Lesson 8 — Activity 2: From Pattern to Formula
Lesson 8 — Activity 2: From Pattern to Formula
Getting Ready
Now that you know how to recognize a pattern, you can start to create formulas that allow you to show the pattern.
Try This:
Look at the pattern below. What are the next numbers in the pattern?
11, 222, 3333, 44444, 555555
6666666
If you had a chart similar to those in Activity 1, you don't really need a formula to get the answers you need. But, what if the missing information was still in the pattern but was a long way away from what you can see?
For example, what if you had the following chart with one part blank and had to fill in the blank?
As you can see, there is a definite pattern, but there is a gap in column x between 4 and 998. You could take a few pieces of paper and write out the whole pattern up to 998, but that would take you way too long!
A much easier way to complete the chart is to make a formula that will allow you to fill in the blank.
The first thing you have to do is figure out what is going on. Patterns might involve adding, subtracting, multiplying, or dividing — or possibly even a combination of two of them. In this case, notice that column y is 11 times more than column x.
This makes the formula for this pattern:
y = 11x (which means y is equal to x times 11)
Now that there is a formula, you can fill in the blank by simply putting the information into the formula:
y = 11x
y = 11(998)
y = 10,978
y = 11(998)
y = 10,978
The complete chart should look like this:
The really nice thing about having a formula for a pattern is that once you have the formula, you can figure out any point in the pattern.
What if x = 1,000,000? No problem. You would just use the formula:
1,000,000 x 11 = 11,000,000
Therefore, y = 11,000,000
Let's try another one. Take a look at the table below.
Do you see the pattern? For every hour that you drive, the distance travelled goes up by 300 kilometres. So what would your formula be?
The formula would be:
Time (hours) x 300
4 x 300 = 1,200 kilometres
If we travelled for 5 hours, the formula would be:
5 x 300 = 1,500 kilometres
Self-check!
Try this!
Create a formula that shows the pattern in the chart below.
Hint: Look at what you have to do (add, subtract, multiply, or divide to column x to get column y).
Because column y is always one more than column x, the formula is:
x + 1 = y
Now, use the formula you just made to complete the chart below.
The pattern is x + 1 = y.