Question Video: Deducing Information about Patterns Involving Shapes Mathematics

What comes next?

01:58

Video Transcript

What comes next?

We’ve been given a pattern made up of three different squares. To help us complete the pattern, first, we need to look closely. What do you notice about this pattern? Well, the first square has been divided into four equal parts. And all four parts have been shaded gray. If we look at the second square in the sequence, what’s changed? Well, we’ve still got a square which has been divided into four equal parts. But this time only three parts have been shaded gray. If we look at the third square in the sequence, we can see that this square only has two parts shaded gray. So it looks like the number of shaded parts is decreasing.

We can think of the shaded parts as triangles. The first square has four shaded triangles. Then we’ve got three, then two. So the next square in the sequence should have one shaded part or one triangle shaded.

Which of our shaded triangles should we delete? Let’s look more closely. This was our first square, and this is the first triangle which was erased or not shaded, on the left-hand side. This was the second triangle to be erased or not shaded. Which triangle should we delete next? It will be this one. This is the square that comes next. We looked closely at the pattern to see what we noticed, we worked out what changed each time, and we completed the pattern using this square.

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