Notice and wonder

Notice the house in the following picture, and wonder how you could describe it using words and numbers.

If you were describing this three-dimensional object, what mathematical language would you use?

Have you learned any words before that can help you to do this?

Record your ideas in a notebook or a method of your choice.

Task 1: Attributes of three-dimensional objects

Every three-dimensional object has some key attributes in common. There are faces, vertices, and edges.

Complete the Table of Three-Dimensional Objects: Faces, Vertices, and Edges in your notebook or using the following fillable and printable document. You can also use another method of your choice.

Check your answers by accessing the Answer Table of Three-Dimensional Objects: Faces, Vertices, and Edges printable document.

Task 2: Three-dimensional object scavenger hunt

Find or think of at least one real-life example of each of the three-dimensional objects from the Table of Three-Dimensional Objects activity you just completed. Determine what shapes are in each object. Record your ideas in a notebook or a method of your choice.

Task 3: From two-dimensional to three-dimensional

Can you determine the three-dimensional object based on the examples or descriptions?

Each example portrays a two-dimensional shape and is described as:

• a top view of the three-dimensional object
• a side view of a three-dimensional object
• or a front view of the three-dimensional object

Determine what three-dimensional object the following view represents, and create it using any method of your choice.

For example, consider the following question.

1. The following square is a top view of a three-dimensional object.
   
   
   1. What three-dimensional object could it be?
   2. Draw, create, or record a detailed description of the three-dimensional object.
   3. Is there more than one answer?

Think of what is important when representing three-dimensional objects. When answering, you must consider all objects that could have a square face. Using the chart from Task 1, we know that a cube and a square-based pyramid have at least one square face.

Could this be the top view of any objects about which you have learned? A pyramid would have to balance on its point. So, it is not a pyramid.

Maybe this is a cube, or a rectangular-based prism? A rectangular-based prism might have two square faces, or it might not.

Your turn!

Answer these questions.

Question 1: The following triangle is a front view of a three-dimensional object.

1. What three-dimensional object could it be?
2. Draw, create, or record a detailed description of the three-dimensional object.
3. Is there more than one answer?

When you are ready, press ‘Answer’ to access the solution.

Answer

Question 2: The following rectangle is a side view of an object. The height is short, and the width is about three times the length of the height.

1. What three-dimensional object could it be?
2. Draw, create, or record a detailed description of the three-dimensional object.
3. Is there more than one answer?

When you are ready, press ‘Answer’ to access the solution.

Answer

Question 3: The following triangle is a side view of a three-dimensional object. It is an isosceles triangle with equal-length sides and a shorter length base.

1. What three-dimensional object could it be?
2. Draw, create, or record a detailed description of the three-dimensional object.
3. Is there more than one answer?

When you are ready, press ‘Answer’ to access the solution.

Answer

Task 4: Nets of three-dimensional objects

Another way to represent a three-dimensional object is using a net.

For example, the following is a net of a cube.

It has six faces that are all congruent squares. If you folded along all of the black lines, this net would become a cube, and the black lines would become the edges. You can use a physical or virtual net to explore. Reflect on and answer the following questions:

1. How are an object and its net similar? How are they different?
2. What details does a net provides about a three-dimensional object?
3. When might it be useful to use a net?

Match each three-dimensional object to the corresponding net. Check your answers to see if your thinking is accurate.

Task: Design a building

Design a new convention centre for the community.

Make a plan to either build or create a digital model of your building (using nets).

Represent the top view, side view, and front view in your plan.

You can build, draw, or you can record a detailed description in a notebook or a method of your choice.

Use at least three different three-dimensional objects in your structure.

Answer the following questions:

1. What shapes did you include in your convention centre?
2. What are the attributes of each of the objects?
3. What two-dimensional shapes are in the top view, side view, and front view of your structure?
4. What strategy did you use to create the nets?

If you would like, you can complete the Designing a Building Model Activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Animation of three-dimensional shapes

You have already used at least 3 different three-dimensional objects in your structure. You may have used a rectangular-based prism, a triangular-based prism, or a square-based pyramid. Take a moment to explore the interactives. For this learning activity, don’t worry about the surface area or volume buttons. Just press 'Unfold Shape'.

Reflection questions

Reflect on and answer the following questions.

1. Describe the relationship between two-dimensional shapes and three-dimensional objects.
2. Which three-dimensional object involves the most steps to create a net?
3. What is something new you learned about three-dimensional objects?
4. What is a future job or career that you are interested in? Do you think it will require the skills used today?

Record your ideas in a notebook or a method of your choice.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Connect with a TVO Mathify tutor