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.
