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

Title:

Factorials: Let's have a Dinner Party!

Overview/Annotation:

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):
Mathematics
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").


Mathematics
MA2019 (2019)
Grade: 6
15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

b. Write expressions to represent verbal statements and real-world scenarios.

c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given contextual or mathematical problems both when known models exist (for example formulas) or algebraic models are unknown,
  • Interpret the parts of the model in the original context.
  • Create the algebraic model of the situation when appropriate.
  • Use appropriate mathematical terminology to communicate the meaning of the expression.
  • Evaluate the expressions for values of the variable including finding values following conventions of parentheses and order of operations.
Teacher Vocabulary:
  • Expressions
  • Term
  • Coefficient
  • Sum
  • Product
  • Factor
  • Quotient
  • Variable
  • Constant
  • Difference
  • Evaluate
  • Order of Operations
  • Exponent
  • Absolute Value
Knowledge:
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.
Skills:
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.
Understanding:
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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.15.1: Define algebraic expression and variable.
M.6.15.2: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.3: Translate verbal and numerical expression using all operations.
M.6.15.4: Define coefficient, constant and term.
M.6.15.5: Match mathematical terms with correct mathematical symbols.
M.6.15.6: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.7: Calculate an expression in the correct order. with or without a calculator (Ex. exponents, mult./div. from left to right, and add/sub. from left to right).
M.6.15.8: Choose the correct value to replace each variable in the algebraic expression (Substitution).
M.6.15.9: Calculate a numerical expression, with or without a calculator (Ex. V=4x4x4).
M.6.15.10: Recognize the correct order to solve expressions with more than one operation.

Prior Knowledge Skills:
  • Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Recognize key terms to solve word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Define simple expression.
  • Recall simple equations.
  • Recognize properties of addition and multiplication.
  • Recall addition, subtraction, multiplication, division symbols.
  • Define parentheses, braces, and brackets.
  • Define numerical expression.
  • Recognize expressions.
  • Apply properties of operations as strategies to add and subtract.
  • Recall properties of operations as strategies to add and subtract.
  • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
  • Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
  • Recognize key terms to solve word problems.
  • Apply properties of operations as strategies to multiply and divide.
  • Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
  • Recall the formula for area (L × W).
  • Recognize that unit squares are equal.
  • Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
  • Recall basic addition and multiplication facts.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.15 Evaluate algebraic expressions when given specific values for the variables (e.g. x + 2, where x = 4).


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.  

paper

pencil

large chart paper

Colored cards for sorting students into groups

 

Technology Resources Needed:

Projector

Computer

 

Background/Preparation:

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

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

  Procedures/Activities: 

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.

 



Attachments:
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  Assessment  

Assessment Strategies


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

Acceleration:

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?

Intervention:

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 keepvid.com 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.