1-1 Variables and ExpressionsClass Notes : 1-1 Variables and ExpressionsClass Notes Ms. Christoph
Algebra 1
Lesson 1-1 Objective: : Lesson 1-1 Objective: to write algebraic expressions.
Focus Question : Focus Question How is an algebraic expression different from a numerical expression?
Algebra uses symbols to represent quantities that are unknown or that vary.
Background : Background Algebra is a language that is comprised of symbols and letters.
Symbols represent operations and numbers.
Letters represent unknown quantities.
Background (con’t) : Background (con’t) When symbols are combined into a mathematical phrase, the phrase is an expression, such as 15+23 (written this way 15 + 23 always = 38)
When variables are combined with symbols, the phrase is an algebraic expression, such as X + 23
Background (con’t) : Background (con’t) The expression X + 23 equals different values depending on the number assigned to X
Before Algebra I you learned this: 8 + = 12
A mathematical quantity is: : A mathematical quantity is: anything that can be measured or counted. Some quantities remain constant (stay the same) or they may vary (change).
What does the word
“vary” mean?
See page 4 : See page 4
Writing an Equation : Writing an Equation An equation is an algebraic expression that contains an equal sign. (3+2=5)
If the expression on either side of the equal sign have the same values, then the equation is true. (and vise versa)
An open sentence is an equation contains one or more variable. Example
Writing an Equation : Writing an Equation Suppose the video store sells DVD movies for $19.99 each. What equation would you use to express the total price, p, of a given #, X, of movies? [hint: mentally start with buying 2 movies, then 3, to see which equation would work] (this gives you a pattern)
p = x + 19.99 B) 19.99 - X= p
C) 19.99 (x) = p D) 19.99 (p) = x
explanation : explanation The number of movies that you buy times 19.99 that gives you the total price.
Relate: the total price is 19.99 times the # of DVD’s bought
Define: let X = # of DVD’s purchased
let p = total purchase price
Write: p = 19.99 (x)