Begin the class by introducing the term combinations. Ask students
to explain what a combination is. Guide students to a mathematical
definition of combinations. Next, ask students to brainstorm different
types of combinations. Students may suggest some of the following:
- ice cream cones
- menu combinations
- safe or padlock combinations
In today's lesson, students will explore combinations involving shirt and short outfits. Distribute the Shorts and Shirts activity sheet to each student. Students will be coloring outfits to determine the total number of combinations possible.
Give each student eight crayons in the following colors: red, green, yellow, blue, orange, brown, black, and purple.
Review the problem by reading it with the students:
Each shirt must be a solid color, either yellow,
orange, blue or red. Each pair of shorts must be a solid color, either
brown, black, green, or purple. How many different outfits can be made?
No two outfits should be the same.
Guide students to predict how many different outfits can be colored.
They should record their predictions on the activity sheet. (Note:
Some students may predict 8 outfits by adding 4 shorts and 4 shirts.
Other students may predict 16 outfits by multiplying 4 shorts and 4
Allow enough time for students to color their combinations on
the activity sheet. Place students in pairs to compare their results.
As a class, discuss the results. Students should have the following 16 correct combinations:
Yellow shirt, Brown shorts
Yellow shirt, Black shorts
Yellow shirt, Green shorts
Yellow shirt, Purple shorts
Orange shirt, Brown shorts
Orange shirt, Black shorts
Orange shirt, Green shorts
Orange shirt, Purple shorts
Blue shirt, Brown shorts
Blue shirt, Black shorts
Blue shirt, Green shorts
Blue shirt, Purple shorts
Red shirt, Brown shorts
Red shirt, Black shorts
Red shirt, Green shorts
Red shirt, Purple shorts
Ask students to compare their predictions to the correct total
number of combinations. Students who made the correct predictions could
share their reasoning with the class.
In addition to the organized list shown above, students may also make a table or a tree diagram to solve this problem.
Ask students to think about a general rule or pattern for
determining the total number of combinations. Students should see that
they could have multiplied the number of shirts possible (4) by the
total number of shorts possible (4) to get a correct total number of
16 combinations. As appropriate, tell students that this is an example
of the counting principle. You may wish to give additional examples of
the counting principle.
You may also ask students to use the
Bobbie Bear tool. Students can pick an outfit for Bobbie Bear and customize the outfit similar to the one on the activity sheet.
Questions for Students
1. How did your prediction compare to your actual answer? How do you explain this?
[Student responses will vary depending upon their predictions and how close they are to the actual answer. Students who made incorrect predictions should be able to now explain how to find the actual number.]
2. Which method would be more efficient for finding the total number of outfits: multiplying, drawing a tree diagram, or making a table?
[Students should respond by saying multiplying, because that will be the quickest way to determine a count.]
3. Which method would be more useful for identifying the different combinations (outfits) possible: multiplying, drawing a tree diagram, or making a table?
[Students should respond by saying either a tree diagram or making a table, because these two methods list the possibilities (whereas multiplying simply gives you a count).]
4. In your own words, what is the counting principle?