ALEX Lesson Plan


Factorials: Let's have a Dinner Party!

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  This lesson provided by:  
Author:Lynda Wilder
System: Blount County
School: Hayden Middle School
The event this resource created for:CCRS
  General Lesson Information  
Lesson Plan ID: 33157


Factorials: Let's have a Dinner Party!


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.

 Associated Standards and Objectives 
Content Standard(s):
MA2015 (2016)
Grade: 6
13 ) Write, read, and evaluate expressions in which letters stand for numbers. [6-EE2]

a. Write expressions that record operations with numbers and with letters standing for numbers. [6-EE2a]

Example: Express the calculation, "Subtract y from 5," as 5 - y.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. [6-EE2b]

Example: Describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). [6-EE2c]

Example: Use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2.

NAEP Framework
NAEP Statement::
4A3a: Use letters and symbols to represent an unknown quantity in a simple mathematical expression.

NAEP Statement::
4A3b: Express simple mathematical relationships using number sentences.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.13- Describe a given mathematical or real-world problem with an expression including one unknown.
M.AAS.6.13a- Evaluate expressions at specific values of their variables (e.g., m + x = ?, where x = 3 and m = 2).
M.AAS.6.13b- Identify parts of an expression using mathematical terms (e.g., sum, product, difference, quotient).

MA2015 (2016)
Grade: 6
17 ) Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6]

NAEP Framework
NAEP Statement::
8A4a: Solve linear equations or inequalities (e.g., ax + b = c or ax + b = cx + d or ax + b > c).

NAEP Statement::
8A4b: Interpret "=" as an equivalence between two expressions and use this interpretation to solve problems.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.17- Match a phrase to the corresponding one- step one-variable expression (e.g., "a number plus 3" matches "x + 3").

Local/National Standards:

Mathematical Practice Standards:

3.  Construct viable arguments and critique the reasoning of others.

7.  Look for and make use of structure.

8.  Look for  and express regularity in repeated reasoning.


Primary Learning Objective(s):

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

Additional Learning Objective(s):

 Preparation Information 

Total Duration:

31 to 60 Minutes

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:





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

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


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.
  13. Handout the worksheet that goes with the book Anno's Mysterious Multiplying Jar
  14. Read aloud the book, Anno's Mysterious Multiplying Jar or use the video. (if your school system does not allow you to access youtube you may download the video using Keepvid.)
  15. As the book is being read, students will fill in the number pattern for each factorial.  Groups will share their answers.


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


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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 Multilying Jar Video - This book is a picture book about factorials.  This video is a youtube video. (If your school system blocks youtube, then you make go to and download the video.  This site provide free downloads.)

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.