.   Procedure:  &  Understanding the Problem  @  1. What data do you now have to solve the problem?  -  2. What are you trying to find?    Develop a Plan  O  1. What additional information do you need to solve this problem?  Y  2. Does finding any of this information involve solving other problems?  =  3. Are there any graphical methods you can use?  7  4. What mathematical methods can you use?  \  5. Is equipment available that you can use to find the needed information?    Carry out the plan  L  1. Make a rough estimate for any or all parts of the solution.  <  2. Solve the problem showing all of your work.    Check the results  o  1. From your rough estimate of the solution, compare the estimates to your calculated results.    2. For any part of your solution for which you did not make an estimate, calculate the result again to make sure there are no errors.  1 Applied Mathematics Lab #_____  N Unit 1 - Learning Problem-Solving Techniques Team Name___________  > Team Specifications Sheet Member #1___________  < Start Date_____________ Member #2___________  ; Due Date______________ Member #3___________  )  Member #4___________  8 Lab Title: DESIGNING A TIME-MEASURING DEVICE   Procedures:     V  1. Use the stopwatch to measure the time required for 10 complete swings.  {  2. Divide this time by 10 to get the time of one complete swing. This time is called the pendulum's period.    3. Vary the length of the string 3 inches to 12 inches, in increments of 1 inch, and determine the period for each length.    4. For each length, record the following in a table: the pendulum (string) length, the time for 10 complete swings (three trials for each length), the average of these trials, and the period in seconds from the average.  1  5. Have someone in your group agree to do an activity (such as jumping jacks, curl-ups, push-up, etc.) 50 times. Use your pendulum and a stopwatch to measure how long the exercise takes. Compare the result of your pendulum clock to the result of the stopwatch. How did your clock do?  0 Applied Mathematics Lab #_____  B Unit 1 - Learning Problem-Solving Techniques Page #2  = Team Specifications Sheet Team Name___________  & Length - of line in inches  9 Trials - seconds needed to complete 10 swings  Q Average - of three trials (add up all three trials, then divide by 3)  * Period - average divided by 10   Length (inches)   Trial 1 (seconds)   Trial 2 (seconds)   Trial 3 (seconds)   Average (seconds)   Period (seconds)   3"             4"             5"             6"             7"             8"             9"             10"             11"             12"                  0 Applied Mathematics Lab #_____  M Unit 1 - Learning Problem-Solving Techniques Name________________  = Individual Planning Sheet Team Name___________  &  Understanding the Problem  @  1. What data do you now have to solve the problem?  -  2. What are you trying to find?    Develop a Plan  O  1. What additional information do you need to solve this problem?  U  2. Does finding any of this information involve solving other problems?  =  3. Are there any graphical methods you can use?  7  4. What mathematical methods can you use?  X  5. Is equipment available that you can use to find the needed information?    Carry out the plan  L  1. Make a rough estimate for any or all parts of the solution.  <  2. Solve the problem showing all of your work.    Check the results  o  1. From your rough estimate of the solution, compare the estimates to your calculated results.    2. For any part of your solution for which you did not make an estimate, calculate the result again to make sure there are no errors.  *L2$Hl Dh 4 Applied Mathematics Lab # _______  : Unit # 3 - Measuring In English & Metric Units   Teacher Information   Lab Title: "GUESS WHAT IT IS?" - Measuring the length of objects in metric and identifying other objects when given their metric dimensions.  - Goals and/or career applications:  =  Practice (or learn) correct measuring techniques  G  Practice (or learn) how to read a metric ruler/meter stick  J  Identify which metric length is appropriate for various tasks  l  for example: km for long distances, m for 'household', cm & mm for small objects or distances)  P  Understand and have mental picture of standard metric measurements.  [  Discuss and understand metric dimensions when given in directions/instructions  q  Career applications are found in all areas, especially when products are part of international trade   Materials needed:        Metric rulers, meter sticks, tape measurers, 3x5 index cards of various colors, prearranged places for groups of students to go    Team formation:   O  This lab can work with 2, 3, or 4 students in a group (I prefer 3)    Each student will have his/her work checked by another student for accuracy. Team cooperation will be enhanced by an element of competition.  + Suggested timeline: 45 minutes   Lab preparation:   Y  Prearrange & examine close-by areas where kids will go to measure objects   <  Divide kids into groups of 2,3 or 4 (I like 3)    Give each group a selection of metric measuring tools and 3 index cards per student and a piece of paper (clip boards help if available)  H  Give them a time limit and appoint a time keeper per group     Send them out to their designated areas with the instructions to measure 3 objects (a combination of sizes) & record each on a separate index card. DO NOT NAME OBJECT ON THE CARD   ]  When they return, collect their index cards and redistribute them to a new group    Send each group out again to their new location with the corresponding measurement cards. With a specific, shorter time limit they are to come back with their intelligent guesses of the objects that were measured by the first group.    Back in the room, each group presents their findings. The original group corrects the work and prizes (?) are distributed to the "winning" team.  ^ Helpful hints: Be sure to check out the areas that kids will be sent to beforehand  J  Remind kids of safety issues (no standing on chairs, etc.)   e  Make sure each student has their measurements checked by another student in the group   +  Allow one challenge per team  .  Tolerances of accuracy will be:  S  m = + or - .5 cm (5 mm) cm = + or - 1 mm (.1 cm)      Q Submitted by DeeDee Olmer, Edmonds-Woodway H.S., (206) 670-7910      *Lh$Hl Dh 5 Applied Mathematics Lab # ______  *L2$Hl Dh = Unit 3 - Measuring In English & Metric Units   ( Team Specification Sheet        Lab Title: "GUESS WHAT IT IS?" - Measuring the length of objects in metric and identifying other objects when given their metric dimensions.  - Goals and/or career applications:  =  Practice (or learn) correct measuring techniques  G  Practice (or learn) how to read a metric ruler/meter stick  J  Identify which metric length is appropriate for various tasks  l  for example: km for long distances, m for 'household', cm & mm for small objects or distances)  P  Understand and have mental picture of standard metric measurements.  [  Discuss and understand metric dimensions when given in directions/instructions  q  Career applications are found in all areas, especially when products are part of international trade   Materials needed:        Metric rulers, meter sticks, tape measurers, 3x5 index cards of various colors- each team has same color, 3 cards per member  *L[$Hl Dh    *L2$Hl Dh " Statement of problem:     In small groups, students will go to a predetermined area and measure some common objects. The group will then exchange their measurements and location with another group and "discover" what was measured by the previous group.   Procedure:       J  Each group needs the measuring tools and the index cards     Your group will measure 9 (assuming there are 3 to a group) common objects found in a particular place. Each member will be responsible for measuring 3 of those 9.  :  These will be recorded on the team data sheet    On the index card, you will write the dimensions IN METRIC of a common object. You will NOT write the name of the object you measured on the index card.    Record these measurements on the group's data sheet. Have the measurements checked by someone else in the group - they sign the group data sheet  L  Your group's location is ______________________________________  G  You will have __________ minutes to complete this part.   o  When you return, you'll exchange cards & locations and discover what was measured by another group  C  You have _____________ minutes to accomplish this task  /  Time Keeper is ___________________  1  Record Keeper is ___________________     *Lh$Hl Dh 5 Applied Mathematics Lab # ______  *L2$Hl Dh > Unit 3 - Measuring In English & Metric Units    Team Data Sheet        Lab Title: "GUESS WHAT IT IS?" - Measuring the length of objects in metric and identifying other objects when given their metric dimensions.  j Procedure: Each member will choose 3 common items to measure. Record this information below.  @  Measurements will checked by another group member.    Each measurement will be recorded on an index card to be exchanged with another group later. DON'T IDENTIFY THE ITEM ON THE INDEX CARD.    Name    common items  !  measurements    checked by      " ______________________  " ______________________  " ______________________  " ______________________  " ______________________  " ______________________          " ______________________  " ______________________  " ______________________  " ______________________  " ______________________  " ______________________          " ______________________  " ______________________  " ______________________      " ______________________  " ______________________  " ______________________       *Lh$Hl Dh 5 Applied Mathematics Lab # ______  *L2$Hl Dh @ Unit 3 - Measuring In English & Metric Units   A Team Data Sheet Team Member ___________________  ; Task # 2 Team Member ___________________  ?  Team Member ___________________    Lab Title: "GUESS WHAT IT IS?" - Measuring the length of objects in metric and identifying other objects when given their metric dimensions.   Procedure: Given a set of index cards with measurements and a location, your group will try to identify the object that was measured.    measurements  &  guess of object   correct ?                                                                          / Team Score: _______/9 = _________%  ` This was graded by the team of ________________, _________________ & _______________  *L$Hl Dh \ Applied Mathematics Lab #______  I Unit 3. Estimating and Measuring in English and Metric Units  % Teacher Information Sheet  > Lab Title: COMPARISON BETWEEN METRICS AND ENGLISH  5  WHEN MEASURING BOLT SIZES  - Goals and/or Career Applications:  T  Be able to recognize millimeter sizes as being compared to fractions  9  Metrics are used extensively in industry   Materials Needed  B  Bolt sizes 1/4" 3/8" 1/2" 5/8" 3/4" 7/8" 1" diameter  +  English/Metric vernier caliper  !  English/Metric ruler    Calculator    Graph paper       Team Formation  $  Two students to measure  1  one student using a vernier caliper  '  one student using a ruler  %  One student as recorder  |  All students will make a chart showing the comparison between fractions, decimals, and millimeters.     All students will do a graph showing millimeter sizes on vertical and fractions sizes on horizontal coordinates.      3 Suggested Timeline: 60 to 100 minutes   Lab Preparation:  N  Before doing the Lab, students should practice using the caliper.   Helpful Hints:  9  Use of ruler using fractions and millimeters      I Submitted by: Larry Lester, South Kitsap, (360) - 876-7318  0   *L2$Hl Dh *L$Hl Dh \ Applied Mathematics Lab #______  I Unit 3. Estimating and Measuring in English and Metric Units  " Team Information Sheet  H Lab Title: COMPARISON BETWEEN METRIC AND ENGLISH BOLT SIZES  , Goals and/or Career Applications  W  To be able to show comparison between fractions, decimals and millimeters  8  To become aware of metric use in industry    Materials needed:  *  One vernier caliper per group  /  One English/metric ruler per group  -  An assortment of bolts per group  :  One piece of graph paper per student   Statement of Problem and Procedures: This activity involves measuring the diameter of an assortment of bolts. The bolts need to be measured with a ruler and a vernier caliper in fractions and millimeters. Another part of the problem is to convert the fractions to decimals. A chart is developed showing the comparison between fractions , decimals, and millimeters and a graph is drawn to show the comparison between fractions and millimeters.   4  One student measures bolts in fractions  8  One student measures bolts in millimeters  K  One student records measurements in fractions and millimeters  ^  All students prepare a chart showing comparison of millimeters and fractions.  z  All students do a graph showing fractions on vertical coordinate and millimeters on horizontal coordinate.  U  Suggested scale for graph: 1 mm=5 mm 1/4 in.=1 in       1 Applied Mathematics Lab #_____  5 UNIT #4 - Using Graphs, Charts and Tables   Teacher Information *C$Hl Dh *L$Hl Dh @ Lab Title: GRAPHING DIAMETER & CIRCUMFERENCE VALUES  - Goals and/or Career Applications:  9  Develop measurement skills for all fields.   E  Develop data handling skills by graphing for all fields.  `  To understand the special relationship between diameter and circumference values.       Materials needed:    1# coffee can, soup can, 1-inch dowel, 5-gal. bucket, (cans of varying sizes for groups of 4), graph paper, cloth measuring tape, ruler. Optional - string to measure circumference, vernier caliper or dial caliper.          2 Team Formation: Suggest groups of 3-4  + Suggested Timeline: 50 minutes   Lab Preparation:  D  Work tables with items for each team in trays or boxes.       Helpful Hints:  L  See Unit 7 student workbook pages 22 & 23 for additional ideas.  * Grading Criteria (Checklist):  a  Use evaluation checklist on student's accuracy of measurements and quality of graph.   Additional Options:      G Submitted by: R.L. Tinder, Hoquiam High, 1-360-532-3760.       9 Applied Mathematics Team Name___________  I Unit 4 - Using Graphs, Charts, & Tables Member #1___________  < Team Specification Sheet Member #2___________  @ Start Date___________________ Member #3___________  ? Due Date____________________ Member #4___________  *C$Hl Dh ( USING GRAPHS CHARTS & TABLES *L$Hl Dh ; Title: GRAPHING DIAMETER & CIRCUMFERENCE VALUES  / Goals and / or Career Applications:    Develop measurement skills for all fields. Develop data handling skills by graphing for all fields. To understand the special relationship between diameter and circumference values.   Materials needed:    1# coffee can, soup can, 1-inch dowel, 5-gal. bucket, (cans of varying sizes for groups of 4 ), graph paper, cloth measuring tape, ruler. Optional - string to measure circumference, vernier caliper or dial caliper.  ! Statement of Problem:  N  Graph the relationship between diameter and circumference values.       Procedure:    Label the horizontal axis - diameter measurements and the vertical axis - circumference measurements. The units on the vertical axis are 1 division = 1 inch. The units on the horizontal axis are 1 division = .5 inch. Measure the diameter and the circumference of a can then plot the intersecting point on the graph. Plot the remaining values of the other cans and connect the points with a line or lines.  1 Applied Mathematics Lab #_______  2 Unit 4 - Using Graphs, Charts & Tables  ' Teacher Information Sheet   1 Lab Title: COMPARING BREAKFAST CEREAL  * Goals and Career Applications:  &  Collect and organize data  "  Construct a bar graph  <  Read and interpret information from a bar graph  K  Communicate in writing, contrast/comparison, of data collected  )  Present results to the class  J  Development of data gathering, analysis, and marketing skills   Materials needed  `  Labels that list the nutrition info from at least three different breakfast cereals  F  Drawing materials (graph paper, rulers, accu-lines, etc.)  '  Color markers/crayons/etc.   Team Formation  !  Three members per team (students may be given the team information sheet only, then allowed to solve as an open-ended problem, or each team member can be given an individual specifications sheet and each team given the team specifications sheet for a more guided lab).   Suggested Time Line:  )  Varies according to students   Lab Preparation:    Purchase several boxes of cereal (contents could be consumed during the lab), or have students bring the nutrition information from their favorite type of cereal.  B  Get large sheets of paper to be used for team graphs.   Helpful Hints:  Z  see Applied Math Unit 4 Teachers Guide, pages T-20/T-21 for solution example   Optional Activities:    Research other listed nutrients and calories from label. Do any of these appear to be related? If you know the amount of carbohydrates, can you predict the calories?  Q Submitted by: Sandy Christie, Eisenhower High School, (509) 575-3270   Applied Mathematics  3 Unit 4 - Using Graphs, Charts, & Tables  " Team Information Sheet  1 Lab Title: COMPARING BREAKFAST CEREAL  * Goals and Career Applications:  &  Collect and organize data  "  Construct a bar graph  <  Read and interpret information from a bar graph  K  Communicate in writing, contrast/comparison, of data collected  )  Present results to the class  J  Development of data gathering, analysis, and marketing skills   Materials Needed:  `  Labels that list the nutritional information from three different breakfast cereals  F  Drawing materials (graph paper, rulers, accu-lines, etc.)  '  Color markers/crayons/etc.  $ Statement of the Problem  *L$$Hl Dh <  In this activity you will compare the amount of carbohydrate, fat and protein in a serving of three different cereals. You will also make the comparisons for the cereal (1) without milk and (2) after one-half cup of whole milk has been added. Use the graphs you draw to answer the following questions:  n  1. Which cereal with milk has the most protein? Which cereal without milk has the most protein?  f  2. Which cereal with milk has the most fat? Which cereal without milk has the most fat?  z  3. Which cereal with milk has the most carbohydrates? Which cereal without milk has the most carbohydrates?    4. What nutrients are added by the milk? Is there a nutrient that is present in the cereal served with milk that is not present in the cereal without milk? If so, which nutrient?  *L$Hl Dh @ Applied Mathematics Name___________________#____  R Unit 4 - Using Graphs, Charts, & Tables Team Name___________________  . Individual Specifications Sheet   * Start Date____________________  ) Due Date_____________________   Procedures:  d 1. Collect nutrient information from a cereal label and share with other team members.   Y  Type of cereal__________________(must be different than other team members!)  I  Carbohydrates ____________ w/one-half cup milk______________  B  Fat ____________ w/one-half cup milk______________  D  Protein ____________ w/one-half cup milk______________  a 2. Choose a nutrient to graph __________________ (must be different for each member)  K  Cereal__________________ without milk_______ with milk________  K  Cereal__________________ without milk_______ with milk________  K  Cereal___________________without milk_______ with milk________  A 3. Graph your nutrient on a separate sheet of paper.  p  a. You will need to make two bar graphs of your nutrient. One with milk and one without milk.  :  b. Choose a title that describes each graph.   J  c. Choose labels for the bottom and left side of each graph.   H  d. Pick a color to represent each of the cereals on your graph - these should be the same for all team members. At the upper right of each graph make a legend that lists the name of the cereals. Next to the name of the cereal, draw a 1-inch long mark of the color your team chose to represent that cereal.    e. Choose the units for the left side of the graph. Make vertical bars for each cereal type on your graph and complete your graph using an acculine and/or ruler.   4. After completing the Team Specs Sheet, write a lab summary that includes the answers to the questions listed under, Statement of the problem, likes/dislikes of the lab, what was learned, and suggested changes.  9 Applied Mathematics Team Name___________  I Unit 4 - Using Graphs, Charts, & Tables Member #1___________  < Team Specification Sheet Member #2___________  @ Start Date___________________ Member #3___________  ( Due Date____________________  1 Lab Title: COMPARING BREAKFAST CEREAL   Procedures:   1. Choose 3 different types of cereal, each team member will collect nutrient information on their individual specs sheet.   2. Team data:                                                                                          \ 3. Individually graph your nutrients and attach to your individual specs sheet.  J 4. On large sheets of paper, make two more bar graphs, one with and one without milk, that includes all of the nutrients and cereals on each graph. (hint - list each nutrient along the bottom of the graph with each cereal type having three vertical bars, one for each of the nutrients - thats nine vertical bars)    5. Using your team graph, answer the questions from the beginning of this activity (Statement of the problem section of the Team Information Sheet). Write your answers individually on your Individual Specs Sheet.  r 6. Prepare a team presentation on the above questions, using your team graph to support your answers.  2 Applied Mathematics Lab #______   UNIT #6   Teacher Information  % Lab Title: BALLOON CLIMB  / Goals and / or Career Applications:  5  Recognize standard vocabulary of slope.   8  Recognize how to make slope measurements.   ;  Gather accurate data and produce a line graph.  >  Able to express the problem in a readable sketch.  @  Able to average data and express on the line graph.   Materials needed:  +  balloons (large) 2 per group    string 60 '    paper clips 2    plastic straws 1    tape measures 1  #  calculator as needed  $  graph paper as needed  &  crayons / colored pencils  *  level (optional) 1 per class    large outside caliper ((optional) could spend a day and have the class make their own out of scrap 1/4" plywood, nut and bolt and three washers.)   2 Team Formation: Suggest groups of 3-4  . Suggested Timeline: 90 + 30 min.    Lab Preparation:  ,  You need a large room with about 50' of horizontal distance, hallways could be good. Also you need a higher ceiling and a method for students to gain elevation to hold the string up at the tall ends of the slope. A wood shop or a lunch room with benches or tables are good locations.   Helpful Hints:    Only one student blows up the balloon to reduce health risks and to insure that each breath into the balloon is going to be the same.   d  One student will have to hold the balloon while an other student takes the measurement.  D  Warn the students not to make sounds with the balloons.  E  Possible review of terms: Rise / Run , Pitch and Grade.    Extension Options:   P  You could do velocity calculations if you time the balloon flights.  I Submitted by: Chuck Boyd, Lake Roosevelt High, 1-509-633-1442  @ Applied Mathematics Name___________________#____  I Unit 6 - Working with Angles Team Name___________________  . Individual Specifications Sheet   * Start Date____________________  ) Due Date_____________________  & Lab Title: BALLOON CLIMB  - Goals and/or Career Applications:  [  Carpenter, Roofer, Ski Resort Workers, Military Artillery, Surveyors, Plumbers    Cartographers, Road Contractor, Civil Engineer, Cement Mason, Irrigation Specialist (Farmer), Aero-Space Engineering   Materials needed:    Balloons (large), String, paper clips, straw, tape measurers, calculator, graph paper, large outside caliper (self made ?), crayons/colored pencils  ! Statement of Problem:  g  In this lab students will measure the angle of a string and the slope distance an inflated balloon will travel up it. Students should divide up into groups of 3-4. Two will hold the string at a designated angle while the others measure the angle and inflate a balloon. The inflated balloon will be attached to the string with tape and straw   Procedure:  [  1. Gather horizontal distance and slope distance data on the following slopes.  J  a. Horizontal blaster (See how far the balloon can travel).  &  b. 2' RISE over 10' RUN    c. 4:12 PITCH    d. 15 % GRADE  D  e. Vertical lift off (How much thrust is generated?)  V  2. Illustrate, using line graphing, the data comparing the five results.  ]  3. Identify the five sets of data on the line graph using notes and line types.  @  4. Collect and line graph data for class average.     5. Write summary.  V  Pick an occupation from list above and describe why this lab might apply    to that career.   [  6. Student comments: Include at least a complete sentence for the following.  ,  a. What you liked / disliked.  9  b. What career you might consider and why.  ?  c. Suggestions to increase accuracy / efficiency  d Helpful Hints:   v  THE SAME PERSON ON EACH TEAM SHOULD INFLATE THE BALLOON WITH THE SAME AMOUNT OF BREATHS FOR EACH EVENT.  Y  The point of origin on the graph will be the same for all five sets of data.  N  Sketch large enough to write labels and measurements near object.  C  Use leaders/arrows for notes / labels / measurements.  T  Always double check for complete set of ACCURATE measurements and data.  Q  Keep all data neat / organized / simple so it makes sense to anyone.  D SUBMIT THIS SHEET WITH YOU DATA AND SKETCHES FOR GRADING  ? Unit 8 - Working with Shapes in Three Dimensions   & Teacher Information Sheet   * Lab Title: THE CUBIT COMPANY  9 Goals and Work Related Career Applications:   X  To provide students with experience in calculating surface area and volume.  ?  Career path applications: packaging and marketing  ) Materials needed per team:     36 - 3/4" blocks     ruler  '  writing and graphing paper  0  1 large piece of construction paper  q  1 pair scissors     masking tape    glue stick   Team Formation:   !  4 students per team.  T  Each team will have an arranger, recorder, draftsman, and copy writer.     All work must be checked and revised as necessary by at least two team members using the principles of Continuous Quality Improvement (CQI).  5 Suggested Timeline: 100 - 150 minutes  F Lab Preparation: Room arranged to provide team workspace.   Helpful Hints:   5  Review surface area and volume formulas;  '  review percentage (Unit B)   Optional Activities:  D  Real World Math, Design Projects, Sugar Cube Packaging.  R Submitted by Tim Phelan, Ingraham High School, Seattle, (206) 281-6080   ? Unit 8 - Working with Shapes in Three Dimensions   # Team Information Sheet   ,  Lab Title: THE CUBIT COMPANY  9 Goals and Work Related Career Applications:   X  To provide students with experience in calculating surface area and volume.  @  Career Path applications: packaging and marketing.  ) Materials needed per team:     36 - 3/4" blocks     ruler  '  writing and graphing paper  0  1 large piece of construction paper    1 pair scissors    masking tape    glue stick  O Statement of problem: The Cubit Company is currently marketing packages of 36 - 3/4" cubes in a 6 x 6 array. The Cubit Company president, Ms. Cube, has requested her marketing teams to investigate alternative packaging arrangements and prepare a proposal to reduce the packaging costs required for marketing their product.   Procedure:       C  1) Arrange the 36 blocks in 6 different arrangements.  v  2) Draw a 3-dimensional design for each arrangement with the measurement of all sides clearly labeled.  U  3) Write a letter to the company president that includes the following:  2  a) tell the purpose of your letter;  +  b) describe your box design;    c) give the data showing that your box will hold the same number of cubes as the present box but will use less cardboard ( compare your box to the box currently used);  =  d) tell the percent of cardboard you will save  n  e) give a minimum of 2 reasons why your design would be more appealing to customers.  *  4) Include a two-dimensions drawing to show how the box can be cut out of cardboard with the measurement of all sides labeled (use a straight edge to do the drawing, drawings do not have to be to scale, but must be clearly labeled).  f  5) Include a sample box made out of construction paper and containing all 36 cubes.   Grading will be done on accuracy or computations, accuracy and completeness of drawings and labeling, clarity of the written letter, and durability of the box.  ] Applied Mathematics Lab # ______  1 Unit 10 - Working with Scale Drawings  % Teacher Information Sheet      L Lab Title: PUT CARPET AND VINYL FLOORING IN DR. JOHN'S OFFICE  , Goals and/or Career Applications  .  Recognize geometrical figures  T  Calculate area of quadrilaterals (4 sided objects, e.i. rectangles)  g  Research and know how to buy carpet and vinyl flooring by lineal yards or square yards  1  Convert units in the same system  E  Measure lines (in fractions of inches) using a ruler   Materials needed  2  These materials are for the store:   [  Xerox legal paper in at least 3 different colors to represent carpet samples  a  5-10 strips are needed of same color, cut 2 sheets 1 1/2 " x 14 "   U  Note: you could get 5 strips using only piece of legal size paper  e  Sheet of gift wrapping paper in at least 4 patters to represent vinyl flooring samples  z  4-8 strips of same patterned wrapping paper: cut 3/4 " x length of paper   z  4-8 strips of same patterned wrapping paper: cut 1 " x length of paper   R  Graph paper representing the floor plan (blueprint) of John's office  /  Scissors, glue stick, scotch tape  I Team Formation. Groups/teams of 3 to 4 students.      ? Suggested Timeline: 100 minutes class period   Lab Preparation:    Design any floor plan on the 1/4 in graph paper, and let the students divide it in 3 different rooms. Two rooms need carpet, and one room vinyl flooring. Use the same floor plan for each student.    In real life, carpet comes in standard 12 foot widths. Vinyl flooring comes in standard 6 and 8 foot widths. The standard length of a roll is 100 ft. Paper materials cut should reflect measurements in the scale: 1/4 in = 2 ft.  Z  Teacher should be the clerk of the flooring company and control the sale of those materials. Post clearly the prices, and colors. To make it easy, every carpet should be the same price of $ 12.50 per square yd., and the prices of vinyl flooring should be, $7.05 per square yd. for the 6 ft. roll, and $8.75 for the 8 ft. roll.     Teacher should only sale to students who have completed table on team spec. worksheet. One student should be assigned to be the buyer for the group. He/she should be able to tell you how many lineal feet of material and color they want.    Helpful Hints:    Before doing the lab, review area of rectangles, conversion of units in the same system, and measuring with graph paper.   L  Practice with students according to the sample work below.     Teacher should check TOTAL AREA on table 1. The total area should be the same for every student, because the blueprint is the same.  % Mathematical conversions:  h  Find the area of a rectangle: length x width examples   q  Change scales. 1/4 in = 2 ft 1 in = 8 ft  v  Change units. 1 yd = 3 ft 18 ft = 6 yds.   p  Lineal yards = # of feet / 3 1 yd = 4 sq. yds 4 yd = 16 sq. yds.     Cost of carpet Cost/sq. yd. x total square yds.   I Submitted by: Ana Miller, Renton High School (206) 204-3600  M  Lab # ______   Applied Mathematics  1 Unit 10 - Working with Scale Drawings  " Team Information Sheet  L Lab Title: PUT CARPET AND VINYL FLOORING IN DR. JOHN'S OFFICE      * Goals and Career Applications:  t  Finished carpenters, carpet/vinyl flooring installers and clerks, house owners, commercial contractors.  4 Statement of the Problem and Procedures:    John needs to replace the carpet in two places of his office, and the vinyl flooring in another place as shown in the blueprint (floor plan). Presently, his floors are covered with the same old orange carpet.  + John has collected information about prices of different sizes of vinyl flooring and carpet, all in different colors and designs. You, as his decorator, are going to help John to select the colors of carpet and the vinyl flooring, and then find the total costs of the materials chosen.    After you have the information, you need to buy the flooring and then do the simulation by pasting it on your floor plan.   Materials Needed:   e  Do not get the materials until you have completed individual work Cost/sq. yd  m  Strips of plain color paper for carpet: 1 1/2 " x 14 " $ 12.50  l  Strips of patterned paper for the flooring: 3/4 " x 14 " $ 7.05    1 " x 14 " $ 8.75  K  1/4 " graph paper for floor plan (blueprint) of John's office  0  Scissors, glue stick, scotch tape   Applied Mathematics Lab # _____ Unit 10 - Working with Scale Drawing Team Name _________________  V Team Specification Sheet Member # 1 _________________  Q Start Date: _________________ Member # 2 _________________   Due Date : _________________ Member # 3 _________________   9  Member # 4 _________________  ^  Complete the following table using information on table 2 to buy your materials.  g  Number of lineal yards needed and cost  v  Region 1 Region 2 Region 3  a Team Member # 1 ___________ ___________ ___________  l  Cost ___________ ___________ ___________  a Team Member # 2 ___________ ___________ ___________  k  Cost ___________ ___________ ___________  Z Team Member # 3 ___________ ___________ ___________  l  Cost ___________ ___________ ___________  J Team Member # 4 ___________ ___________ ___________  E  Cost ___________ ___________ ___________   i  After you have pasted the carpet and vinyl flooring, write your observations, i.e., if you   . bought too little or too much etc.   Team Member 1 ________________________________________________________________________________________________________________________________________________________________________________________________________________________   Team Member 2 ________________________________________________________________________________________________________________________________________________________________________________________________________________________   Team Member 3 ________________________________________________________________________________________________________________________________________________________________________________________________________________________   Team Member 4 ________________________________________________________________________________________________________________________________________________________________________________________________________________________  .    }  Lab # _______   Z Team # _____ Team member (#) ______________  " Individual Specs Sheet  * Start Date____________________  ) Due Date____________________   Lab Procedures:  Q 1. Fill in the following table No. 1. Use your ruler and blueprint.  K  and calculate the area for each region and total area.   x  Region length width Area    1/4 in ft yd 1/4 in ft yd square yards  e  1 _____ _____ _____ _____ _____ _____ _________  e  2 _____ _____ _____ _____ _____ _____ _________  e  3 _____ _____ _____ _____ _____ _____ _________  v  TOTAL AREA ______________      b 2. Fill in the following table No. 2. Choose the color of carpet and vinyl flooring    room 1 room 2 room 3        Specify type of   m flooring __________ __________ __________  * Width of flooring   m  in yards __________ __________ __________   Area of flooring  k per lineal yd. __________ __________ __________      _ Area of rooms __________ __________ __________    Total amount  g of flooring needed __________ __________ __________  \ Cost of material/sq. yd __________ __________ __________  g Total Cost/room __________ __________ __________   Now that you know the total carpet and vinyl flooring you need, think the proper way of placing the carpet. Remember, you buy carpet or vinyl flooring from a roll. You need to think of the way to cut your flooring materials to completely cover your rooms. It is a good idea to buy a little more flooring to make sure you cover all your floors. Always try to cut your carpet with the least number of seams. Proceed to buy the materials you need. Remember that you need to buy enough to cover the ar ea completely. Glue flooring samples to the blueprint. Do not buy flooring until you are sure you have studied all the ways you could install the flooring.   , Applied Math Lab #_____  : Unit (#) - (Title of the Applied Math Unit)   & Teacher Information Sheet   / Lab Title: (DESCRIPTION OF LAB)  - Goals and Career Applications:    Materials needed:    Team Formation:   $ Suggested Timeline:    Lab Preparation:    Helpful hints:   # Optional Activities:   J  Submitted by: (Teacher Name), (School Name), (school phone)   , Applied Math Lab #_____  : Unit (#) - (Title of the Applied Math Unit)   # Team Information Sheet   / Lab Title: (DESCRIPTION OF LAB)  , Goals and Career Applications:    Materials needed:   2 Statement of problem and procedures:   4 Applied Math Team Name___________  Q Unit (#) - (Title of the Applied Math Unit) Member 1 ___________  @ Team Specification Sheet Member 2 ___________  = Start Date:__________ Member 3 ___________  < Due Date: __________ Member 4 ___________    Lab #_____  / Lab Title: (DESCRIPTION OF LAB)   Procedure:   4 Applied Math Team Name___________  Q Unit (#) - (Title of the Applied Math Unit) Member (#)___________  ; Individual Specification Sheet Lab #_____  ( Start Date:__________   & Due Date: __________   / Lab Title: (DESCRIPTION OF LAB)   Procedure:   4 Applied Math Team Name___________ *F$Hl Dh 4 Unit ____ Member (#)___________ *L$Hl Dh ? Generic Lab/Problem Solving Worksheet Lab #_____  ( Start Date:__________   & Due Date: __________    Lab Title:    Procedure:  J 1. Use the 4 step problem solving method checklist if needed.  - 2. Show all work in proper order    1. Understand    2. Develop    3. Carry Out    4. Check  % 3. Show all work/Be neat *F$Hl Dh