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# Using Combinations to Solve a Puzzle

### Collection Developed by:

Collection Credits

### Collection Funded by:

Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.

## Resources for this Lesson:

Connections

Everyday Math (2004)
Teacher Lesson Guide, pp. 105, 462, 920
Teacher Reference Manual, pp. 145-148
Student Reference Book, pp. 69

Standards

to:

Not yet reviewed.

### Overview

In this Cyberchase activity, students watch video segments in which two puzzles are presented. Each puzzle requires students to consider nine combinations and eliminate possibilities by using clues in order to find the correct solution. Each time, the students are shown a video and given an opportunity to solve the problem before they watch the CyberSquad generate the solution. The mathematics explored shows how two dimensions, with three variables each, produces nine combinations. The assessments test whether students can predict the number of combinations needed to solve similar problems.

2-5

1 hour

### Media Resources

Transporting to Ms. Fileshare QuickTime Video
Fixing the Teleporter–Part 1 QuickTime Video
Fixing the Teleporter–Part 2 QuickTime Video

### Part I: Learning Activity

1. Students work in pairs for this activity.

2. Distribute the Lunch Choices handout.

3. Ask students to complete the handout and then review their answers. The students will watch a video segment in which the Cybersquad chooses an array as their preferred method of representation. Support all correct solutions, but focus on the array to prepare students for the Cyberchase video.

4. Read the following to the students: "Ms. Fileshare, the librarian, is trapped by Hacker on the 20th floor in a room that is now filling with water. The CyberSquad must quickly determine how to get to the room. They must choose among three choices of transportation: the mail tube, the cybrary cart, or the teleporter pad. You will first watch a video clip and try to figure out which method of transportation is best. Then, you will see how the Cyberchase Kids solve the problem."

5. Play the Transporting to Ms. Fileshare QuickTime Video . Pause the segment after approximately two and a half minutes, when Jackie says, "I don't know about you, but I need to see what I'm thinking."

6. Distribute the Find Ms. Fileshare handout .

7. Ask students to try to solve the puzzle in the Find Ms. Fileshare handout.

8. Play the remaining part of the "Transporting to Ms. Fileshare" video segment to see how the Cybersquad solves the same puzzle. The video starts when Inez states, "We know that each vehicle can only go to one room on the 20th floor."

9. Compare the methods students used to solve the problem with those used by the Cybersquad.

10. Read the following to your students, "Now the Cyberchase Kids and Ms. Fileshare are stuck in the science room while Hacker is off causing trouble. And to make matters worse, the teleporter is broken. To fix it, the CyberSquad must again solve a problem. This time there are three choices of color (red, yellow and blue) and three objects (chair, lamp and projector). They must find the correct combination to make the teleporter work. You will watch another video clip in which the CyberSquad tries to solve the puzzle. To solve this second puzzle, see if you can use the same method used for the other problems."

11. Distribute the Fixing the Teleporter handout .

12. Play the  Fixing the Teleporter–Part 1 QuickTime Video .

13. Have students try to solve the puzzle on the Fixing the Teleporter handout. Ask students to share their results with one other pair of students.

14. Play the Fixing the Teleporter–Part 2 QuickTime Video  to find out how the Cybersquad figures out how to fix the teleporter.

15. Compare the methods students used to solve the problem with the strategy used by the Cybersquad in the video segment.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to work out the number of combinations for two dimensions, one of which has 3 choices, the other having 4 choices.

Assessment: Level B (above proficiency): Students must figure out where a student went on vacation by identifying the location and mode of transportation used, given three choices of each.