In this checkpoint, we’ll go through an interesting area in thinking skills that involves shapes, both 2D and 3D. These questions are typically in thinking skills questions, some abstract reasoning questions and even some mathematics questions.

With 2D shapes, we look at rearrangements – that is, given certain shapes, how to we go about making other shapes and also dissecting which shapes make up larger shapes.

With 3D shapes, we’ll look at three things:

• Views – that’s how a certain 3D shapes looks “2D”
• Perspective – the different “2D” ways a 3D shape can look depending on the perspective of the viewer e.g., front, side, top, bottom, angle.
• Nets – how a flat 2D net can make a 3D shape and conversely, what a 3D shape would look like if its surface area was reduced to a flat surface.

Given this, this checkpoint is split into three parts:

1. 2D Shapes: Arrangements
2. 3D Shapes: Nets
3. 3D Shapes: Views & Perspectives

So, let’s get into it!

PART 1 – 2D Shapes: Arrangements

2D Shapes and Arrangements

Smaller shapes can be used to make larger shapes and knowing how shapes can fit together can help you answer questions that ask you to identify arrangements that can or cannot be made from certain shapes. Let’s look at the basic line cuts and see what kind of shapes would fit together and what composite shapes could be made (watch video for full discussion).

Additionally, you also need to know about:

• Rotations - Essentially, you’re looking for ‘invisible’ multiple points where at each point, the shape has been rotated by a given degree (see images below and watch video for explanation).
• Stacks and/or flips – a flip is when the image is reflected on an invisible axis that could be horizontal, vertical or even a diagonal. A stack is when multiple layers are piled on top of each other and then flipped. In a flip, what you see is the reverse e.g., left to right (in the case of a horizontal flip and top becomes bottom in a vertical flip. With a stack, what you see on the top is now at the bottom (see images below and watch video for explanation).

Rotation

Underdark / CC BY-SA

Lukas Stockner / CC BY-SA

Stacks and flips

How to answer questions with 2D Shapes and Arrangements

As questions with 2D shapes can vary, here is guidance on how to approach them:

1. Look at the requirement – is there a requirement to rotate or flip? If so, draw arrows to do so. Is there a requirement to find arrangements? If so, then work to split the arranged images.
2. When you have questions to find an arrangement, people naturally tend to ‘build up’ but this is a longer process and is often fraught with risks. The easier thing to do is to split up the composed image, this allows you to ‘chip away’ and makes it easier (and quicker) to get to the right answer. Remember your common combinations and how angles can slot together from the first video.
3. Select your answer.

The common errors people make with these questions is

• Not following the process (splitting) and assuming just because a composite shape doesn’t ‘look like’ any of its parts, that it would not be the answer.
• Interpreting the wording incorrectly or not following certain instructions such as neglecting to “flip”.

Let’s see it in action now with a worked example.

Example Question/s

Watch video for explanation of the following question/s:

Key Rules to remember

• If the image is flipped horizontally (on a vertical axis), what is left in the original image is then on the right in the mirror image, and vice versa (see image “Horizontal Flip”).
• If the image is flipped vertically (on a horizontal axis), what is at the top in the original image is then on the bottom in the mirror image, and vice versa (see image “Vertical Flip”).
• In stacks, if a stack is flipped, you’ll inherit the rules from flips (see previous checkpoint). Then you’ll also need to do a secondary step and organise the layers based on visibility. Being (1) The original bottom layer is now at the top and is the most visible. This means that if your bottom layer is opaque, then you won’t see anything else (layers beneath) and (2) The original top layer is now at the bottom and is the least visible.
• Split up composition shapes rather than ‘building up’ as that takes longer and can be prone to more error.

PART 2 – 3D Shapes: Nets

What are nets?

A net is the ‘cut out’ 2D shape that if put together, will make a 3D shape. Nets are important as they are the surface area of a 3D shape and knowing nets will help you to better understand views and perspective of 3D shapes.

There’s nothing better than learning by doing, so get out a pen and paper – we’re going to construct the nets ourselves for the following 3D shapes (see video for full discussion).

As you can see, there can be various types of nets for the same shape. Additionally, when looking at 3D shapes, you should also consider that rotation can have additional dimension. It’s just not around 1 point, it can rotate on an axis, much like the Earth but there are other types of rotation to consider—vertical, diagonal or horizontal (which makes things a bit more complicated).

How to answer questions with nets

Questions involving nets usually ask students to identify the net belonging to the shape or isolate out the incorrect net. These questions test student’s ability to envisage what the 3D shape would look like given a net and this is usually made easier if you understand what common 3D shapes look like. Here’s guidance on how to approach questions involving nets:

1. Read the requirement – if asked to find the net (you could work backwards or forwards – whichever works best for you).
2. Match up parts between the net and the same by considering dimensions – look at angles (are they the right ones or in the right place), size of pieces in relation to others and their placement (left, right, top, bottom) – and relate these to your understanding of nets of common shapes.
3. Anchor a point to be at the bottom (or a static point) where you can reconstruct your net. This allows you to piece it together and visualise what it would look like if it were ‘formed’.

Let’s see it in action now with a worked example.

Example Question/s

Watch video for explanation of the following question/s:

Which of the following nets can be folded to make an open box?

A. Net 1 only
B. Nets 1 and 2 only
C. Nets 2 and 4 only
D. Nets 1 and 4 only

Key Rules to remember

• Familiarise yourself with common nets – this allows you to recognise common shapes if they appear in an exam.
• Consider dimensions such as angles, sizes and placement.
• You can work backwards or forwards – deconstruct a 3D piece or build up a 2D piece, whichever you feel most comfortable with but remember to start with an anchor point.

PART 3 – 3D Shapes: Views & Perspectives

Views and Perspectives

Well done! You’re now at the final part of this checkpoint. Building on our learning of 3D shapes, we’re now going to look at views and perspectives.

Why? Because questions involving how certain shapes will appear when viewed in a particular angle are not uncommon in ‘thinking skills’ exams (and in some abstract reasoning and in some mathematical reasoning questions too!).

So, let’s have a look at what the ‘view’ from different perspectives (top, side [left, right], front, bottom) would be like for the following shapes (see video for full discussion):

How to answer questions involving perspective and views

While every view/perspective question is different, here is general guidance you can follow.

1. Look at the requirement and figure out how you could approach it in the easiest way – comparison of spacing, size, shape etc…. Is there a pre-existing pattern or shape you could consider or use?
2. See if you can eliminate any from the start to ‘zoom in’ and save time.
3. Regardless of the shape, the view takes the widest outline first and then what is closest. Know where your view is: front, side (left or right?), top, bottom.
4. Look at spacing between items – what gaps are large or small in comparison.
5. Know your directions: north, south, east, west or NESW in clockwise order.
6. Select your answer.

Let’s see it in action now with a worked example.

Example Question/s

Watch video for explanation of the following question/s:

A university wants to install a set of modern sculptures (see image of sculptures in colour).

A person in the helicopter is drawing a set of shapes to represent what she is seeing from up there. She has drawn the images accurately. Which one these is her drawing?

Key Rules to remember

• Regardless of the shape, the view takes the widest outline first and then what is closest. Know where your view is: front, side (left or right?), top, bottom.
• Look at spacing between items – what gaps are large or small in comparison.
• Know your directions: north, south, east, west or NESW in clockwise order.

Practice time!

Now, it's your turn to practice.

Here’s a thought experiment #17.

Remember, there is no formal answer and this experiment is provided to help stimulate your creativity and critical thinking (a ‘thought experiment’ is provided at the end of every checkpoint except checkpoint 18).

Thought experiment 17:

There is a lot of emphasis on schools. Does going to a perceived ‘good’ school ensure future success in life? What would qualify a school to be considered ‘good’?

Take your time to work through this thought experiment as it is not assessed and provided to help develop your deeper thinking skills. Think about various components of the question. What questions will you ask yourself and how do you answer your questions?

Now, let’s turn to the checkpoint questions.

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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