2. 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 !

3. 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.)

4. 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 1992. u 12. Gold

5. 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

6. 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.

7. 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 5 + 13 = 18

8. 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 9 - 6 = 3

9. 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.

10. 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 3. 5 = 15 ä 3(5) = 15 (3)(5) = 15  (3)5 = 15 3 * 5 = 15 The numbers 3 and 5 are factors of 15.

11. 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.

12. 1.2 “Expressions and Variables” ä Are there any questions about Using Number Operation?

13. 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

14. 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.

15. 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.

16. 1.2 “Expressions and Variables”  An algebraic expression is a collection of numbers, variables, operations, and grouping symbols as show on the next slide.

17. 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.

18. 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.

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

20. 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.  = 26 + 5 Multiply 2 x 13.  = 31 Add 26 + 5.

21. Example 3 Evaluating an Algebraic Expression  b. Evaluate 3 x 2 - 11 x when x = 6.  Solution  Value = 3 x 2 - 11 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.

22. Example 3 Evaluating an Algebraic Expression  b. Evaluate 3 x 2 - 11 x when x = 6.  Solution  Value = 3 x 2 - 11 x Write original expression.  = 3(6 2 ) - 11(6) Substitute 6 for x.  = 3(36) - 11(6) Evaluate the power (OoO).  = 108 - 66 Multiply (OoO).  = 42 Subtract (OoO).

23. 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.

24. 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.

25. 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

26. 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.  = 8 + 12 Multiply.  = 20 Add. simplify } simplify

27. 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)

28. 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.

29. 1.2 “Expressions and Variables” ä Are there any questions about Modeling with Formulas?

30. Classwork: ä 930 Danny Dana  9 / 28 ä Math 7 - Dequer 1. 2 Pg.9: 1-22 1. Work Quietly and On-Your-Own ! Write problem and answer in words for 3 - 10 and in numbers for 11 - 14.

31. Classwork: ä 930 Danny Dana  9 / 28 ä Math 7 - Dequer 1. 2 Pg.9: 1-22 1. You may now get help from and/or give help to your near neighbors.

32. 1.2 “Guided Practice” Pg. 9: 1-22 factor term  1. factor 2. term 68 - The sum of 28 and 40 is 68.  3. 68 - The sum of 28 and 40 is 68. 9 - The quotient of 63 and 7 is 9.  4. 9 - The quotient of 63 and 7 is 9. 13 - The difference of 40 and 27 is 13.  5. 13 - The difference of 40 and 27 is 13.

33. 1.2 “Guided Practice” Pg. 9: 1-22 48 - The product of 12 and 4 is 48.  6. 48 - The product of 12 and 4 is 48. 83 - The difference of 90 and 7 is 83.  7. 83 - The difference of 90 and 7 is 83. 37 - The quotient of 111 and 3 is 37.  8. 37 - The quotient of 111 and 3 is 37. 78 - The product of 13 and 6 is 78.  9. 78 - The product of 13 and 6 is 78.

34. 1.2 “Guided Practice” Pg. 9: 1-22 20 - The sum of 7, 5 and 8 is 20.  10. 20 - The sum of 7, 5 and 8 is 20. 15 + 33 = 48  11. 15 + 33 = 48 20 x 7 = 140  12. 20 x 7 = 140 18 - 9 = 9  13. 18 - 9 = 9 360  9 = 40  14. 360  9 = 40

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

36. 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!

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

38. M at h HumorHumorHumorHumor SHE NEVER LIKES MY BEST IDEAS !

39. 1.2 “Guided Practice” Pg. 9: 1-22 9 23  15. 9 16. 23 1 3  17. 1 18. 3 3 1  19. 3 20. 1 6 97  21. 6 22. 97

40. 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.)

41. 1.2 “Guided Practice” Pg. 9: 1-22 9 23  15. 9 16. 23 1 3  17. 1 18. 3 3 1  19. 3 20. 1 6 97  21. 6 22. 97