A pattern is a group of objects, shapes, or numbers that are arranged following a rule.
These are examples of patterns.
The patterns above are all repeating patterns. They repeat over and over.
In this lesson, let's explore a different kind of pattern, a growing pattern.
First, let's review.
The set of items in the pattern is called a sequence.
To add to the sequence, we follow a rule.
What's the rule for the sequence above?
You got it:
Rule: 2 circles then 1 star
In a repeating pattern, the same sequence is repeated over and over. The same elements repeat.
Growing patterns are different.
A growing pattern is a pattern where the rule adds an increasing number of elements with each run of the rule.
In the pattern above, we start with 1 yellow flower and 1 pink flower.
In the second sequence, we see 1 yellow flower and 2 pink flowers.
The third sequence shows 1 yellow flower and 3 pink flowers.
Can you guess what the next sequence looks like? 🤔
Very good. There will be 1 yellow flower and 4 pink flowers.
If we stack up the sequences together, we'll see that each row increases.
The pattern is growing:
And that is why it's called a growing pattern.
To work with growing patterns, we have to learn their rule.
Let's look at this pattern again.
To find the rule of a growing pattern, look at how the pattern increases as it moves from one sequence to the next.
We see that the number of yellow flowers always stays the same.
But we add 1 extra pink flower each time we make a new sequence.
Based on this, what's our rule?
Rule: If n is the number of times we're applying the rule, add n 🌸's after one 🌻.
The first time we run the rule, n is equal to 1, so we draw 1 🌸 after 1 🌻.
The second time we run the rule, n is equal to 2, so we draw 2 🌸's after 1 🌻.
The rule actually uses a variable. The variable n changes each time we run the rule.
Great job. 👏
What comes next?
To make it easier to figure this out, let's place each application of the rule in a new row.
What row comes next in the pattern?
First, we count the number of blue cars.
The next row will have 4 blue cars before the red car.
What's the rule of our pattern?
Rule: Add n × 🚙 before one 🚗, where n is the number of times you're applying the rule.
The rule is easy to see, but a bit tricky to write down.
You can think of n as the nth sequence in the pattern. So when n equals 4, you're making the 4th row of cars.
If you arrange these rows one after another, it looks like this:
Perfect! 👏 You did great in the lesson.
Now, try some practice questions.