This is an interactive mediarich lesson in which students examine
the methods of showing all possible ways that two or more sets of
objects can be combined. Prior to beginning the lesson, students
will be asked to bring in a funky tshirt and a crazy pair of sunglasses.
When the introductory activity begins, groups of students are asked
to select three of the funniest tshirts and two of the craziest
sunglasses brought in by their group members. Groups will then be
asked to make as many combinations of funny tshirts and sunglasses
as possible. They will discover that to eliminate duplicate combinations,
they must write them down. Students will also discover that six
combinations are possible with three tshirts and two sunglasses.
If the numbers of each item are multiplied, the total number of
combinations can be predicted before combining. The activity continues
with the teacher giving each group two more funny accessories, whether
they are boas or fake jewelry. Groups are then asked to predict
the number of combinations and then to list them. The class then
views clips from the Cyberchase episode "A Day at the Spa"
to see how the Cyberchase team overcomes problems using combinations.
The video also presents other possible ways to show total combinations:
tables and tree diagrams. The video activities end with an examination
of using combinations to make the lunch menu at a deli more interesting.
After the video, students will go on the Internet and play the interactive
online Cyberchase game "Disguise Combos." The game asks
them to predict the number of possible combinations of wigs and
glasses possible for each of the Cyberchase team members. The lesson
culminates in a fashion show. Groups pick three or four of their
funniest combinations and model them for all the other groups.
Students will be able to:
 Use lists, tables, and treediagrams to represent total combinations;
 Select the appropriate method for representing total combinations;
 Predict the number of combinations using multiplication.
National
Council of Teachers of Mathematics grades K12
http://www.nctm.org/standards/standards.htm
 Understand numbers, ways of representing numbers, relationships
among numbers, and number systems. (Number and Operations)
 Solve problems that arise in mathematics and in other contexts.
(Problem Solving)
 Communicate their mathematical thinking coherently and clearly
to peers, teachers, and others. (Communication)
 Recognize and apply mathematics in contexts outside of mathematics.
(Connections)
 Select, apply, and translate among mathematical representations
to solve problems. (Representation)
Video:
Cyberchase #111: A Day at the Spa
Web sites:
Disguise
Combos
http://pbskids.org/Cyberchase/games/combinations/combinations.html
A game on the PBS Kids Cyberchase site, this activity applies
student knowledge of the combinations by challenging them to create
as many disguises as possible for the Cyberchase team.
Per Group of Three or Four students:
 At least 3 different Tshirts, and 2 different pairs of sunglasses
(provided by students)
 2 different costume accessories of the same type (boas, costume
jewelry, scarves, hats, wigs, etc.) per group. Vary the categories
among the groups.
