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Clowning Around

  • Lesson
Number and Operations
Location: Unknown

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.

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.

pdficonClowns Activity Sheet 

Review the problem by reading it to the students.

Each clown needs a mouth. Draw either a smile or frown 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 


Red Hat, Smile

Green Hat, Smile

Yellow Hat, Smile

Blue Hat, Smile


Red Hat, Frown

Green Hat, Frown

Yellow Hat, Frown

Blue Hat, Frown


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



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

[There would be twelve clowns colored.]


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.

NCTM Standards and Expectations

  • Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.3
    Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.4
    For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

-Kindergarten, Number & Operations

  • CCSS.Math.Content.K.NBT.A.1
    Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP7
    Look for and make use of structure.