Factorials: Let's Have a Dinner Party!

Learning Resource Type

Lesson Plan

Subject Area





In collaborative groups of four, students will act out a dinner party where four dinner guests will attend. The students must act out the different ways to arrange four dinner guests. 

This is a College- and Career-Ready Standards showcase lesson plan.

Mathematics (2019) Grade(s): 6


Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.



  • Expressions
  • Term
  • Coefficient
  • Sum
  • Product
  • Factor
  • Quotient
  • Variable
  • Constant
  • Difference
  • Evaluate
  • Order of Operations
  • Exponent
  • Absolute Value


Students know:
  • Correct usage of mathematical symbolism to model the terms sum, term, product, factor, quotient, variable, difference, constant, and coefficient when they appear in verbally stated contexts.
  • Conventions for order of operations.
  • Convention of using juxtaposition (5A or xy) to indicate multiplication.


Students are able to:
  • Translate fluently between verbally stated situations and algebraic models of the situation.
  • Use operations (addition, subtraction, multiplication, division, and exponentiation) fluently with the conventions of parentheses and order of operations to evaluate expressions for specific values of variables in expressions.
  • Use terminology related to algebraic expressions such as sum, term, product, factor, quotient, or coefficient, to communicate the meanings of the expression and the parts of the expression.


Students understand that:
  • The structure of mathematics allows for terminology and techniques used with numerical expressions to be used in an analogous way with algebraic expressions, (the sum of 3 and 4 is written as 3 + 4, so the sum of 3 and y is written as 3 + y).
  • When language is ambiguous about the meaning of a mathematical expression grouping, symbols and order of operations conventions are used to communicate the meaning clearly.
  • Moving fluently among representations of mathematical situations (words, numbers, symbols, etc.), as needed for a given situation, allows a user of mathematics to make sense of the situation and choose appropriate and efficient paths to solutions.

Primary Learning Objectives

Students will use a real-life problem to calculate permutations and/or factorials.  


As students enter the classroom, the teacher will hand out a colored card to each student.  Students will be arranged in groups of four.  Prepare enough different colored cards to provide for the four groups.

Before (activate prior knowledge) - Essential Question:  

The teacher will ask: "Give examples of ways that you use multiplication in your life?" Groups will share one way they use multiplication in real life.  (3 - 5 minutes)

During: (Actively engage students) (35 minutes)

The teacher will say: "Today you will pretend to be at a dinner party. You have four guests at your dinner party. How may ways can you arrange the seating of the guests?"

  1. Handout the Dinner Party Guest Cards to each group.
  2. On a sheet of paper, the students should write down the letters A, B, C, D. 
  3. Students line up the cards in the order of A,B,C,D.
  4. As the students move the cards around in different arrangements, they will record the arrangement on their paper and the chart paper.
  5. Students should record the total number of arrangements they found (24).
  6. Groups will call out one arrangement and as the other groups find the same arrangements on their paper, they will put a check mark by the arrangements. (answer to dinner party)
  7. Students will discuss any patterns that they noticed as they were arranging the letters. Groups will share with the other groups any patterns they noticed.
  8. At this point, tell the students that the mathematical term for these type of arrangements are called factorials or permutations.  
  9. On the board, the teacher will write 4!. Ask the students if they recognize anything written on the board. (Misconception:  Based on their background experience, they will think that the ! is an exclamation symbol.) Tell the students that in math, this symbol is used for permutations or factorial. The teacher should read 4! as four factorial.
  10. On the board write, 4! = 4 X 3 X 2 X 1 = 24.  Ask them to describe the number pattern.  
  11. Four students should be selected to come to the front of the room (with a dinner guest card).  They are to sit in one of the chairs in the order of A,B,C,D.  The teacher will call out the different arrangements and the dinner guests will move to their new seat. Students will see the different arrangements.  
  12. Other groups of four dinner guests may come to the front of the room and act out the arrangements.

After: (Assess)  Use a Quick Write to quickly assess understanding of factorials.

Assessment Strategies

The Quick Write will be used to assess enduring understanding of factorials.


Enrichment Activity for Factorials:  Students will calculate the number of arrangements for the word, STEGALL.  Key Question:  Will the double L's make a difference in the answer?


Khan Academy Video  This video is on permutations.

Anno's Mysterious Multiplying Jar Video - This book is a picture book about factorials.  This video is a YouTube video. (If your school system blocks YouTube, then you may go to keepvid.com and download the video. This site provides free downloads.)

Total Duration

31 to 60 Minutes


Students should be fluent in multiplication facts and recognizing number patterns.

Teacher should prepare Dinner Guest Cards before the students arrive for class.

Materials and Resources

Set of Cards that have the following letters on them:  A, B, C, D.  (Cards)  One set for each collaborative group.  



large chart paper

Colored cards for sorting students into groups


Technology Resources Needed




Approved Date