Video: Deducing Information about Patterns Involving Shapes

What is the next shape in the pattern?

03:36

Video Transcript

What is the next shape in the pattern?

Here we’re given three different shapes. And they follow on from each other in a pattern. Our job is to find the next shape in the pattern. What comes after these three shapes? There are lots of ways we could use to find the answer to this question. So, let’s go through a few of them.

The first way we could find the answer is to look at the actual shape made by the circles. Each set of circles makes a triangle. And the triangles get smaller each time. So, we might expect the next shape in the pattern to be a triangle too. But if the triangles are getting smaller and smaller, how can we make a triangle smaller than this? Perhaps there is a better way to find the next shape.

What if we look at how each triangle is made up? The first triangle starts with one circle on its own, then there’s a row of two, a row of three circles, and finally a row of four circles. The second triangle again begins with a row of one, then a row of two, but this time, we stop at a row of three. And the final shape only has a row of one and a row of two.

So, there are four rows in the first triangle, three rows in the second triangle, and two rows in the last triangle. The next shape in the pattern must only have one row. In other words, we’d expect it to only have one circle. Doesn’t look like a triangle at all really, but it is the next shape in the pattern.

Another way we can tell that this is the next shape in the pattern is by looking at the total number of circles that each shape contains. As we’ve already seen, the first shape contains a row four, a row of three, a row of two, and one at the top. Four plus three equals seven plus two equals nine and then plus one more equals 10. There are 10 circles in the first shape.

The second shape contains a row of three, a row of two, and one at the top. Three add two equals five plus one equals six circles altogether. So, how do we get from 10 to six? We take away four. And if we look at the triangles, we know that these are the four circles on the bottom row.

We know the next shape in the pattern has a row of two and a row of one. So, that’s three circles altogether. And how do we get from six to three? We take away three. And of course, if we look at the diagram, we can see that those are three circles on the bottom row.

The number of circles decreases by four between the first two shapes, then by three. So, how do we expect it to decrease between the last two shapes? We’d expect the number of circles used to go down by two. And three take away two equals one.

So, there are lots of different ways we could look at this question. We could look at how the shapes change, the number in each row change, and also the total number of circles altogether change. But the answer will always be the same. The next shape in the pattern is one circle on its own.

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