2. Welcome to Interactive Chalkboard Mathematics: Applications and Concepts, Course 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 1-1A Plan for Problem Solving Lesson 1-2Divisibility Patterns Lesson 1-3Prime Factors Lesson 1-4Power and Exponents Lesson 1-5Order of Operations Lesson 1-6Algebra: Variables and Expressions Lesson 1-7Algebra: Solving Equations Lesson 1-8Geometry: Area of Rectangles

5. Lesson 1 Contents Example 1Use the Problem-Solving Plan Example 2Use the Problem-Solving Plan

6. Example 1-1a MONEY After shopping at the mall, you came home with $3. You spent $4 on candy, $8 on a movie, and $5 on arcade games. How much money did you start with? ExploreYou know the amount of money that was spent on each item at the mall as well as the amount of money left over. You need to find how much money you started with. PlanTo find the total amount of money that was started with, add the amount spent on each item at the mall along with the amount left over.

7. Example 1-1b ExamineThe answer seems reasonable. To check it, subtract all of the money spent at the mall and confirm that $3 is left over. Solve Answer: $20 You started with $20.

8. Example 1-1c HOCKEY During the regular season, David scored 18 more goals than Bobby. Bobby scored 14 goals. How many goals did David score during the regular season? Answer: 32

9. Example 1-2a COOKING The table shows how much dry rice is needed to make cooked rice for dinner. Based on the information, how many cups of cooked rice and how many servings will 4 cups of dry rice provide? Dry Rice (cups) Cooked Rice (cups) Servings 12 8 2416 3624 4? ?

10. Example 1-2b ExploreYou know the cups of cooked rice and the number of servings for 1, 2, and 3 cups of dry rice. You need to find the cups of cooked rice and the number of servings for 4 cups of dry rice. PlanSince an exact answer is needed and the question contains a pattern, use mental math.

11. Example 1-2c Solve 2 4 6 ? +2 For the cups of cooked rice, the pattern shows an increase of 2 cups of cooked rice for each additional cup of dry rice. So, for 4 cups of dry rice you would get 8 cups of cooked rice. +8 8 16 24 ? +8 For the number of servings, the pattern shows an increase of 8 servings for each additional cup of dry rice. So, for 4 cups of dry rice you would get 32 servings of cooked rice.

12. Example 1-2d ExamineSince and the answer is correct. Answer: 8 cups of cooked rice; 32 servings

13. Example 1-2e EXERCISE The table below shows the number of minutes Sue has spent working out each day over the past 5 weeks. Based on this information, determine how many minutes per day Sue will spend working out during week 6. Week Minutes Per Day Working Out 110 215 321 428 536 6 ? Answer: 45 min

14. End of Lesson 1

15. Lesson 2 Contents Example 1Use Divisibility Rules Example 2Use Divisibility Rules Example 3Use Divisibility Rules

16. Example 2-1a Tell whether 3,225 is divisible by 2, 3, 5, or 10. Then classify the number as even or odd. Answer: The number 3,225 is odd. It is divisible by 3 and 5. 2: No; the ones digit, 5, is not divisible by 2. 3: Yes; the sum of the digits, 12, is divisible by 3. 5: Yes; the ones digit is 5. 10: No; the ones digit is not 0.

17. Example 2-1b Tell whether 2,448 is divisible by 2, 3, 5, or 10. Then classify the number as even or odd. Answer: 2, 3; even

18. Example 2-2a BUSINESS A bakery requires 3 pounds of sugar for a large batch of cookies. If they have 38 pounds of sugar left, can they use all the sugar for large batches of cookies? Answer: The bakery cannot use all the sugar they have left for large batches of cookies. Use divisibility rules to check whether 38 is divisible by 3. and 11 is not divisible by 3. So, 38 is not divisible by 3.

19. Example 2-2b SCHOOL The tables in a classroom at school each seat 5 students. If there are 26 students in the class, can they all be seated at these tables so that each table is full and everyone has a seat? Answer: no

20. Example 2-3a Tell whether 480 is divisible by 4, 6, or 9. Answer: 480 is divisible by 4 and 6. 4: Yes; the number formed by the last two digits, 80, is divisible by 4. 9: No; the sum of the digits, 12, is not divisible by 9. 6: Yes; the number is divisible by both 2 and 3.

21. Example 2-3b Tell whether 324 is divisible by 4, 6, or 9. Answer: 4, 6, 9

22. End of Lesson 2

23. Lesson 3 Contents Example 1Identify Prime and Composite Numbers Example 2Identify Prime and Composite Numbers Example 3Find Prime Factorization

24. Example 3-1a Tell whether 13 is prime, composite, or neither. Answer: Since there are exactly two factors, 1 and the number itself, 13 is a prime number. The factors of 13 are 1 and 13.

25. Example 3-1b Tell whether 35 is prime, composite, or neither. Answer: composite

26. Example 3-2a Tell whether the number 20 is prime, composite, or neither. Answer: Since 20 has more than two factors, it is a composite number. The factors of 20 are 1 and 20, 2 and 10, and 4 and 5.

27. Example 3-2b Tell whether the number 41 is prime, composite, or neither. Answer: prime

28. Example 3-3a Find the prime factorization of 96. Answer: The prime factorization of 96 is Write the number that is being factored at the top. Choose any pair of whole number factors of 96. Continue to factor any number that is not prime. Except for the order, the prime factors are the same.

29. Example 3-3b Find the prime factorization of 72. Answer: 2  2  2  3  3

30. End of Lesson 3

31. Lesson 4 Contents Example 1Write Powers and Products Example 2Write Powers and Products Example 3Use Powers to Solve a Problem Example 4Write Prime Factorization Using Exponents

32. Example 4-1a The base is 5. Since 5 is a factor four times, the exponent is 4. Write using an exponent. Then find the value of the power. Answer: 625

33. Example 4-1b Write using an exponent. Then find the value of the power. Answer: 16,384

34. Example 4-2a The base is 8. The exponent is 3. So, 8 is a factor three times. Write as a product. Then find the value of the product. Answer: 512

35. Example 4-2b Write as a product. Then find the value of the product. Answer: 1,296

36. Example 4-3a Answer: So, the elevation of King’s Peak is about 4,096 meters. ELEVATIONS The highest point in Utah is King’s Peak. It stands just a bit higher than meters. What is this elevation? Write as a product. Then find the value of the product.

37. Example 4-3b Answer: 64 ft SWIMMING POOL The length of a new swimming pool being built at the community recreation center is listed as feet. What is the length of the new pool?

38. Example 4-4a Write the prime factorization of 126 using exponents. Answer: The prime factorization of 126 is This can be written as

39. Example 4-4b Write the prime factorization of 144 using exponents. Answer:

40. End of Lesson 4

41. Lesson 5 Contents Example 1Use Order of Operations Example 2Use Order of Operations Example 3Use Order of Operations Example 4Use Order of Operations with Powers Example 5Use Order of Operations with Powers Example 6Apply Order of Operations

42. Example 5-1a Answer: 33 Multiply 3 and 9. Add 6 and 27. Find the value of the expression

43. Example 5-1b Answer: 48 Find the value of the expression

44. Example 5-2a Answer: 11 Subtract 3 from 10 first. Add 4 and 7. Find the value of the expression

45. Example 5-2b Answer: 6 Find the value of the expression

46. Example 5-3a Answer: 11 Subtract 2 from 3. Divide 90 by 3. Add 30 and 1. Subtract 20 from 31. Find the value of the expression

47. Example 5-3b Answer: 7 Find the value of the expression

48. Example 5-4a Answer: 73 Multiply 5 and 2. Add 64 and 10. Subtract 1 from 74. Find the value of the expression Find

49. Example 5-4b Answer: 64 Find the value of the expression

50. Example 5-5a Answer: 21 Add 4 and 3. Divide 49 by 7. Multiply 7 and 3. Find the value of the expression Find

51. Example 5-5b Answer: 72 Find the value of the expression

52. Example 5-6a MONEY Trina, her parents, and her grandmother eat dinner at a popular diner. Each person orders a soda, sandwich, fries, and dessert. Find the total cost of the meal without tax. To find the total cost, write an expression and then evaluate it using the order of operations. ItemCost soda$1 sandwich$5 fries$2 dessert$3

53. Example 5-6b Answer: The total cost of the meal without tax is $44. Words Expression 4 x $1 + 4 x $5 4 x $2 4 x $3 ++ cost of 4 sodas plus cost of 4 sandwiches cost of 4 fries cost of 4 desserts plus

54. Example 5-6c CLOTHING Maris is shopping at a new clothing store. T-shirts are priced at $9 each, jeans are priced at $17 per pair, and sweaters are priced at $14. Maris buys 4 t-shirts, 2 pairs of jeans, and 3 sweaters. Find the total cost of her purchases without tax. Answer: $112

55. End of Lesson 5

56. Lesson 6 Contents Example 1Evaluate Algebraic Expressions Example 2Evaluate Algebraic Expressions Example 3Evaluate an Algebraic Expression Example 4Evaluate an Algebraic Expression

57. Example 6-1a Answer: 15 Evaluate Replace c with 5. Subtract 5 from 20.

58. Example 6-1b Answer: 16 Evaluate

59. Example 6-2a Add 14 and 13. Evaluate Answer: 27 Replace p with 14 and q with 13.

60. Example 6-2b Answer: 5 Evaluate

61. Example 6-3a Evaluate Answer: 5 Replace x with 4. Multiply 2 and 4. Subtract 3 from 8.

62. Example 6-3b Answer: 25 Evaluate

63. Example 6-4a A 24B 36C 48D 144 MULTIPLE-CHOICE TEST ITEM Find the value of Read the Test Item Solve the Test Item Replace a with 2. Multiply 6 and 2. Add 12 and 12. Multiply 4 and 3. Answer: A You need to find the value of the expression.

64. Example 6-4b Answer: B MULTIPLE-CHOICE TEST ITEM Find the value of the expression A 11B 15C 21D 47

65. End of Lesson 6

66. Lesson 7 Contents Example 1Find the Solution of an Equation Example 2Solve an Equation Mentally Example 3Use Guess and Check

67. Example 7-1a Which of the numbers 5, 6, or 7 is the solution of the equation Answer: The solution of is 6 because replacing b with 6 results in a true sentence. Are Both Sides Equal? Value of b no5 yes 6 no7

68. Example 7-1b Answer: 11 Which of the numbers 9, 10, or 11 is the solution of the equation

69. Example 7-2a Answer: 7 Solve mentally. The solution is 7. THINK What number minus 5 equals 2? You know that

70. Example 7-2b Answer: 9 Solve mentally.

71. Example 7-3a Answer: The solution is 25. So, the average life span of a horse is 25 years. ANIMALS On average, a cat lives 12 years. This is 13 years less than a horse lives. Solve the equation to find the average life span of a horse. Use guess and check. Try 24.Try 25.

72. Example 7-3b Answer: 16 years old AGE Samantha is 9 years old. This is seven years less than her sister Dinah’s age. Solve the equation to find Dinah’s age.

73. End of Lesson 7

74. Lesson 8 Contents Example 1Find the Area of a Rectangle Example 2Use Area to Solve a Problem

75. Example 8-1a Find the area of a rectangle with length 15 feet and width 10 feet. Answer: The area is 150 square feet. Area of a rectangle Replace with 15 and w with 10. 10

76. Example 8-2b Area of Indoor Pool Area of a rectangle Multiply. Replace with 25 and w with 21. To find the difference, subtract. Answer: The area of the outdoor pool is 725 square meters greater than the area of the indoor pool.

77. Example 8-1b Find the area of a rectangle with length 9 meters and width 13 meters. Answer:

78. Example 8-2a SPORTS The outdoor Olympic swimming pool in Volos, Greece, measures 50 meters long and 25 meters wide. The indoor swimming pool measures 25 meters long and 21 meters wide. What is the difference between the areas of the outdoor pool and the indoor pool? Area of Outdoor Pool Area of a rectangle Multiply. Replace with 50 and w with 25.

79. Example 8-2c GARDENS Bill and Jose each have a large garden in their backyard. Bill’s garden measures 18 feet long and 12 feet wide. Jose’s garden measures 22 feet long and 8 feet wide. What is the difference between the areas of the two gardens? Answer:

80. End of Lesson 8

81. Online Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 1 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath1.net/extra_examples.

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