Video: Finding the Rule for a Shape Pattern

Look at this pattern and choose the correct words to complete the rule. Rule: To get the next shape we _ squares. [A] add 1 [B] add 2 [C] add 4 [D] add 6 [E] add 8

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Video Transcript

Look at this pattern and choose the correct words to complete the rule. And the rule we’re given is “To get to the next shape we blank squares.”

In this question, we’re given a pattern of changing shapes. And we’re asked to look carefully at each shape and to come up with a rule that describes how each shape changes as we move from one to the other. And we’re given five possible ways to complete the rule. To get to the next shape, we could add one square, add two squares, add four squares, add six squares, or add eight squares.

Let’s go through the shapes one by one and see how each shape changes as we move through the pattern. Look at shapes one and two. What has changed as we move from shape one to shape two? Well, shape two still has a blue square in the centre. But it now has four orange squares, one attached to each of the four sides of the blue square. Four squares have been added.

Let’s see whether this rule continues between shape two and shape three. If we compare shapes two and three, we can see that each of the four orange squares in shape two now has another orange square added to it. And so four more orange squares have been added to the pattern. So we seem to have found our pattern.

Let’s just check shapes three and four. Shape four has four more squares that are added on each of the arms of the shape. And so our plus four pattern continues from shape one all the way through to shape four. We found our answer by looking carefully at each shape and thinking about how the design changed.

Another way to find the answer would be to count the number of squares. Let’s use this method just to check that our pattern is correct. Shape one has one square. And if we add four to that, we get five squares in shape two, which there are. And if we add four to that, we get nine squares in shape three, which there are. And if we add four to that, we get 13 squares in shape four, which there are.

And so the correct rule from our list of choices is to get to the next shape, we add four squares.

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