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Page 1 of 4 Describing Patterns BEFORE Now WHY? You performed whole number operations. You’ll describe patterns using whole number operations. So you can find the next number of basketball teams, as in Ex. 18. In the Real World Word Watch Review Words add, p. 687 subtract, p. 687 multiply, p. 689 divide, p. 690 Summer Movie Club You are a member of a summer movie club at your local movie theater. The club meets every Wednesday in July to watch a movie. If the first meeting is on July 6, on what other dates in July will the club meet? EXAMPLE 1 Recognizing and Extending a Pattern To answer the question about the summer movie club above, start with July 6th and repeatedly add 7 days to the date. Date of first meeting: July 6 Date of second meeting: July 13 Date of third meeting: July 20 Date of fourth meeting: July 27 7 7 7 Because July has only 31 days, July 27th is the date of the last club meeting in July. Numerical Patterns To describe and extend a numerical pattern, try finding a relationship between the first and second numbers. Then see if the relationship is true for the second and third numbers, the third and fourth numbers, and so on. EXAMPLE with Reading The three dots at the end of a list of numbers mean that the numbers and the pattern continue without end. 2 Extending a Numerical Pattern Describe the following pattern: 2, 7, 12, 17, . . . . Then write the next three numbers. You add 5 to the previous number to get the next number in the pattern. 5 5 5 2, 7, 12, 17, 22, 27, 32, . . . 5 5 5 Lesson 1.1 Describing Patterns 5 Page 2 of 4 EXAMPLE with Review Need help with whole number operations? See pp. 688–690. 3 Extending a Numerical Pattern Describe the following pattern: 2, 6, 18, 54, . . . . Then write the next three numbers. You multiply the previous number by 3 to get the next number in the pattern. 3 3 3 2, 6, 18, 54, 162, 486, 1458, . . . 3 Your turn now numbers. 3 3 Describe the pattern. Then write the next three 1. 28, 24, 20, 16, . . . 2. 256, 128, 64, 32, . . . Visual Patterns To describe and extend a visual pattern, try looking for repeated colors and shapes, a change in the position of figures in the pattern, or a change in the number of figures in the pattern. EXAMPLE 4 Extending a Visual Pattern Hawaiian Leis A Hawaiian lei is a flower wreath that is sometimes given to symbolize friendship. What are the next three flowers that should be put on the lei shown? yellow carnation red carnation orchids Solution Look for repeated flowers to find a pattern. The lei starts with a carnation, two orchids, another carnation, and then two orchids again. Notice that the carnations alternate between yellow and red. ANSWER The last flower on the lei is a red carnation, so the next three flowers should be two orchids and then a yellow carnation. Your turn now Describe the pattern. Then draw the next figure. 3. 6 Chapter 1 Number Sense, Patterns, and Algebraic Thinking 4. Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 705 Getting Ready to Practice Vocabulary Match the pattern with its description. 1. 0, 2, 4, 6, . . . A. Subtract 5 from the previous number. 2. 30, 25, 20, 15, . . . B. Divide the previous number by 10. 3. 1, 4, 16, 64, . . . C. Add 2 to the previous number. 4. 10,000, 1000, 100, 10, . . . D. Multiply the previous number by 4. Describe the pattern. Then draw the next three figures. 5. 6. 7. Guided Problem Solving A radio station plays the day’s top pop song during the afternoon at 2:10, 2:40, 3:10, 3:40, and so on. If you assume the pattern continues, when will you next hear the top pop song? 1 What is the relationship between the first time the song is played and the second time the song is played? 2 Check that the relationship is true for all the other playing times. 3 Use the relationship to find the next time the song will be played. Practice and Problem Solving with Example 1 2 3 4 Homework Exercises 17–18 8–16, 23–25 8–16, 23–25 19–21, 27 Describe the pattern. Then write the next three numbers. 8. 1, 2, 4, 8, . . . 9. 100, 91, 82, 73, . . . 10. 640, 320, 160, 80, . . . 11. 2, 9, 16, 23, . . . 12. 0, 11, 22, 33, . . . 13. 4, 12, 36, 108, . . . 14. 80, 72, 64, 56, . . . 15. 729, 243, 81, 27, . . . 16. 1, 6, 36, 216, . . . 17. Critical Thinking Write the first four numbers in the pattern start with 6 and repeatedly add 8. Online Resources CLASSZONE.COM • More Examples • eTutorial Plus 18. Basketball There are 64 teams in the first round of a college basketball tournament. In each round after the first, there are half as many teams as in the previous round. How many teams are in the next three rounds? Describe the pattern. Then draw the next figure. 19. 20. Lesson 1.1 Describing Patterns 7 Page 4 of 4 21. Bracelets Sketch the next three beads that will continue the pattern. 22. Writing Write a numerical pattern. Then describe the pattern. Science Describe the pattern. Then write the next three numbers. 23. 45, 88, 131, 174, . . . 24. 4, 28, 196, 1372, . . . 25. 1458, 486, 162, 54, . . . 26. Writing Draw a visual pattern. Then describe the pattern. 27. The Moon The diagrams below show the different phases of the moon over time. Draw the next two phases of the moon. Interpret Describe the pattern. Then write the next three letters. 28. A, C, E, G, . . . 29. A, Z, B, Y, . . . 30. Z, W, T, Q, . . . Challenge Describe the pattern. Then write the next three numbers. ■ The Moon 31. 2, 3, 6, 11, 18, . . . The gravitational pull from the moon causes the water level on Earth to change. Such changes are called tides. A complete tide cycle takes about 12 hours. About how many tide cycles occur in one week? 32. 1, 3, 7, 15, 31, . . . 33. 1, 1, 2, 3, 5, 8, . . . Mixed Review Write the number in expanded form. (p. 681) 34. 55 35. 804 36. 2410 37. 3395 Round the number to the place value of the red digit. (p. 683) 38. 34 39. 382 40. 167 41. 9146 Basic Skills Find the sum, difference, product, or quotient. 42. 792 546 43. 301 148 44. 809 23 45. 168 7 Test-Taking Practice INTERNET State Test Practice 46. Multiple Choice Which operation describes the numerical pattern 1, 3, 9, 27, . . . ? CLASSZONE.COM A. Add 3. B. Subtract 3. C. Multiply by 3. D. Divide by 3. 47. Short Response Draw a visual pattern that is related to the numerical pattern 1, 3, 5, 7, . . . . Explain how the two patterns are related. 8 Chapter 1 Number Sense, Patterns, and Algebraic Thinking