What you should learn

To translate verbal expressions into mathematical expressions and vice versa

NCTM Curriculm Standards 2, 4, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Variable

Algebraic Expressions

Factors

Product

Power

Base

Exponent

Evaluate

Introduction: Many people enjoy going to the beach in the summer. Many sunbathers use sunscreen lotions to protect themselves from the sun.

The Sun Protection Factor (SPF) scale gives numbers that represent the length of time you can stay in the sun without burning if you have lotion on. Let's say you can stay in the sun with no sunscreen for 10 minutes without burning. If you put on SPF 5 lotion, you can stay in the sun for 10 minutes X 5 or 50 minutes, or a little less than one hour. Use the table below to see the pattern.

The letters m and s are called variables, and m X s is an algebraic expression. In algebra, variables are symbols that are used to represent unspecified numbers. Any letter may be used as a variable. We selected m because it is the first letter of the word "minutes" and s becuase it is the first letter of "SPF".

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

7mn 3k

In alegraic expressions, a raised dot or parentheses are often used to indicate multiplication. Here are ways to represent the product of x and y.

In each of the multiplication expressions, the quantities being multiplied are called factors, and the result is called the product.

It is often necessary to translate verbal expressions into algebraic expressions.

Verbal Expression	Algebraic Expression
7 less than the product of 3 and a number x	3x - 7
the product 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
half as big as last night's crowd (c = size of last night's crowd)	c/2

Exercise 1: Write an algebraic expression for each verbal expression.

a. three times a number x subtracted from 24

24 - 3x

b. 5 greater than half of a number t

 

 

 

Another important skill is translating algebraic expressions into verbal expressions

Exercise 2: Write a verbal expression for each algebraic expression.

a. (3 + b) y

The sum of 3 and b divided by y

b. 5y + 10x

 

 

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

For example: means x * x

Symbols	Words	Meaning
	5 to the first power 5 to the second power or 5 squared 5 to the third power or 5 cubed 5 to the fourth power three times a to the fifth power x to the nth power	5 5 * 5 5 * 5 * 5 5 * 5 * 5 * 5 3 * a * a * a * a * a x * x * x * x * ... * x

Exercise 3: Write a power that represents the number of smallest squares in the large square

There are 8 squares on each side.

The total number of squares is = 8 * 8 or 64

 

You can use the key on a calculator to square a number.

ENTER: 8 and the answer should read 64

Activity: Exploration Programing

BASIC is a computer language. The symbols used in BASUC are similar to those used in algebra.

means exponent

Numerical variables in BASIC are represented by capital letters. The program below can be used to add, subtract, multiply, divide and find powers.

60 PRINT " A B = " ; A B

Your Turn

a. Let a = 10 and b = 3. Use the program to find 10 + 3, 10 - 3, 10 * 3, 10/3, and

b. Let a = 9 and b = 3. Use the program to find 9 + 3, 9 - 3, 9 * 3, 9/3, and

c. Let a = 5.2 and b = 2. Use the program to find 5.2 + 2, 5.2 - 2, 5.2 * 2, 5.2/2, and

 

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 15 - 19 odd

Alternative Homework: Enriched: 16 - 46 even, 47 - 50

Extra Practice: Students book page 756, Lesson 1-1

Extra Practice Worksheet: Click Here.

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