AT THE START OF CLASS -- You should HAVE OUT: u 1. PENCIL, ERASER, and Calculator. u 2. LAST NIGHT’S HOMEWORK. u 3. Mathbook and blank paper.  PLEASE BE QUIET AFTER THE BELL RINGS !

Class/Homework Monday 9/27  Pgs. 5-6: 4, 6, 8, and 12. ( can continue on classwork paper, but label clearly ! )  (You may do any of the odd numbered problems, if you want extra practice and check them on Pg. SA-1.)

Pgs. 5-6: 4, 6, 8, and 12. Answers not on SA1. u 4. Wed. 140, Thurs. 170 The attendance increases by 30 each day. u 6. The volume of gas decreases. u 8. It was least in 1988 and greatest in u 12. Gold

1.2 “Expressions and Variables” ä If you wanted to find out how much taller you grew since last year, what number operation would you use? ä subtraction

1.2 “Expressions and Variables” ä Goal 1 -You should review how to use the four basic number operations. ä Goal 1 - You should review how to use the four basic number operations. ä There are 4 basic number operations: ä addition, subtraction, multiplication and division. ä Each of these operation can be described verbally and symbolically.

Example 1 Finding Sums and Differences ä a. Addition ä Verbal Description sum  The sum of 5 and 13 is 18. ä Symbolic Description ä = 18

Example 1 Finding Sums and Differences ä b. Subtraction ä Verbal Description difference  The difference of 9 and 6 is 3. ä Symbolic Description ä = 3

1.2 “Expressions and Variables”.  In Example 2, notice that multiplication can be specified by the symbols x,., or by parenthesis. ä Division can be specified by , /, or by a fraction bar.

Example 2 Finding Products and Quotients ä a. Multiplication ä Verbal Description product  The product of 3 and 5 is 15. ä Symbolic Descriptions  3 x 5 = = 15 ä 3(5) = 15 (3)(5) = 15  (3)5 = 15 3 * 5 = 15 The numbers 3 and 5 are factors of 15.

Example 2 Finding Products and Quotients ä b. Division ä Verbal Description quotient  The quotient of 14 and 7 is 2. ä Symbolic Descriptions ä 14  7 = 2 14 / 7 = 2 The numerator is 14 and the denominator is 7.  14 / 7 = 2 The numerator is 14 and the denominator is 7.

1.2 “Expressions and Variables” ä Are there any questions about Using Number Operation?

1.2 “Expressions and Variables” ä On a family vacation, you plan to spend one day driving on a road with a speed limit of 40 mi/h.  If you drive at the speed limit, how far will you travel along the road in: ä 1 hour = 40 mi ä 2 hour = 80 mi ä 3 hour = 120 mi

1.2 “Expressions and Variables” h  How would we write an expression for the distance traveled in h hours? ä 40h mi ä Goal 2 -You should learn how to evaluate expressions that contain variables. ä Goal 2 - You should learn how to evaluate expressions that contain variables.

1.2 “Expressions and Variables”  A variable is a letter that is used to represent one or more numbers.  The numbers are values of the variable.

1.2 “Expressions and Variables”  An algebraic expression is a collection of numbers, variables, operations, and grouping symbols as show on the next slide.

Algebraic Algebraic Expression Verbal Description  5 n 5 times n  4 x 2 4 times the square of x  2 a + bc 2 times a, plus b times c ä The third expression above is a sum.  The parts that are added to form the sum, 2 a and bc, are the terms of the expression.

Evaluating Algebraic Expressions Evaluating Algebraic Expressions  Replacing each variable in an algebraic expression with a number is called substituting.  The number you get after simplifying is called the value of the expression. ä To evaluate an expression, use the steps on the next slide.

Evaluating Algebraic Expressions Evaluating Algebraic Expressions Write the algebraic algebraicexpression. Substitute values for the variables. Simplify the numericalexpression.

Example 3 Evaluating an Algebraic Expression  a. Evaluate 2 n + 5 when n = 13.  Solution  Value = 2 n + 5 Write original expression.  = 2(13) + 5 Substitute 13 for n.  = Multiply 2 x 13.  = 31 Add

Example 3 Evaluating an Algebraic Expression  b. Evaluate 3 x x when x = 6.  Solution  Value = 3 x x Write original expression.  = 3(6 2 ) - 11(6) Substitute 6 for x. ä Note: The value of the variable must be substituted for every occurrence of the variable in an algebraic expression.  For 3 x 2, only the x variable is squared not the coefficient 3.

Example 3 Evaluating an Algebraic Expression  b. Evaluate 3 x x when x = 6.  Solution  Value = 3 x x Write original expression.  = 3(6 2 ) - 11(6) Substitute 6 for x.  = 3(36) - 11(6) Evaluate the power (OoO).  = Multiply (OoO).  = 42 Subtract (OoO).

1.2 “Expressions and Variables” ä Are there any questions about Evaluation Expressions with Variables? ä Why should you learn this stuff? ä Learning to use variable expressions is a key part of learning algebra. ä Algebraic expressions allow you to mathematically model real-life situations.

1.2 “Expressions and Variables” ä Goal 3 -You should learn how to use formulas to model life-like situations. ä Goal 3 - You should learn how to use formulas to model life-like situations. ä Algebraic expressions are often used to model life-like and real quantities.  You can translate a verbal model into an algebraic model by using labels.  Algebraic models are sometimes called formulas.

VerbalAlgebraic Model  Label  Model The area of rectangle is the product of its length and its width. A = area l = length w = width A = lw The distance traveled is the product of the rate and the time. d = distance r = rate t = time d = rt

Example 4 Evaluating a Formula  Evaluate the formula P = 2 l + 2 w when l = 4 and w = 6.  Solution  P = 2 l + 2 w Write original expression.  = 2(4) + 2(6) Substitute 4 for l and 6 for w.  = Multiply.  = 20 Add. simplify } simplify

Example 5 Finding a Distance ä A rover driving on the moon’s surface travels at a speed of 60 ft/min.  How far will it travel in 90 min?  Solution ä Verbal Model Distance = Rate x Time  Labels = d  Labels Distance = d (feet) = r  Rate = r (feet per minute) = t  Time = t (minutes)

ä Solution ä Verbal Model Distance = Rate x Time  Labels = d  Labels Distance = d (feet) = r  Rate = r (feet per minute) = t  Time = t (minutes)  Algebraic Model d = rt Write algebraic model.  = (60)(90) Substitute 60 for r and 90 for t.  = 5400 Multiply to Simplify. ä In 90 minutes the rover will travel 5400 ft.

1.2 “Expressions and Variables” ä Are there any questions about Modeling with Formulas?

Classwork: ä 930 Danny Dana  9 / 28 ä Math 7 - Dequer 1. 2 Pg.9: Work Quietly and On-Your-Own ! Write problem and answer in words for and in numbers for

Classwork: ä 930 Danny Dana  9 / 28 ä Math 7 - Dequer 1. 2 Pg.9: You may now get help from and/or give help to your near neighbors.

1.2 “Guided Practice” Pg. 9: 1-22 factor term  1. factor 2. term 68 - The sum of 28 and 40 is 68.  The sum of 28 and 40 is The quotient of 63 and 7 is 9.  The quotient of 63 and 7 is The difference of 40 and 27 is 13.  The difference of 40 and 27 is 13.

1.2 “Guided Practice” Pg. 9: The product of 12 and 4 is 48.  The product of 12 and 4 is The difference of 90 and 7 is 83.  The difference of 90 and 7 is The quotient of 111 and 3 is 37.  The quotient of 111 and 3 is The product of 13 and 6 is 78.  The product of 13 and 6 is 78.

1.2 “Guided Practice” Pg. 9: The sum of 7, 5 and 8 is 20.  The sum of 7, 5 and 8 is = 48  = x 7 = 140  x 7 = = 9  =  9 = 40   9 = 40

MathHumor MISS WORMWOOD. MY DAD SAYS WHEN HE WAS IN SCHOOL, THEY TAUGHT HIM TO DO MATH ON SOMETHING CALLED A SLIDE RULE.

HE SAYS HE HASN’T USED A SLIDE RULE SINCE, BECAUSE HE GOT A FIVE-BUCK CALCULATOR THAT CAN DO MORE FUNCTIONS THAN HE COULD FIGURE OUT IF HIS LIFE DEPENDED ON IT!

GIVEN THE PACE OF TECHNOLOGY, I PROPOSE WE LEAVE MATH TO THE MACHINES AND GO PLAY OUTSIDE ! MathHumor

M at h HumorHumorHumorHumor SHE NEVER LIKES MY BEST IDEAS !

1.2 “Guided Practice” Pg. 9:    

Class/Homework Tuesday (9/28) u Pgs. u Pgs. 9-11: 26, 38, 40, 50, 58, and 66 u (can u (can continue on classwork paper, but label clearly ! )  (You  (You may do any of the odd numbered problems, if if you want extra practice and check them on Pg. SA-1 and 2.)

1.2 “Guided Practice” Pg. 9:    