Algebraic Expressions

ALGEBRAIC EXPRESSIONS

IMPORTANT IDEAS: An algebraic expression is a mathematical

expression that contains a variable.

An algebraic expression can be evaluated (solved) by replacing a variable with a number, then following the order of operations (which steps do you do first?)

Notice that variables are often written in italics so they are not confused with units of measure.

LET’S TALK ALLOWANCE! Suppose you get $5 per week. About how

much would you get in a year?

$5 x $50 = $250

Suppose you were offered $100 now, plus $1 a week for the rest of the year. Which would you prefer and why?

Most might prefer $100 now, so they can buy what they want now without having to save up for it.

But… which choice gives you more money in one year?

How do you know?

READ “EXPLORE” PAGE 16

If Tehya chooses choice 1, how much money will she be paid?

How do you know?

$1040

There are 52 weeks in a year.

52 x 20 = $1040

If Tehya chooses choice 2, how much money will she get paid?

How do you know?

$1024

There are 52 weeks in a year.

52 x 12 = $624

$624 + $400 = $1024

WHICH METHOD WOULD PAY TEHYA MORE MONEY? EXPLAIN! Choice #1

$1040 is greater than $1024.

Why might Tehya choose the method that pays less?

She might be short of money and need (have an immediate use for) $400 right away. She only loses $16 dollars by taking $400 cash right now.

CHOICE 1 How can you calculate the money Tehya has

received after 6 week?

After 25 weeks?

Multiply 6 by $20 to get $120

Multiply 25 by $20 to get $500

What rule can you write to calculate the money received at any time during the year for choice 1?

MULTIPLY THE NUMBER OF WEEKS BY $20! $20 x w

“w” is the variable. Remember a variable can be any letter.

$20 x t = $20 x w

From now on I will use * on slides to mean “multiplied by” so we are not getting confused by the “x” meaning “multiplied by”.

4x * 2 and 4b * 2 are the same.

4x + 2 and 4b + 2 are the same.

A variable is a symbol that represents a set of numbers. Choice of variable does not affect the expression.

Remember to use the correct order of operations, or you might get a different/incorrect answer.

3 + 4k

If you use k=2, but do not follow the correct order of operations, the answer you get is 14.

If you use the correct order of operations, the answer you get is 11.

Order of Operations

YOU HAVE WORKED WITH VARIABLES BEFORE… For example, in formulas for area and

perimeter.

Remember… the constant term of an expression is called constant because the value of that term is not affected by the value of the variable.

Let’s review page 17.

PRACTICE, PAGE 18 #s 1-10.