Sonia D. Farassati
Introduction
Standards
Objectives
Activities
Assessment
Results
Resources
You can insert a large image here (200-600 pixels wide).

If A equals success, then the formula is

A=X+Y+Z

X is Work, Y is Play, and Z is keep your mouth shut.

Albert Einstien
 Introduction
As a teacher, everyday I deal with students in 9th, 10th, 11th, and even 12th grade who do not master enough the mathematical symbols in order to be able to translate verbal expressions in mathematical expressions.  I believe this is one of the major problems that makes the word problems such a taboo for them.  That's why I spend the first few sessions of my Algebra 1 class, introducing or reintroducing these concepts to them, by trying to find as many definitions as possible for each one of these symbols.  After all Algebra is often defined as the branch of mathematics in which letters are used to represent numbers and signs are used to represent operations, where the rules are basically the same as the rules for arithmetic.

Subject:  Algebra 1A
Topic: Introduction to Algebra
Grade Level:  9th
Student Lesson name and URL:  Variables and expressions
 

Standards Addressed
Students use mathematical symbols (+, -, =, >, <), concepts and terms to communicate mathematical reasoning orally, in writing, and graphically.
 

Instructional Objectives
Students will learn to translate verbal expressions into mathematical expressions and vice versa. 
  Student Activities

Introductory Activity

  • 1)  Students are provided with all mathematical symbols (+, -, ×, ÷, =, >, <) and they will try to describe each one of these symbols with as many expressions as they can.
  • 2)  Then they wil be placed in 7 groups, in order to put thier expressions together.
  • 3)  The next step will be that one student from each group wil come to the board and share the expressions that they found to describe each symbol.
  • 4)  The last step will be that, they will be provided with about 20 different word problems that they need to translate them into algebraic expressions.
This activity will allow them to understand and memorize different ways of describing each symbol, and helps them to feel more comfortable with word problems that they need to solve all through this Algebra 1 class. Enabling Activity(ies)

In this regard students will be given some instructions similar to following:

The letters m and s are called variables, and m × s is an algebraic expressions.  In algebra, variables are symbols that are used to represent unspecified numbers.  Any letter may be used as a variable.

An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations.  Here are some examples of algebraic expression

X - 2               t × 2s                7mn ÷ 3k

In algebraic expressions, a raised dot or parentheses are often used to indicate multiplication.  The symbol " × " is often avoided because it may be confused with the variabe " X ".  Here are ways to represent the product of X and Y:

XY        X·Y           X ( Y )        ( X )( Y )        ( X ) Y        X × Y

An expression like x² is called a power.  The variable x is called the base, and 2 is called the exponent.  The exponent indicates the number of times the base is used as a factor.  For example

x²  means x·x         and         12³ means  12×12×12

  Culminating Activity
 
Verbal Expressions
 Algebraic Expression
7 less than the product of 3 and a number x
3x - 7
the procuct of  7 and s divided by the product of 
8 and y
7s ÷ 8y
four years younger than Sarah (s = Sarah's age)
s - 4
three times a number x subtracted from 24
3x-24
5 to the third power or 5 cubed
5³  or  5×5×5

Write an algebraic expression for each verbal expression.
1.  the product of the fourth power of a and the second power of b.
2.  six less than three times the square of y.

Write a verbal expression for each algebraic expression.
3.  7³
4.  3x² + 4

Write each expression as an expression with exponents.
5.  4 · 4 · 4
6.  a · a · a · a · a

Assessment
 A test with 20 to  25 questions, 5 to 4 points each.
  Results
After implementing your lesson (sometime between January & March), insert a chart of your pre-test, post-test, and culminating assessment data. Web Resources & Supplementary Materials

Introductory Activity
List and link the web resources for this activity here. Also link supplementary materials such as PDF files and /or document files.

Enabling Activity
List and link the web resources for your learning activity(ies) here. Also link supplementary materials such as PDF files and /or document files.

Culminating Activity
List and link the web resources for your culminating activity here. Also link supplementary materials such as PDF files and /or document files.


 
 
 
 
 
 
 
 
 
 
 
 
 
 

Reseda High School, Los Angeles Unified School District C
http://reseda-hs9.lausd.k12.ca.us
18230 Kittridge Street, Reseda, CA  91335
(818) 342-6186

Sonia D. Farassati
Email:  farasati@aol.com
Last Revised: 08/02/2000