Lesson Video: Growing Shape Patterns | Nagwa Lesson Video: Growing Shape Patterns | Nagwa

# Lesson Video: Growing Shape Patterns Mathematics

In this video, we will learn how to recognize growing patterns of shapes and find the missing shape in a growing pattern.

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### Video Transcript

Growing Shape Patterns

In this video, we’re going to learn how to recognize growing patterns of shapes and find the missing shape in a growing pattern.

This is a growing pattern. Bruno the dog is thinking about his shape biscuits. Bruno’s favorite thing to think about is food. What do you notice about the shapes in his pattern? The pattern starts with a heart shape followed by a bone shape. Next is another heart shape followed by two bone shapes. Then we have a heart followed by three bones and a heart shaped biscuit followed by four bone-shaped biscuits.

Did you notice what was happening to the number of bone-shaped biscuits each time? First, we had one bone-shaped biscuit. After the next heart, there were two bone shapes. After the third heart, there are three bones. And after the fourth heart, there are four bones. So the number of bone-shaped biscuits is increasing, or growing, each time. And that’s why this is called a growing pattern. A growing pattern is a pattern which gets bigger or grows in the same way each time.

So what’s the rule for our growing shape pattern? Well, it’s a repeating pattern with a heart shape and a bone shape. And we have to add one more bone each time. That will make Bruno very happy. We call each section of a pattern like this its terms. How could we complete this term? What would the next shape in our growing pattern be?

We know each term begins with a heart shape followed by a number of bones. And we know the rule of the pattern says that we need to add one more bone each time. One, two, three, four, five, we need five bones. There we go. We completed our growing pattern.

So far, in this video we’ve learned that a growing pattern is a pattern which gets bigger in the same way each time. The opposite of a growing pattern is a shrinking pattern. Shrinking pattern is a pattern which gets smaller in the same way each time.

Can you work out the rule for this shrinking pattern? The first term in the pattern has four triangle-shaped biscuits and one octagon biscuit. The second term has three triangle biscuits and one octagon biscuit. So it looks like the rule is to subtract one triangle biscuit each time. Let’s check. First, we had four triangle biscuits, then three, now two. The number of triangle biscuits decreases by one each time. The number of triangle biscuits is shrinking or decreasing each time.

Let’s have a go at answering some questions now where we have to find the next shape in a growing or shrinking pattern or the next term in a growing or shrinking pattern. And we’re also going to think about the rules for our growing or shrinking patterns.

What are the next three shapes?

In this question, we’re given a shape pattern. We have to find the next three shapes. We know we have to read this pattern from left to right because the missing shapes are at the end. The pattern starts with a rectangle. Then we have a triangle. Next, we have two rectangles, followed by two triangles. Then we have three rectangles, followed by our three missing shapes.

Can you tell what sort of pattern this is? This is a growing pattern. The number of each shape is growing or increasing. We start with one of each shape, then we have two of each shape, then we have three of each shape. And we know a growing pattern is a pattern which gets bigger in the same way each time. We’re adding one more of each shape each time. So we can say the rule of this pattern is to add one more rectangle and one more triangle each time.

So if we have three rectangles, we need to have three triangles. The next three shapes are three triangles. The pattern started with one rectangle and one triangle and continued by adding two rectangles and two triangles. Then we had three rectangles. And we knew we needed three more triangles. The next three shapes in this growing pattern are three triangles.

Complete the pattern.

In this question, we’re given a pattern. And we have to complete the pattern by thinking about what comes next. So let’s look more closely at the pattern to try and identify the rule. What’s changing each time? The pattern begins with one pink square. Then we have two pink squares, followed by three pink squares. This is a growing pattern. The number of pink squares is increasing or growing each time.

The rule of the pattern is to add one more pink square each time. So we need to add one more pink square. And we know that one more than three is four. We call each of the sections of this pattern the pattern’s terms. So we’ve completed the next term or the missing term in this pattern by drawing the next four pink squares.

How many stars will be in Row 10 of this pattern?

In this question, we’re given a pattern. The pattern begins in Row 1, which contains a square. In Row 2, we have a square and a star. So the difference between Row 1 and Row 2 is that we’ve added a star. In Row 3, we have a square and two stars. The number of stars is increasing by one each time. First, we had no stars, then one, then two stars. And Row 4 has a square and three stars.

We have to work out how many stars there will be in Row 10 of the pattern. If Row 1 has no stars, Row 2 has one star, Row 3 has two stars, and Row 4 has three stars, then we can say that the number of stars in each row is one less than the number of the row. Zero is one less than one, one is one less than two, and so one less than 10 is nine. There will be nine stars in Row 10 of this pattern.

What is the next shape in the pattern?

In this question, we’re given a shape pattern. And we have to find the next shape. To do this, we need to look closely at the pattern and try and figure out the rule. Each of the shapes in our pattern is like a triangle made from circles. The first shape has four circles on the bottom row or the base, three circles on the next row, then two, and one circle on the top. The next shape has three circles on the base of the bottom of the triangle. And then it has two circles on the next row and one on the top.

What’s different about these two shapes? Well, if we compare them, we can see that the number of circles on the bottom or the base of each of these triangular shapes is decreasing. We start with four, then we have one less: three. And the number of circles on the bottom row of the next shape is two. Four, three, two, one. The next shape must have one circle on the base. So the next shape in the pattern is made from just one circle.

A pattern started with this shape. It has four rows of circles. The first row has one circle. The second row has two circles. The third row has three circles. And the bottom row or the fourth row has four circles. The next shape only has three rows. It’s like the bottom row has been deleted. The next shape in the pattern has two rows. And the final shape in the pattern just has one circle or one row. We can think of this as a shrinking pattern. The number of rows and the number of circles is decreasing each time.

We found the next shape in the pattern by comparing the shapes and seeing what changed. We worked out this is a shrinking pattern. The number of rows of circles decreased each time. The missing shape in the pattern is one circle.

What have we learned in this video? We have learned how to identify and complete growing patterns. We also learned how to identify and complete shrinking patterns.