Lesson Title: Understanding and solving for variables in mathematic equations.
Lesson Length: 3 Class periods (about 4 hours)
Grade Level: 9th Grade
Math Course: IMP 1
Overview:
What is the purpose of the Lesson?
 The purpose of the lesson is to have students understand why math uses variables
when writing expressions and equations. The goal of the lesson is to give the students
the tools to manipulate variables and the ability to create their own problems using
variables.
 The students should learn how to use a balance to solve a mystery quantity (variable)
 Students should develop their own procedure for solving algebraic equations that
contain variables.
 To have students create their own algebraic equations that contain variables and to
have them understand the meaning of the equations that they develop.
What is it about?
 Expressions and equations that have variables allow us to create general equations
that vary instead of remaining constant. This allows us to avoid writing equations
and expressions for every specific case when there is an underline pattern between the
cases.
How does this lesson fit into an overall learning cycle?
 This lesson is the first step of learning why we use variables and how to solve for
variables when they are in an equation. This is one of the most key concepts in
algebra. This concept is the very basis for most scientific calculations and
fundamental rules. This will be their first real exposure to variables outside of the
substitution and evaluation topic which I will address right before this unit. They will
continue to use this concept through the rest of their high school math programs and
hopefully in their work environment also.
This lesson covers the math state standard
9.2.2
VARIABLES, EQUATIONS, AND INEQUALTIES: The student uses
variables, symbols, real numbers, and algebraic expressions to solve equations
and inequalities in a variety of situations.
9.2.2.1
Solves linear equations and inequalities in one variable with whole
number coefficients and constants with rational number solutions
analytically, graphically, and intuitively such as 2x+1=9 or
2x+13<8.
9.2.2.2
Uses symbols, variables, expressions, inequalities, equations and
simple systems of equations to represent problem situations that
involve variable quantities.
Student Outcomes:
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Students will be able to define, describe, and identify what a variable is by the end of
the lesson.
Students will be able to summarize why we use variables when writing equations and
expressions.
Students should be able to synthesize their own equations that illustrate using
symbolic notation (variables).
Definitions
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Variable-A letter or symbol that stands for one or more numbers
Equation- An algebraic or numerical sentence that shows two quantities are equal
Evaluate- In a numerical expression, perform the operations and write the expression
as one number. In an algebraic expression, replace the variable with a number and
perform the operation in the expression.
Substitute- Replace a variable with a given number
Expression- An algebraic sentence with no equal sign
Instructional Plan
Engage Phase
1. Class begins with a guided three step interview process. The students are placed
in groups and assigned roles based on their position in the group. Students are
asked to identify both their favorite nursery rhyme and their favorite piece of
playground equipment. This helps transition into a discussion about see-saws and
the nursery rhyme of Jack Sprat which leads into a discussion on the mechanicals
of balances. This leads into a conversion of the task for the day
2. Next we will be discussing variables and how to solve for variables. Provide a
brief background on variables and review the substitution and evaluation unit
previously covered.
Explore Phase
1. At the beginning of the class teacher will explain the balance, its purpose, and
how to conduct the worksheet. An explanation of the materials provided and the
expectations of the worksheet. Class period will consist of working on the
worksheet and explain how it is related to variables.
2.
Students will be grouped in their quad seating arrangement. Any members
missing from the group will be required to make up the lesson. Empty spaces will
be filled with students that do not have a full group of four.
3. The classroom activity will involve students trying to figure out the weight of
various balloons filled with sand. The balloons will be color coded to insure
consistence when doing the experiment. They will try to determine what the mass
of the balloons using a balance beam. The goal is to get balloons on one side of
the balance and on the other side weights. At that point students will have to
determine what the weight of an individual balloon would be. Students will be
given a worksheet that provides the instructions on how to conduct the
experiment. A copy of the worksheet will be provided with lesson plan format.
At the conclusion they will be required to develop a procedure for determining the
mass of one balloon. They will also be required to develop a problem on their
own and be able to present it to their small group. They must be able to explain
their procedure so the other students can understand their thought process.
Explain Phase
1. Have one representative from each group explain to the class how they solved
one of the problems on the worksheet. Have a discussion on what the
balloons represented, how we could write them mathematically. What is the
procedure for solving the equations? Have them work on the homework #7
and #8 in the IMP 2 book.
2. Key questions that students should be able to communicate at the conclusion
of the lesson plan include.
I. What are variables?
II. Why do we use variables?
III. How do we determine the symbol for the variables?
IV. What do the variables become when substitution is involved?
V. How to do solve for variables in an equation?
VI. What is the procedure for solving equations?
VII. Why are equations with variables useful?
VIII. Can the students create their own equations or expressions with
variables?
Elaborate Phase
1. Students will use this knowledge to work on the homework #6 (p.20-21) and #7
(p.22) in the IMP 2 book which is an extension by using word problems to
determine the weights of different mystery bags.
2. A follow-up activity would be using cups (labeled x), plates (labeled y), and
pennies (to represent real numbers). Students will attempt to figure out how many
pennies one cup equals. In other situations they will be asked to determine how
many pennies one plate equals. The value of the plates and cups will vary
depending on the problem. In other problems students will be given an equation
with both cups, plates, and pennies and they will be required to do a substitution
problem. Students will be given an assignment sheet to guide their practice. The
goal is to have them understand a procedure on how to solve equations with
variables.
Assessment Plan
Assessment will be conducted informally through teacher listening to the balloon
balancing activity. Assessment will also occur by looking at individual student papers for
the activity. Assessment will also occur through completion of homework #7 and #8.
Informal assessment will occur during the cup, plate, and penny class activity. Formal
assessment will occur by looking at the worksheets concerning the second activity.
Assessment will occur during unit test and through later mastery of new mathematical
concepts based on this lesson plan.
Safety plans
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Review general classroom safety precautions
Clearly articulate consequences for improper use of classroom activity materials.
References
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IMP 2 book, Key curriculum Press.
Math forum website for initial idea of the cups and the pennies.
http://mathforum.org/library/problems/sets/alg_onevariable.html