Illuminations: Clowning Around

Clowning Around

In this lesson, students are encouraged to discover all of the combinations for a given situation. Students apply problem-solving skills (including elimination and collection of organized data) to draw their conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal.

Learning Objectives
 
Students will:
  • determine the number of clown faces that can be made with two mouth possibilities and four colored-hat possibilities
  • generalize the number of combinations that can be made from a given number of possibilities

Materials
 

Instructional Plan

Distribute the Clowns activity sheet to each student. Students will be using the activity sheet to determine possible combinations by coloring. Each student needs a red, green, yellow, and blue crayon.

Clowns Activity Sheet Clowns Activity Sheet

Review the problem by reading it to the students.

Each clown needs a mouth. Draw either a smile or forwn for each one. Each clown needs a colored hat: red, green, yellow, or blue. How many different clowns can we create? (No two should be the same.)

Guide students to predict how many different clowns can be created. Students should record their predictions on the activity sheet.

Next, allow enough time for students to color and to count the total number of combinations.

Students should count a total of eight different clowns. The combinations are:

Smile, Red hat
Frown, Red hat
Smile, Green hat
Frown, Green hat
Smile, Yellow hat
Frown, Yellow hat
Smile, Blue hat
Frown, Blue hat

Students should compare their predictions to the actual total number of combinations. Ask students who predicted the correct number of combinations to share with the class how they chose their predictions.

In addition to the organized list, as shown previously, students may make a table to solve this problem.

For example:

 

Red Hat

Green Hat

Yellow Hat

Blue Hat

Smile

Red Hat, Smile

Green Hat, Smile

Yellow Hat, Smile

Blue Hat, Smile

Frown

Red Hat, Frown

Green Hat, Frown

Yellow Hat, Frown

Blue Hat, Frown

Extensions
 

What if six colors could be used for the hats? (Add orange and brown.)

(Solution: There would be twelve clowns colored.)

NCTM Standards and Expectations
 
Number & Operations Pre-K-2
  1. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

References
 
  • Marcy Cook. "IDEAS: Combinations." The Arithmetic Teacher. 36, 1 (September 1988) 31-36.
  
1 period   

NCTM Resources

Navigating through Number in preK‑2

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