In this checkpoint, we’ll go through shape patterns first and then symmetry.

Shape patterns

In mathematics, shapes can form patterns. In doing so, through mathematics we can find patterns that hold to find the nth line etc…. To do this you need to:

• Look at the image.
• See if any visual patterns can be detected. Look at (a) number of sides, any increments and how much it is changing by, isolate what’s changing or constant and then express it as a simple pattern.

Let's do this with each of the following images (watch video explanation):

Symmetry

Symmetry means that one shape becomes exactly like another when you move it in some way (turn, flip or slide).

For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first so for example, facing away. Symmetry is the same as a 'mirror image'. If an image is not symmetrical, it is called asymmetric.

Why is symmetry important?

It can help you calculate mathematical problems.

How?

• Calculate one side (one half of the symmetrical image).
• The other side is equal to the 1st part.
• To get to the total, you just have to multiply (x 2) by 2.

Let me illustrate with the following examples below (see video explanation).

Example Question/s

Watch video for explanation of the following question/s:

The next 3 questions refer to the following information:

A cube has 6 faces with numbers of 1 to 6. The hidden corner is H.

Face 1 and 3 are opposites, face 2 and 4 are opposites as well as 5 and 6.

The cube can be rolled over an edge. If it is rolled over edge AB, face 3 will be at the bottom.

The corner labels are retained after rolling.

Viewer's position stay as it is initially.

Given the starting position above, if the cube is rolled over AB, then rolled over CB, which face is at the bottom?

A 1 B 2 C 3 D 4

The cube was rolled once that resulted to the figure below:

What edge had the cube rolled over?

A AB B CD C EF D GH

The cube was rolled over edge AH, and then rolled over an unknown edge again. Given the final position of the cube below, what edge had the cube rolled over after AH?

A EH B AB C BG D AD

Key Rules to remember:

• Look visually to find the pattern. In particular, pay attention to the number of sides, increments (increasing by?), isolate what's increasing, stable etc… and then express it as a simple pattern.
• Use the power of symmetry – to get the total x 2

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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