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Modeling the breakdown of an expression

 Activity Directives:
 
 
Modeling an expression by using a specific symbol to represent the form of the variable
Activity Directions:
1.       Give each group three expressions that accommodates their ability for the given task
a.       Each group will have a worksheet that they will need to fill out for their models
                                                               i.      Worksheet
1.       3 different expressions they will need to model
2.       Symbol description for each of the given forms of the variable s
a.       Each item or symbol represents one item, when added gives the coefficient of the variable form.
3.       Space for the work used to complete problem
a.       What was combined
4.       What was the simplified answer to the expression
5.       There will be three problems (the three different expressions) where each step needs to be completed
                                                             ii.      Rubric / Checklist
1.       15 points
a.       Model each expression with symbols that represent the variable form
b.      Combine like terms or similar symbols
c.       Steps used in order to combine the term
d.      Modeled form of simplified expression
2.       5 points
a.       Class participation
b.      On task
3.       10 points
a.       Cooperative activity
b.      Modeling and showing each group how they simplified the expression
4.       10 points
a.       Modeled Form
b.      Written form
 
2.       Give each group the manipulatives they will need in order to create the models of their expression

 
3.       Pass out note cards that have plus (positive) and minus (negative) signs for the students to use to separate the terms in the given expression they are modeling.   Constants will be written on notecards that will represent the constants in the expressions. Numbered notecards represent the absolute value. The operations will determine the value. Sheets of paper will represent one constant and will be used for simple adding and subtracting of each constant value. (Constants) will be part of the manipulatives that will be provided for them.

 
4.       Room set up to accommodate groups and the activity

 
5.       Objectives that students should be able to identify
a.       The absolute value of a number
                                                               i.      The distance from 0
                                                             ii.      Combination of the inverse operation of same absolute value will cancel the numbers
                                                            iii.      Recognition of Like Terms
                                                           iv.      Understanding of a Coefficient
                                                             v.      Substituting something else for a given value does not change the value
 

Summary:
Conceptual Model of Defining the breakdown / simplification of an expression in order to solve an equation:
{Expression, coefficient, equivalency, similarities, variables, Operations, and constant}
 
Combination of like terms homework
-Representing each like term with a symbol
-Differentiating each term from like terms
~ Each exponential form of the variable can be represented as a symbol (using substitution) in order to show the definition of coefficients, because each represented symbol for the exponential form of the variable, or multiple variables stringed together represent an item for each coefficient of the variable. The distribution of the coefficient on the (symbol of the exponential form of the variable or multiplied variables) will be represented as the value to determine the coefficient or number of symbols that are to be represented
*Removal of the coefficient of the given term will allow for the representation of how many items are represented
                -Each (item, symbol, or variable), is equivalent to, in some cases-(single or multiple variable s multiplied by each other), OR in others (an expression represented by the exponential form of the variable s) - (in other words, the coefficient is not included)
-Ordering the expression with terms that have similar exponential form of the variable from highest to lowest / putting each symbol that are similar to each other, next to each other, in order to represent similar shapes need to be combined and simplified to one term in the given expression
 
For the Activity:
~ For the given (number, value, or quantity) of specific (items, or symbols) represented, will be determined by the expressional representation of the (quantity or value) of the given coefficient

~ Coefficient = how many items created by the like terms combined
                Example: 5J = J+J+J+J+J
                                With the Coefficient being (5) the quantity or amount of smiley faces
~(Variable, item, or symbol) represents a specific shape (that is equivalent to only one of them) Demonstrating why there is always a one in front of every variable written or not…
~ Constants will be represented by a written number in the space for each given expression
~Assessment will be done by having each representational manipulative model of the given expression being checked by teacher and cooperative learning
Cooperative learning will include: (5 groups, to find analogies, and comparisons of other groups) – Each group will have specific equations that are different from other groups, to eventually create a Round Robin Brain storming activity, that allows for examination of other groups and there modeled expressions of terms to create a {(GTH) of decision making, experimental inquiry, problem solving, invention, and Systems Analysis} – Using (what if…?) questions
 
Vocabulary Included in lesson
{ Equation, Expression, term, like term, symbol , variable, Equivalent, Exponential form s of a variable, distributed, substituted, coefficient, constant, quantity, similar, Combination or simply combine, Operations,
 
 
The breakdown of a term within an expression
                Representation of one expression to represent another expression, setting, the two equivalently written expressions, written in different forms to express each other using different symbols / using algebraic substitution for one expressional defined variable to represent another expressional defined variable to create a substitution way of representing a variable. The simplicity of one expression to represent another expression. Factoral and Multiplicative reasoning can explain differently written expressions set equivalent to each other.
 
 
 
 
 

 
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Conneaut Schools
400 Mill Street, Suite B
Conneaut, OH 44030

Phone: 440.593.7200

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