Lesson 7 — Activity 1: Identifying Patterns
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Lesson 7 — Activity 1: Identifying Patterns
Getting Ready
Have a look at the picture below.
It shows the same tree in each of the four seasons. Each year the tree may look similar in each of the seasons. We could say that the seasons follow a pattern.
Patterns exist in nature and in everyday life. Patterns occur over and over again; patterns show relationships.
Try This:
Can you think of some examples of patterns that occur in everyday life?
Remember, it must be something that happens over and over again. (You may recall some examples of patterns that were given in the Math in Real Life video you watched at the beginning of this course.)
Some examples may include:
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construction materials, everything from walls to roadways; in walls, roofs, and doors
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days of the week or months of the year
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growth of plants
These are just a few examples, you may have thought of different ones.
You will find a lot of patterns in math as well.
When you have a number pattern in math, it means that the numbers in a group follow a specific rule that allows one number to work with the next number. This may sound complicated, but it isn't.
If you have the numbers 2, 4, 6, 8, you have a pattern. This is a pattern because you add 2 to each number to get the next number. Knowing that, you can figure out what the next number is. All you have to do is add 2 to the last number.
8 + 2 = 10
The next number in the pattern is 10.
8 + 2 = 10
The next number in the pattern is 10.
What would be the next number in the pattern? Again, add 2 to the last number.
(The next number would be 12.)
It is important to note that not all groups of numbers follow a pattern. For example, the numbers 1, 3, 9, 10, 11 follow no pattern. However, it is important to look and see if you can find a pattern in a group of numbers.
It may involve adding, subtracting, multiplying, or dividing to get the next number in the pattern. You have to try each method before you can decide whether you have a pattern or not.
Watch this video on different types of patterns. Pay special attention to patterns 1, 2, and 4 as they are similar to what you will be working with in the remainder of this activity. Pattern 3 is more complex than you will be dealing with but it is there so that you can see that patterns can be very complicated.
Notice that there were three things that were done in the video that helped to identify the type of pattern that was present.
1. See if you can subtract each pair of consecutive numbers and get the same answer. If you can, you have a simple addition pattern (example 1 in the video). This is also known as an arithmetic sequence.
For example, if you have the pattern 5, 10, 15, 20 and want to know the next number in the pattern, you check like this:
- 10 – 5 = 5
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15 – 10 = 5
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20 – 15 = 5
Notice that the difference between each group of numbers is 5. That
makes this pattern an arithmetic sequence. To find the next number you
simply add 5 to 20.
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20 + 5 = 25
The next number in the pattern is 25.
2. If you do not have a consistent difference between the numbers, see if there is a pattern to the differences (example 4 in the video).
For example, if you have the pattern 2, 4, 7, 11 and want to know the next number in the pattern, you check like this:
- 4 – 2 = 2
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7 – 4 = 3
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11 – 7 = 4
Notice that the difference between each group of numbers increases by 1. This means that the next number has to be 5 more than the last number.
- 11 + 5 = 16
The next number in the pattern is 16.
3. If neither of the above patterns is visible, try dividing each group of numbers. If you come up with a constant answer, you know you have a geometric sequence (example 2 in the video).
For example, if you have the pattern 2, 4, 8, 16 and want to know the next number in the pattern, you check like this:
- 4 ÷ 2 = 2
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8 ÷ 4 = 2
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16 ÷ 8 = 2
Notice that the answer is 2. This means that to get the next number
in the pattern, you have to multiply the last number by 2.
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16 x 2 = 32