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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
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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.
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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
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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.
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Chapter 1
Number Sense, Patterns, and Algebraic Thinking