Bell Ringer #1 Complete the following questions in your notebook. What do you think a “variable” is? Hint: Think about what “varies” means. What is an “expression”?

Variables and Expressions Mr. Haupt 9/8/16 C.C.2.2.HS.D.1

Variables Variables are letters or symbols that are used in place of a value that can change. The word “variable” means “something that is liable to change.”

For Example How can we evaluate 5a? “a” is the variable, and the result when we evaluate it depends on what value we set for “a”. What is the result when a = 2? What about when a = -4 All you have to do is plug the given values in for the variable and solve.

Try evaluating these… 6x when x = 8 121 divided by c when c = 11 7d – 9 when d = -4

Expressions Expressions are number sentences without any equal signs. Expressions always have one or more math functions in them (addition, subtraction, etc.) You have already seen some examples on the previous slides.

Expressions We use a lot of different words when making algebraic expressions. Each of the following slides will have a list of words, with stars next to the most commonly used words.

Addition Plus* And* Added to Greater than* More than Increased by Total* Sum of*

Subtraction Minus* Difference between* From Less Less than* Fewer than* Decreased by* Take away

Multiplication Times* Product of* Double, Triple, etc.* Twice Of (as in a fraction of something) You will no longer see multiplication like this anymore: 3 x 5. Why do you think that is?

Division Quotient of* Half of, a third of, etc.* Goes into* Per Divided by* You will still see the divide sign, but not as much as the backslash (/) and fractional forms.

Equals Is* Is the same as Gives Will be Was Is equivalent to*

Be careful… The way that expressions are written can be important. In addition and multiplication, the order doesn’t matter. 5 plus 2 is the same as 2 plus 5. 10 times 12 is the same as 12 times 10. But the order and wording DOES matter when using subtraction and division. 7 minus 12 is very different from 7 less than 12. The quotient of 14 and 2 is not the same as the quotient of 2 and 14.

Time to translate… Write an algebraic expression for the following verbal expressions: Eight less than twenty four. The quotient of fifty six and seven. The product of twelve and five. The difference between fifty and thirteen. The sum of fourteen and ninety.

And in reverse… Write verbal expressions for the following algebraic expressions. 4 – 16 12 * 13 36/6 6 + 4 + 10

Expressions with exponents An exponent expression has two parts. A base, and an exponent (or power). In the expression 82 we have a base, which is 8, and an exponent, or power, of 2. The exponent tells us how many of the base are multiplied together. This one says there are two eights. Eight times eight is sixty four.

Exponent phrases A power of 2 is also called “squared.” A power of 3 is also called “cubed.” Anything after that is just referred to as “to the power of ‘x’.”

More translating Turn these algebraic expressions into verbal expressions. 82 153 412 86 + 54

And back again…(again) 5 * b * b * b * b The sum of 6 squared and 4 to the fifth power. The product of 10 cubed and 2 to the seventh power.

Last one! Are exponent expressions the same when you switch the number? Meaning, is 4 to the 7th power the same as 7 to the 4th power?