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