Patterns and Sequences

Transcription

1 Practice A Patterns and Sequences Choose the sequence that matches each pattern. 1. Start with 12; subtract 2. A 2, 4, 6, 8, 10, 12, B 12, 11, 10, 9, 8, 7, C 12, 14, 16, 18, 20, D 12, 10, 8, 6, 4, 2, 3. Start with 5; add 4. A 5, 4, 3, 2, 1, B 5, 9, 13, 17, 21, C 5, 10, 15, 20, 25 D 4, 9, 14, 19, 24, Identify a pattern in each sequence. 2. Start with 3; multiply by 2. F 3, 5, 7, 9, 11, G 3, 6, 12, 24, 48, H 2, 6, 18, 54, 162, J 3, 4, 5, 6, 7, 8, 9, 4. Start with 1; multiply by 10. F 1, 10, 100, 1,000, G 1, 10, 20, 30, 40, H 10, 100, 1,000, 10,000, J 10, 20, 30, 40, 50, 5. 1, 4, 7, 10, 13, 6. 15, 13, 11, 9, 7. 5, 10, 15, 20, 8. Position Value of Term Name the next three terms in each sequence. 9. 1, 6, 11, 16, 21,,,, 10. 2, 4, 6, 8, 10,,,, _ 11. Position Value of Term The temperature was 79 F on Friday, 76 F on Saturday, and 73 F on Sunday. If this weather pattern continues, what will the temperature be on Monday? 13. Tony s Cafe sells four sizes of pizza. The first three sizes are 8 inches, 10 inches, and 12 inches. If this pattern of size continues, what is the largest size pizza the cafe sells?

2 Practice B Patterns and Sequences Identify a pattern in each arithmetic sequence and then find the missing terms. 1. 4, 8, 16, 32,,,, , 95, 90, 85,,,, _ 3. 8, 20, 32, 44,,,, 4. 6, 12, 18, 24,,,, _ Identify a pattern in each sequence. Name the missing terms. 5. Position Value of Term , 250,,, 100,, 0, 7. 1, 15,, 43, 57,, 85, 99, _ 8. 7,, 21, 28,,,, 56, 9. 9,, 13,,,, 21, 23, _ 10. Position Value of Term A forest ranger in Australia took measurements of a eucalyptus tree for the past 3 weeks. The tree was 12 inches tall the first week, 19 inches the second week, and 26 inches the third week. If this growth pattern continues, how tall will the tree be next week? 12. Maria puts the same amount of money in her savings account each month. She had $450 in the account in April, $600 in May, and $750 in June. If she continues her savings pattern, how much money will she have in the account in July?

3 CODE Practice C Patterns and Sequences Identify a pattern in each arithmetic sequence, and then find the missing terms , 17, 21, 25,,,, 2. 48, 45, 42, 39,,,, _ 3. 1,600, 800, 400, 200,,,, 4. 1, 3, 9, 27,,,, _ 5. Position Value of Term Identify a pattern in each sequence. Name the missing terms. 6. 2,,, 16, 32,, 7. 8,, 24,, 40,, 56, _ 8. Position Value of Term The sequence 1, 1, 2, 3, 5, 8, 13, is called the Fibonacci Sequence. Identify the pattern in the sequence, and name the next three terms. 10. The pattern below shows a special sequence called triangular numbers. Draw the next figure in the pattern, and name the next triangular number in the sequence

4 Review for Mastery Patterns and Sequences Find the next three numbers in the sequence. 8, 12, 16, 20, 24,,,, Step 1: Look at pairs of numbers to find the pattern. 8, 12, 16, 20,,,,, = = = 20 The pattern is to add 4. Step 2: Use the pattern to name the next three numbers = = = 36 The next three numbers are 28, 32, and 36. Find the next three numbers in each sequence. 1. 5, 8, 6, 9, 7,,, 2. 90, 80, 70, 60,,,, _ 3. 2, 8, 4, 16, 8,,,, 4. 10, 14, 18, 22,,,, _ 5. 13, 21, 29, 37,,,, 6. 24, 12, 16, 8,,,, _ 7. 14, 12,10, 8,,,, 8. 1, 7, 13, 19,,,, _ 9. 1, 3, 6, 10,,,, , 38, 36,,,, _ , 45, 36,,,, , 25, 40,,,, _ , 29, 22,,,, , 36, 72,,,, _

5 Challenge Picture Patterns Draw the next three figures in each pattern

6 Problem Solving Patterns and Sequences 1. A giant bamboo plant was 5 inches tall on Monday, 23 inches tall on Tuesday, 41 inches tall on Wednesday, and 59 inches tall on Thursday. Describe the pattern. If the pattern continues, how tall will the giant bamboo plant be on Friday, Saturday, and Sunday? 2. A scientist was studying a cell. After the second hour there were two cells. After the third hour there were four cells. After the fourth hour there were eight cells. Describe the pattern. If the pattern continues, how many cells will there be after the fifth, sixth, and seventh hour? Choose the letter for the best answer. 3. The first place prize for a sweepstakes is $8,000. The third place prize is $2,000. The fourth place prize is $1,000. The fifth place prize is $500. What is the second place prize? A $7,000 C $4,000 B $6,000 D $3, The temperature was 59 F at 3:00 A.M., 62 F at 5:00 A.M., and 65 F at 7:00 A.M. If the pattern continues, what will the temperature be at 9:00 A.M., 11:00 A.M., and 1:00 P.M.? F 66 F at 9:00 A.M., 67 F at 11:00 A.M., 68 F at 1:00 P.M. G 68 F at 9:00 A.M., 70 F at 11:00 A.M., 72 F at 1:00 P.M. H 68 F at 9:00 A.M., 71 F at 11:00 A.M., 74 F at 1:00 P.M. J 70 F at 9:00 A.M., 75 F at 11:00 A.M., 80 F at 1:00 P.M.

7 Reading Strategies Sequence When a story has several parts, such as Star Wars, you want to watch them in order, or in sequence. When a set of numbers is in order, it is called a sequence. A sequence of numbers may have a special pattern. When we talk about the pattern, each number in the sequence is called a term. Read each term of the sequence below. Note how the numbers change from one term to the next. What do you think is the pattern in this sequence? The pattern for this sequence of terms is More terms can be added to a sequence by continuing the pattern. Use this sequence to answer Exercises 1 6: What is the 3rd term in the sequence? 2. What change occurs between the 1st term and 2nd term? 3. What change occurs between the 2nd term and the 3rd term? 4. What change occurs between the 3rd term and the 4th term? 5. Write a rule to describe how to find each term in the sequence. 6. Identify the 6th, 7th, and 8th terms in this sequence.

8 Puzzles, Twisters & Teasers Have You Heard? Did you hear about the student who tried using a broken calculator to evaluate ? Complete each sequence. Use the decoder below to find the letter that corresponds to the answer for each exercise. Place each letter above it s corresponding exercise number below to complete the answer to the puzzle. 1. 3, 6, 9, 12, 2. 8, 10, 12, 14, 16, 3. 8, 16,, 32, 40, 48 4., 10, 15, 20, 25, , 16, 12, 8, 4, 6. 0, 6,, 18, 24, 30 7., 20, 18, 16, 14, , 2, 4, 8, 16, 9. 7, 14, 21,, ,, 12, 24, 48 0 = B 18 = S 5 = Y 22 = E 6 = C 24 = A 12 = O 28 = I 15 = N 32 = D He couldn t even reach

9 LESSON 1-6 Practice A 1. D 2. G 3. B 4. F 5. add 3 6. subtract 2 7.add 5 8. add , 31, , 14, ; 10; ºF inches Practice B 1. multiply by 2; 64, 128, subtract 5; 80, 75, add 12; 56, 68, add 6; 30, 36, Position Value of Term multiply by 2 6. subtract 50; 200; 150; add 14; 29; add 7; 14; 35; 42; add 2; 11; 15; 17; Position Value of Term add inches 12. $ Position Value of Term add multiply by 2; 4, 8, add 8; 16; 32; Position Value of Term multiply by 3 and then add 2 9. The next number in the sequence is the sum of the two previous numbers; 21, 34, Review for Mastery 1. 10, 8, , 40, , 16, , 30, , 53, , 6, , 4, , 31, , 21, , 32, , 18, , 70, , 8, , 288, 576 Practice C 1. add 4; 29, 33, subtract 3; 36; 33; divide by 2; 100, 50, multiply by 3; 81; 243; 729

10 Challenge The 3rd term is 2 less than the 2nd term. 4. The 4th term is 3 less than the 3rd term. 5. Subtract 1 more than you subtracted from the previous term: 1, 2, 3, and so on , 57, 50 Puzzles, Twisters and Teasers SECOND BASE Problem Solving 1. Each day the giant bamboo plant grew 18 inches. The giant bamboo plant will be 77 inches tall on Friday, 95 inches tall on Saturday, and 113 inches tall on Sunday. 2. The number of cells doubled every hour. After the fifth hour there will be 16 cells. After the sixth hour there will be 32 cells. After the seventh hour there will be 64 cells. 3. C 4. H Reading Strategies The 2nd term is one less than the 1st term.