Six of One, Half-Dozen of the Other

 

Introduction 

Length, weight, and capacity can be expressed in terms of various units.  Feeling comfortable with multiple units in mathematics allows you to quickly make comparisons and thoughtful decisions even when the given units vary. 

 

Task

Working together with your group, you will first convert given units of length, weight, and capacity to new units of your choice.  Then you will research additional common items to add to your tables.  Finally, your group will use your skills at conversion to solve a real-world problem.  

 

Instructions 

Complete each problem in order keeping careful notes along the way.  The answers to the problems will be used to create a final project.

 

1.      Working together with your group, your first problem is to place 6 well-known items into the appropriate table.  Begin by making three tables similar to the one below on your own paper.  You will need one for length, one for weight, and one for capacity.  Label each table as Length, Weight, or Capacity.

 

·         Hint:  Leave plenty of room in the third column to show your work and be sure to save the tables, as you will need them for your final project.

 

Item

Given unit

(Show work here to convert to new unit)

New Unit

 

 

 

 

 

 

 

 

 

 

 

 

 

Now take the six items below and fill them into the appropriate table.

 

·         Hint:  Is the first item given as length, weight, or capacity?  Write each item and the given unit into the appropriate table.  You should have 2 items in each table when you are finished.

 

 

2.      Now that you have each of the six items placed in the correct table, work with your group to convert the given unit to a new unit.  For instance, weight in tons could be converted to weight in pounds and height in feet could be converted to height in inches, etc.  Be sure to show all of your work within the table.  When finished, you should have two completed rows on each of your three tables.

 

3.      Now work with your group to choose 3 new common items to research, one weight, one length, and one capacity.  Research the size of each.  For example:  weight of a 4 door passenger car, capacity of an Olympic size swimming pool, length of a city block in the nearest city.   Your research may be done in customary or metric units.  Use the Internet to research.  A quick Google search should give you the necessary information.  Record the item and the given unit within the appropriate table.  Then, convert the length, weight, or capacity to a new unit.  Again, be sure to show all of your work within the table. 

 

·         Hint:  Before moving on to the next problem, check to be sure that you have three completed rows in each of your three tables.  It would also be helpful to double check your work and be sure that your conversions are correct.

 

Now that your group has practiced conversions, it is time to apply the knowledge to solving a real-world problem.  You are planning a camping trip with a friend, but need to make some decisions about what type of food to bring and which location to choose.  Work together to solve the problems.  Remember to save your work to include in your final project. 

 

4.      You are going on a camping trip and need to stock up on trail mix for the outing.  Your local warehouse store is selling a 5-pound bag of trail mix for $26.00.  The same trail mix is sold in the local grocery store in 10-ounce bags.  The smaller bags cost $3.79 each.  Which store has the better price on the trail mix?  How much money would you save by buying the trail mix at the cheaper store?

 

5.      Now that you have the food purchased, you need to pick a location.  You and your friend both like hot weather and would prefer to camp in the warmer location.  You have found that the average summer high in Baja, Mexico is 32 degrees Celsius.   Your friend would prefer Yosemite, where the average summer high is 88 degrees Fahrenheit.  She argues that 88°F has to be much warmer than 32°C. Who is correct?  How much warmer is the hotter destination?  Which location would you choose and why?

 

6.      When you check in at the ranger station, the park ranger offers you two campsites.  The campsites are remote and will require a hike to reach.  You would both prefer the closer campsite in order to save your strength for day hikes.  The first site is located  miles from the station.  The second is 1800 yards away.  Which campsite is closer?  How many yards closer is the nearest site?  If your stride is 2 steps per yard, how many steps would you save by choosing the closer site? 

 

Collaboration 

Compare your tables from problems 1 - 3 with a neighboring group.  The first two rows of each table should be similar.  Which new unit did the other group choose?  Is it the same unit or a different unit?  If it is the same, make sure that the units match.  If the units are different, work together to check each other’s work. 

 

Discuss the new items that were researched and added to the table.  Check the conversions to ensure that the math is done correctly and that work is shown clearly.

 

Finally, compare answers to problems 4 - 6.  Do both groups’ answers to all three problems match?  If not, carefully examine the work of each and determine which group is correct.  Make the appropriate corrections before beginning the final project. 

 

Conclusion 

You have two options for your final project.  You will need to include the answers to each of the six problems no matter which project you choose.  You will also need to include all of your mathematical calculations.  The math can either be neatly hand-written or typed.  Work together to create a project that represents your group’s individual interests and strengths.  You may choose between a written report or an oral presentation with handouts.

 

Written Report 

Work together with your group to create professional looking, finalized versions of the three tables from problems 1 - 3.  Then either neatly hand write or type the worked out mathematic solutions to problems 4 - 6.  Be sure to show all of your work clearly and answer each of the questions asked. 

 

Oral Presentation

Rather than creating a written document, your group may choose an oral presentation.  You will need to show your finalized tables from problems 1 - 3 by either creating a poster, using the blackboard, or creating a handout for your classmates.  You will also need to discuss the solutions to problems 4 - 6.  Consider the following:  Who will discuss each problem? What handouts will you need to prepare in order to help the audience follow along?

 

Grade 

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

 

Score

Content

Presentation

4

Your project appropriately answers each of the problems.  Your mathematical calculations are set up and carried out properly.

 

Your project gives clear mathematical reasoning behind each decision related to the camping problems.

Your project contains information presented in a logical and interesting sequence that is easy to follow.

 

Your written material is professional looking. 

 

3

Your project appropriately answers each of the problems.  Your mathematical calculations are for the most part set up and carried out properly.  Minor errors may be noted.

 

Your project gives mathematical reasoning behind each decision related to the camping problems. Minor errors may be noted.

Your project contains information presented in a logical sequence that is easy to follow.

 

Your written material is neatly presented.

 

2

Your project attempts to answer each of the problems. Some mathematical calculations are set up and carried out properly; however, major errors are noted on some calculations.

 

Your project gives little mathematical reasoning behind each decision related to the camping problems.  Major errors are noted.

Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

 

Your written material lacks a neat, orderly appearance.

1

Your project attempts to answer only some of the problems. Major errors are noted on most mathematical calculations.

 

Your project gives no mathematical reasoning behind each decision related to the camping problems.  Major errors are noted.

Your project is difficult to understand because there is no sequence of information.

 

Your written material is hard to follow due to an overall illegible appearance.

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