Variables and Expressions 1.1 p. 4-7 ÷ ∙ √

What are our objectives???? Today we will work towards three objectives: We will identify expressions as numerical or variable (algebraic), identifying the variable…….if there is one. We will identify operational words. We will then write a variable expression for a word phrase.

The last column uses a numerical expression to show how to find the miles per gallon using miles traveled and gallons used. A numerical expression is an expression that uses only numbers and operational symbols. If we don’t know the numbers of miles traveled, we can use a variable to find the correct expression. A variable is a letter that stands for a number. A variable expression is a mathematical statement that has at least one variable in it. A variable expression will show HOW to find an answer if you do not have all the numerical values. miles ÷ 10 Let m represent miles. The miles per gallon could be shown as m ÷ 10 or. 1 Chart p. 4 Mental division by 10? This is for discussion. It is in your text, but it is not in your notes.

Let’s Recap.... A numerical expression has only numbers and operational symbols. A variable expression has at least one variable and operational symbols.* A variable is.... ………. a letter used to represent a number. We need to talk about this……there are “rules” about writing variables and how many values a variable can represent in one expression! Remind me in two slides…… Can you classify an expression as numerical or variable????????

What Am I ???? Variable ExpressionNumerical Expression 7(3) 4 ÷ ½ 4t4t 15(r) 6 ÷ 2t Back to your notes!!!

As the year progresses….. ….You will be asked to write variables within one term in alphabetical order. 4cba will be written as 4abc …..You will recognize that a variable that is used more than once in a variable expression will represent the same value. In the expression 4abc + c, c MUST represent the same value One more…..When you have a number multiplied by a variable, write the number first…..d5 should be written as 5d.

Well, can you……. Identify an expression as numerical or variable? If it is a variable expression, can you identify the variable? SUCCESS!!!!!!!!!

Moving on……. Now that we have classified an expression as numerical or variable…. We will move on to the second and third objectives for today.

Writing Variable Expressions Given a word phrase, we will create a variable expression that retells its story….. ( This is another way of looking at this skill.) Your variable expression is to tell the same story as the word phrase. To do this, however, you must associate words with mathematical values and operations…. 2

What?.... language and math???? Words show us what operation to use. What do you think of when you hear Sum? Difference? In all? More than? This one is tricky……..it depends on the context. You are using language to create math. After this lesson, you will be able to represent words with variable expressions!!!

Writing Variable Expressions 2 Did you get confused on the second one? Subtraction has “forward” words and “backwards” words Your next chart will help you.

Certain words mean certain things. __________________________________________ OperationSay it.....Write it..... Addition words: totalThe total of 8 and a number8 + n more than5 more than a number increased byA number increased by 12 the sum ofThe sum of 4 and a number Multiplication words: the product of The product of 4 and a number times6 times a number groups of5 groups of 7 Division words: quotient * (order matters!!!!) The quotient of 12 and a number Divided byA number divided by n n n 4n 6 n 5 (7) 12÷ n n÷ 8

There are more.... Subtraction words SAME ORDER.... difference in The difference in 12 and a number 12 - n decreased byA number decreased by 5 minus7 minus a number take away4 take away 3 Backwards words... less than5 less than fewer than9 fewer than a number subtracted fromA number subtracted from 12 n n n n “subtracted by” is not a correct phrase for subtraction.

Let’s try some. Group practice: 1. The sum of a number and 12 ____________________ 2. The product of 12 and 15 ___________________ 3. The difference of a number and 4 _________________ 4. Four less than a number__________________________ 5. The quotient of 11 and 4.5_________________________ 6. Twenty-five less than k ___________________________ 7. Thirty-four times w ___________________ 8. The sum of 135 and p ________________________ 9. The difference of n and 16 _______________________ 10. Sixteen decreased by n_______________________ 11. The quotient of a number and 9 _________________ *** n + 12 (12)(15) n-4 11÷ 4.5 K w p n n n÷ 9 Mark the operational words and write the phrase.

Combining both objectives….. Identify each expression as numerical or variable. If it is a variable expression, write the variable. 1. 4d _________________________ 2. 4(9) 6 ________________________ 3. 2x ________________________ – p ________________________ – 9 + x _____________________ _________________________ Variable; d Numerical Variable; x Variable; p Variable; x Numerical

7. The value in cents of 5 quarters ____________ This section may require some setup to understand. We want to write both a numerical and variable expression for each situation. 5(25) 8. The value in cents of q quarters ____________ q(25)=25q 9. The number of months in 7 years____________ 7(12) 10.The number of months in y years____________ 11.The number of gallons in 8 quarts ____________ 12.The number of gallons in q quarts ____________ y(12)=12y 4 qts. = 1 gallon, so...

13. If one bagel costs $.75, write an expression to show the cost of 12 bagels ______________ 14. What expression would show the cost of b bagels? _______________________________ 15. Write an expression to show the number of hours in 120 minutes ____________________ 16.Write an expression to show the number of hours in m minutes ______________________ 12(.75) b(.75) =.75b

What will this look like on a test????? It costs $8.00 per hour to ice skate at the ice rink. It is another $5.00 to rent skates for the day. Which expression shows how much your charge would be for skating with a skate rental? Let h stand for the hours you skate. a.8(5) + h b h c.8h + 5 d.8 + 5h

Checking on You….. Could you classify an expression as variable or numerical????? Could you translate a verbal expression to a variable or numerical expression using operational words? Okay, let’s extend this a little.

Multiple Operations... The product of 6 and the sum of 4 and a number There are two operation words 6 ( ) 4 + n Why do we need to use the ( ) ? Try this..... Seven less than the product of a number and 11 11n - 7 The difference in the sum of 3 and a number and the product of 5 and another number We are finding the difference in a sum and a product ________ - _____ (3 + n ) - 5 p The product of 6 and the sum of 4 and a number There are two operation words 6 ( ) 4 + n Why do we need to use the ( ) ? Try this..... Seven less than the product of a number and 11 11n - 7 The difference in the sum of 3 and a number and the product of 5 and another number We are finding the difference in a sum and a product ________ - _____ (3 + n ) - 5 p

Which Expression Am I? Twelve less than three times a number w is the same as the quotient of 15 and 5. A. 12(3) – w = 15 x 5 B. (3)w - 12 = 15 x 5 C w = 15 ÷5 D. 3w - 12 = 15 ÷ 5 Look for operational words….. = ÷ Backwards words 3n - 12

In summary…… We have classified expressions as numerical or variable. We have used language to create math. We have “translated” verbal expressions into algebraic and numerical expressions. Okay, let’s practice these skills!