For use with Sadako and the Thousand Paper Cranes by Eleanor Coerr.

How to Fold a Paper Crane

PROGRAM : Least Common Mulitple

Some friends wanted to make paper cranes for Peace Day. If Mary could make one crane every 2 days, Kim could make one crane every 3 days, and Leo could make one crane every 5 days, how many days would it take for them to complete 1000 cranes?

1. Set up a table to display the data.
   1. Press Y = key and clear each Y = by pressing the CLEAR key on Y1 = , Y2 = , etc. To move from one Y = to the next, use your down or up arrow keys.

      First enter rules to display the number of cranes made by each child.

   2. Type into Y1 = X/2
   3. Type into Y2 = X/3
   4. Type into Y3 = X/5

      Now, you need to build a rule for finding the total number of cranes made by all of the children.

   5. Arrow onto Y4
   6. Press VARS
   7. Arrow to Y-VARS
   8. Choose 1: Function
   9. Choose 1: Y1
   10. Press +
   11. Press VARS
   12. Arrow to Y-VARS
   13. Choose 1: Function
   14. Choose 2: Y2
   15. Press +
   16. Press VARS
   17. Arrow to Y-VARS
   18. Choose 1: Function
   19. Choose 3: Y3
   20. You should see Y4 = Y1 + Y2 + Y3
   21. Press 2nd TblSet
   22. Set TblMin and /\ Tbl at 1

2. Modify your table.

   Look at your table, especially the tables in the Y4 column. Since you are interested in the number of completed cranes, why are some of the values displayed in Y4 incorrect?

   The calculator has a feature which allows you to display the values you need in Y4. The iPart function returns only the integer part of a value (in our case the whole number part of the value). CLEAR the rule you had in Y4 and enter the following Y4 = iPart Y1 + iPart Y2 + iPart Y3 .

   1. Arrow into Y4 and CLEAR the rule.
   2. Press MATH
   3. Arrow right to NUM
   4. Choose 3: iPart(
   5. Press VARS
   6. Arrow to Y-VARS
   7. Choose 1: Function
   8. Choose 1: Y1
   9. Press )+
   10. Press MATH
   11. Arrow right to NUM
   12. Choose 3: iPart(
   13. Press VARS
   14. Arrow to Y-VARS
   15. Choose 1: Function
   16. Choose 2: Y2
   17. Press )+
   18. Press MATH
   19. Arrow right to NUM
   20. Choose 3: iPart(
   21. Press VARS
   22. Arrow to Y-VARS
   23. Choose 1: Function
   24. Choose 3: Y3
   25. Press )
   26. You should see Y4 = iPart(Y1) + iPart(Y2) + iPart(Y3)

3. Use your table to answer the following questions.
   1. How long would it take Mary working alone to make 1000 cranes?
   2. How long would it take Kim working alone to make 1000 cranes?
   3. How long would it take Leo working alone to make 1000 cranes?
   4. How often do Mary and Kim finish a crane on the same day?
   5. How often do Mary and Leo finish a crane on the same day?
   6. How often do Kim and Leo finish a crane on the same day?
   7. When is the first time all three kids finish a crane on the same day?
   8. How long will it take the group to make a total of 1000 paper cranes?

   Extension:
   1. Aman decides to join the group. If he can make one crane every 3 days, how many days would the project now take?
   2. Design a problem similar to this one so that a group of no more than five friends will complete exactly 1000 paper cranes in 180 days.

Copyright 1997 by Ann Lawrence & Karen Wyatt
Mountain Brook Junior High School
Mountain Brook, AL
wyattk@mtnbrook.k12.al.edu
http://www.ti.com/calc/docs/act/lawrence01.htm