Bobsled Blunder by fjwuxn

VIEWS: 40 PAGES: 5

									                                           Problem of the Month - Metcalf
                                                  January 2006
                                               HELMET HEADACHE
                                                  Teacher Notes
More Accessible Version:
The U.S. Olympic Bobsled Team has a real helmet headache. The team’s helmets have gotten separated from the
sleds. Shauna Rohbeck and Valerie Fleming have volunteered to put the helmets back with each sled. There are
some two-person bobsleds and some three-person bobsleds and there are 25 helmets. Shauna and Valerie are
able to match all of the helmets to their sleds. Use the table below to help you decide how many 2 and 3 person
bobsleds there could be. Be sure to show all possible combinations and your math thinking. (table provided)
Basic Version:
The U.S. Olympic Bobsled Team has a real helmet headache. The team’s helmets have gotten separated from the
sleds. Shauna Rohbeck and Valerie Fleming have volunteered to put the helmets back with each sled. There are
some two-person bobsleds and some three-person bobsleds and there are 25 helmets. Shauna and Valerie are
able to match all of the helmets to their sleds. How many 2 and 3 person bobsleds could there be? Be sure to
show all possible combinations and your math thinking.
More Challenging Version:
The U.S. Olympic Bobsled Team has a real helmet headache. The team’s helmets have gotten separated from the
sleds. Shauna Rohbeck and Valerie Fleming have volunteered to put the helmets back with each sled. There are
some two-person bobsleds and some three-person bobsleds and one four-person sled. There are 25 helmets.
Shauna and Valerie are able to match all of the helmets to their sleds. How many 2 and 3 and 4 person bobsleds
could there be? Be sure to show all possible combinations and your math thinking.

POSSIBLE SOLUTIONS:
Basic and More Accessible Versions:
      Two Person Sleds             Three Person Sleds
             2                            7
             5                            5
             8                            3
             11                           1
Most students will solve this using a table/organized list. Some more advanced students may
use the algebraic rule 2x + 3y = 25, where x equals the number of 2 person sleds and y equals
the number of 3 person sleds, to solve or check their work.

More Challenging version:
# of 2   x2       # of 3   x3      # of 4   x4      Total
person   helmets person    helmets person   helmets helmets
sleds             sleds            sleds
       3       6         5      15        1       4       25
       6      12         3       9        1       4       25
       9      18         1       3        1       4       25

RUBRIC: (Use this is or any other rubric you would like)
Novice (1) There is no evidence of mathematical reasoning. The student is unable to work effectively toward a solution.

Apprentice (2) The student uses a strategy that is partially useful, but does not lead to a full solution. For example the students
may not have completed the solution which indicates that part of the problem was not understood. There is some evidence of
mathematical reasoning. There is an incomplete explanation and no use or mostly inappropriate use of mathematical language
and representation.

Practitioner (3) This student uses a strategy that leads to a correct solution and uses effective mathematical reasoning. The
practitioner will explain the approach and reasoning used and will use accurate mathematical language and representation.

Expert (4) The solution and comments show a deep understanding of the problem. The student uses a very efficient strategy
and may verify the results and/or evaluate the reasonableness of the solution. The expert may create a rule for solving the task
and/or will make other mathematically relevant comments, connections or extensions.

Created by G. Kilday - Exeter-West Greenwich School District, January 2006
Name ________________________________ Teacher ________________ Date ________
                         Problem of the Month - Metcalf
                                 January 2006

                                  HELMET HEADACHE
                                 More Accessible Version
The U.S. Olympic Bobsled Team has a real helmet headache. The team’s
helmets have gotten separated from the sleds. Shauna Rohbeck and Valerie
Fleming have volunteered to put the helmets back with each sled. There are
some two-person bobsleds and some three-person bobsleds and there are 25
helmets. Shauna and Valerie are able to match all of the helmets to their sleds.
Use the table below to help you decide how many 2 and 3 person bobsleds there
could be. Be sure to show all possible combinations and your math thinking.

# of 2 person      # of helmets for 2- # of 3 person      # of helmets for 3- Total helmets
sleds              person sled         sleds              person sled
        1                  2                   8                  24          26 – doesn’t work




Possible combinations are:




Created by G. Kilday - Exeter-West Greenwich School District, January 2006
Name ________________________________ Teacher ________________ Date ________
                         Problem of the Month - Metcalf
                                 January 2006

                                   HELMET HEADACHE
                                      Basic Version
The U.S. Olympic Bobsled Team has a real helmet headache. The
team’s helmets have gotten separated from the sleds. Shauna
Rohbeck and Valerie Fleming have volunteered to put the helmets back
with each sled. There are some two-person bobsleds and some three-
person bobsleds and there are 25 helmets. Shauna and Valerie are
able to match all of the helmets to their sleds. How many 2 and 3
person bobsleds could there be? Be sure to show all possible
combinations and your math thinking.




Created by G. Kilday - Exeter-West Greenwich School District, January 2006
Name ________________________________ Teacher ________________ Date ________
                         Problem of the Month - Metcalf
                                 January 2006

                                  HELMET HEADACHE
                                More Challenging Version
The U.S. Olympic Bobsled Team has a real helmet headache. The
team’s helmets have gotten separated from the sleds. Shauna
Rohbeck and Valerie Fleming have volunteered to put the helmets back
with each sled. There are some two-person bobsleds and some three-
person bobsleds and one four-person sled. There are 25 helmets.
Shauna and Valerie are able to match all of the helmets to their sleds.
How many 2 and 3 and 4 person bobsleds could there be? Be sure to
show all possible combinations and your math thinking.




Created by G. Kilday - Exeter-West Greenwich School District, January 2006
                 MAKE AN ORGANIZED LIST - Teacher Notes
                 Use an organized list to organize your work and be sure you find all possible options

WHY MAKE AN ORGANIZED LIST?
• The list helps to organize the solver’s thinking.
• The list organizes data making it easy to
• review what has been done and
• identify important steps still to be completed.
• The list provides a systematic record of computations or combinations of given items.

HOW DO YOU MAKE AN ORGANIZED LIST?
1. Decide what choices/categories you have.
2. Make a label for each category.
3. Choose a logical place to start so that you don’t skip any combinations or computations.
4. Fill in one possible combination or computation.
5. MAKE ONLY ONE CHANGE AT A TIME as you add more combinations or computations.
6. Check to make sure you have all possible combinations.

SAMPLE ORGANIZED LISTS:
Izzy’s Ice Cream Shoppe offers vanilla or chocolate ice cream and fudge or strawberry topping. You can have a
cherry on top if you want. How many different one scoop sundaes can Izzy’s make?
  ICE CREAM             TOPPING           CHERRY
Vanilla             Fudge                Yes
Vanilla             Fudge                No
Vanilla             Strawberry           Yes
Vanilla             Strawberry           No
Chocolate           Fudge                Yes
Chocolate           Fudge                No
Chocolate           Strawberry           Yes
Chocolate           Strawberry           No
How many different coin combinations can you use to make 27 cents?
  QUARTERS             DIMES             NICKELS           PENNIES                TOTAL COINS
        1                  0                   0                2                         3

        0                  2                   1                2                         5

        0                  2                   0                7                         9

        0                  1                   3                2                         6

        0                  1                   2                7                         10

        0                  1                   1               12                         14

        0                  1                   0               17                         18

        0                  0                   5                2                         7

        0                  0                   4                7                         11

        0                  0                   3               12                         15
        0                  0                   2               17                         19

        0                  0                   1               22                         23

        0                  0                   0               27                         27
More ???: I made 27 cents using 14 coins. What coins did I use? How can I make 27 cents using the fewest number of coins?
Created by G. Kilday - Exeter-West Greenwich School District, January 2006

								
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