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Splash Screen. Lesson 1-1 A Plan for Problem Solving Lesson 1-2 Powers and Exponents Lesson 1-3 Squares and Square Roots Lesson 1-4 Order of Operations Lesson 1-5 Problem-Solving Investigation: Guess and Check Lesson 1-6 Algebra: Variables and Expressions Lesson 1-7 Algebra: Equations

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  1. Splash Screen

  2. Lesson 1-1A Plan for Problem Solving Lesson 1-2 Powers and Exponents Lesson 1-3 Squares and Square Roots Lesson 1-4 Order of Operations Lesson 1-5 Problem-Solving Investigation: Guess and Check Lesson 1-6 Algebra: Variables and Expressions Lesson 1-7 Algebra: Equations Lesson 1-8 Algebra: Properties Lesson 1-9 Algebra: Arithmetic Sequences Lesson 1-10 Algebra: Equations and Functions Chapter Menu

  3. Solve problems using THE FOUR-STEP PLAN. Lesson 1 MI/Vocab

  4. In Mathematics, there is four-step plan you can use to help you solve any problem. Explore: Knowing the problem. Plan: Finding a way to solve the problem. Solve: Solving the problem. Check: Checking to make sure you solved the problem correctly.

  5. In Mathematics, there is four-step plan you can use to help you solve any problem. • Explore • Read the problem carefully. • What information in given? • What do you want to find out? • Is enough information given? • Is there any information that you don’t need? • Plan • How do the facts relate to each other? • Select a strategy for solving the problem. There may be more than one way to solve the problem. • Estimate the answer.

  6. In Mathematics, there is four-step plan you can use to help you solve any problem. • Solve • Use your plan to solve the problem. • If your plan does not work, revise it or make a new plan. • Check • Does your answer fit the facts given in the problem? • Is your answer reasonable compared to your estimate? • If not, make a new plan and start again.

  7. READINGBen borrows a 500-page book from the library. On the first day, he reads 24 pages. On the second day, he reads 39 pages and on the third day he reads 54 pages. If Ben follows the same pattern of number of pages read for seven days, will he have finished the book at the end of the week? • A • B • C • D A. No, he will have only read 483 pages. B. No, he will have only read 492 pages. C. yes D. not enough information given to answer Lesson 1 CYP2

  8. FOUR-STEP PLAN. Explore: Knowing the problem. Plan: Finding a way to solve the problem. Solve: Solving the problem. Check: Checking to make sure you solved the problem correctly. Ben borrows a 500-page book from the library. On the first day, he reads 24 pages. On the second day, he reads 39 pages and on the third day he reads 54 pages. If Ben follows the same pattern of number of pages read for seven days, will he have finished the book at the end of the week?

  9. READINGBen borrows a 500-page book from the library. On the first day, he reads 24 pages. On the second day, he reads 39 pages and on the third day he reads 54 pages. If Ben follows the same pattern of number of pages read for seven days, will he have finished the book at the end of the week? • A • B • C • D A. No, he will have only read 483 pages. B. No, he will have only read 492 pages. C. yes D. not enough information given to answer Lesson 1 CYP2

  10. Use the Four-Step Plan SPENDINGA can of soda holds 12 fluid ounces. A 2-liter bottle holds about 67 fluid ounces. If a pack of six cans costs the same as a 2-liter bottle, which is the better buy? ExploreWhat are you trying to find? You are trying to find the number of fluid ounces of soda in a pack of six cans. This number can then be compared to the number of fluid ounces in a 2-liter bottle to determine which is the better buy. What information do you need to solve the problem? You need to know the number of fluid ounces in each can of soda. Lesson 1 Ex1

  11. Use the Four-Step Plan PlanYou can find the number of fluid ounces of soda in a pack of six cans by multiplying the number of fluid ounces in one can by six. Solve 12 × 6 = 72 There are 72 fluid ounces of soda in a pack of six cans. The number of fluid ounces of soda in a 2-liter bottle is about 67. Therefore, the pack of six cans is the better buy because you get more soda for the same price. Lesson 1 Ex1

  12. Use the Four-Step Plan CheckIs your answer reasonable? The answer makes sense based on the facts given in the problem. Answer: The pack of six cans is the better buy. Lesson 1 Ex1

  13. FIELD TRIPThe sixth grade class at Meadow Middle School is taking a field trip to the local zoo. There will be 142 students plus 12 adults going on the trip. If each school bus can hold 48 people, how many buses will be needed for the field trip? • A • B • C • D A. 3 B. 4 C. 5 D. 6 Lesson 1 CYP1

  14. Lesson 1 KC1

  15. Use a Strategy in the Four-Step Plan POPULATION For every 100,000 people in the United States, there are 5,750 radios. For every 100,000 people in Canada, there are 323 radios. Suppose Sheamus lives in Des Moines, Iowa and Alex lives in Windsor, Ontario. Both cities have about 200,000 residents. About how many more radios are there in Sheamus’s city than in Alex’s city? ExploreYou know the approximate number of radios per 100,000 people in both Sheamus’s city and Alex’s city. Lesson 1 Ex2

  16. Use a Strategy in the Four-Step Plan PlanYou can find the approximate number of radios in each city by multiplying the estimate per 100,000 people by two to get an estimate per 200,000 people. Then, subtract to find how many more radios there are in Des Moines than in Windsor. SolveDes Moines: 5,750  2 = 11,500 Windsor: 323  2 = 646 11,500 – 646 = 10,854 So, Des Moines has about 10,854 more radios than Windsor has. Lesson 1 Ex2

  17. Use a Strategy in the Four-Step Plan CheckBased on the information given in the problem, the answer seems to be reasonable. Answer: So, Des Moines has about 10,854 more radios than Windsor has. Lesson 1 Ex2

  18. End of Lesson 1

  19. Use powers and exponents. • factors • cubed • evaluate • standard form • exponential form • exponent • base • powers • squared Lesson 2 MI/Vocab

  20. The exponent tells how many times the base is used as a factor. The centered dots indicate multiplication 16 = 2 · 2 · 2 · 2 = 24 Common factors The base is the common factor. Lesson 2 CA

  21. Lesson 2 CA

  22. Numbers written without exponents are in standard form. Example: 2 · 2 · 2 · 2 = 16 Numbers written with exponents are in exponential form. Example: 2 · 2 · 2 · 2 = 24 Standard form Exponential form

  23. Write Powers as Products Write 84 as a product of the same factor. Eight is used as a factor four times. Answer: 84 = 8 ● 8 ● 8 ● 8 Lesson 2 Ex1

  24. Write 36 as a product of the same factor. • A • B • C • D A. 3 ● 6 B.6● 3 C. 6 ● 6 ● 6 D. 3 ● 3 ● 3 ● 3 ● 3 ● 3 Lesson 2 CYP1

  25. Write Powers as Products Write 46 as a product of the same factor. Four is used as a factor 6 times. Answer: 46 = 4 ● 4 ● 4 ● 4 ● 4 ● 4 Lesson 2 Ex2

  26. Write 73 as a product of the same factor. • A • B • C • D A. 7● 3 B.3● 7 C. 7● 7 ● 7 D. 3● 3 ● 3 ● 3 ● 3 ● 3 ● 3 Lesson 2 CYP2

  27. Write Powers in Standard Form Evaluate the expression 83. 83 = 8 ● 8 ● 8 8 is used as a factor 3 times. = 512 Multiply. Answer: 512 Lesson 2 Ex3

  28. Evaluate the expression 44. • A • B • C • D A. 8 B. 16 C. 44 D. 256 Lesson 2 CYP3

  29. Write Powers in Standard Form Evaluate the expression 64. 64 = 6 ● 6 ● 6 ● 6 6 is used as a factor 4 times. = 1,296 Multiply. Answer: 1,296 Lesson 2 Ex4

  30. Evaluate the expression 55. • A • B • C • D A. 10 B. 25 C. 3,125 D. 5,500 Lesson 2 CYP4

  31. Write Powers in Exponential Form Write 9 ● 9 ● 9 ● 9 ● 9 ● 9 in exponential form. 9 is the base. It is used as a factor 6 times. So, the exponent is 6. Answer:9 ● 9 ● 9 ● 9 ● 9 ● 9 =96 Lesson 2 Ex5

  32. Write 3 ● 3 ● 3 ● 3 ● 3 in exponential form. • A • B • C • D A. 35 B. 53 C. 3 ● 5 D. 243 Lesson 2 CYP5

  33. End of Lesson 2

  34. Find squares of numbers and square roots of perfect squares. • square • perfect squares • square root • radical sign Lesson 3 MI/Vocab

  35. The product of a number and itself is the square of that number. Example: The square of 5 is 5 5 = 52=25. Numbers that are multiplied to form perfect squares are called square roots. A radical sign () indicates a square root. Example: • A • B • C • D Lesson 3 CYP1

  36. Find Squares of Numbers Find the square of 5. 5 ● 5 = 25 Multiply 5 by itself. Answer: 25 Lesson 3 Ex1

  37. Find the square of 7. • A • B • C • D A. 2.65 B. 14 C. 49 D. 343 Lesson 3 CYP1

  38. ENTER= x2 19 361 Find Squares of Numbers Find the square of 19. Method 1 Use paper and pencil. 19 ● 19 = 361 Multiply 19 by itself. Method 2 Use a calculator. Answer: 361 Lesson 3 Ex2

  39. Find the square of 21. • A • B • C • D A. 4.58 B. 42 C. 121 D. 441 Lesson 3 CYP2

  40. Lesson 3 KC1

  41. Find 6 ● 6 = 36, so = 6. What number times itself is 36? Find Square Roots Answer: 6 Lesson 3 Ex3

  42. Find • A • B • C • D A. 8 B. 32 C. 640 D. 4,096 Lesson 3 CYP3

  43. Find ENTER= [x2] 676 26 Use a calculator. 2nd Answer: Find Square Roots Lesson 3 Ex4

  44. Find • A • B • C • D A. 16 B. 23 C. 529 D. 279,841 Lesson 3 CYP4

  45. ENTER= [x2] 1225 35 Use a calculator. 2nd GAMESA checkerboard is a square with an area of 1,225 square centimeters. What are the dimensions of the checkerboard? The checkerboard is a square. By finding the square root of the area, 1,225, you find the length of one side of the board. Answer: So, a checkerboard measures 35 centimeters by 35 centimeters. Lesson 3 Ex5

  46. GARDENING Kyle is planting a new garden that is a square with an area of 4,225 square feet. What are the dimensions of Kyle’s garden? • A • B • C • D A. 42 ft × 25 ft B. 65 ft × 65 ft C. 100 ft × 100 ft D. 210 ft × 210 ft Lesson 3 CYP5

  47. End of Lesson 3

  48. Evaluate expressions using the order of operations. • numerical expression • order of operations Lesson 4 MI/Vocab

  49. Lesson 4 KC1

  50. 1. 15 –5 ● 2 + 7 2. 5 ● 32– 7 3. 2 + (23 ● 3) + 6 – 1

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