Teaching Sequence

Work through this resource material in the following sequence:

25 minutes – Tune In: 3D Shapes
40 minutes – Find Out: Creating 3D Shapes
45 minutes – Take Action: Analysing 3D Shapes
10 minutes – Reflection

Tune In: 3D Shapes

Step 1.

Write the Learning Intentions and Success Criteria on the board and read aloud to students.

Students will...

... understand the key features of three-dimensional shapes.
... calculate the approximate area of a two-dimensional shape using formal units.
... understand art elements and principles.

Students can...

... explain what a three-dimensional shape is.
... identify faces, surfaces, edges and vertices (corners) of a three-dimensional shape.
... explain what area is.
... use square centimetres to find an approximate measure of area.
... identify the types of lines in a model.
... discuss strategies to create balance in a mobile.

Step 2.

Watch the following video:

How to Describe 3D Shapes (https://www.youtube.com/watch?v=3-QwWFkz5hw)

Once the video is complete, invite students to share their understanding of 3D shapes, asking the questions:

What is a three-dimensional shape?
What are the features of three-dimensional shapes?
Do all three-dimensional shapes have the same features?

Step 3.

On the board, draw a range of 3D shapes that are appropriate for your class. We recommend the following:

Cube
Rectangular prism
Sphere
Square-based pyramid
Triangular prism
Cylinder
Cone
Octahedron
Icosahedron
Dodecahedron
Triangular pyramid (tetrahedron)
Pentagonal prism

Provide students with the 3D Shapes Venn Diagram sheet and explain that they will be sorting the shapes on the board into the Venn Diagram. Take one of the shapes on the board and explain how you would use the Venn Diagram to classify it. Emphasise to students that they only need to write the name of the shape into their Venn Diagrams, they do not need to draw them.

Allow time for them to sort the rest of the shapes on the board into the Venn Diagram, ensuring shape pictures and names are left displayed for students to see.

Step 4.

Invite students to share their completed 3D Shapes Venn Diagram sheet with a partner and discuss how they sorted the shapes. Encourage students to make suitable changes if they notice errors during their conversations.

Find Out: Creating 3D Shapes

Before beginning this phase of the lesson, ensure that all required materials for the construction task are available in the classroom for students to access. Students will need straws, spaghetti string and scissors as well as their pencils and erasers.

Stawbees - the kit has enough straws and connectors to support the average-sized class in a paired geometric animal sculpture challenge.
Zometool - offers students the chance to easily prototype designs and learn from mistakes while creating their 3D animals models.

Step 1.

Explain to students that they will now be making mobiles based on three-dimensional shapes such as the ones discussed. Show the following clip:

DIY Geometric Mobiles (https://www.youtube.com/watch?v=OXFTxpsvYa4)

Now, project the Making a 3D Model Step-by-Step Instructions for the remainder of this part of the lesson. This page serves as a visual reminder of the steps to make a geometric mobile.

Step 2.

Direct the class to the Student Worksheet, and read aloud the task description below, answering any questions students may have:

Your task is to create a three-dimensional shape to be placed onto a geometric mobile in your class. You may use straws, twine and scissors to create your design.

Creating your Design

A design sketch is to be completed before you make your shape. It must show:

What shape you are making.
What length each edge will be.
What colour straws you will use.
What order you will connect the straws in.

Step 3.

Direct students to the shapes you previously drew on the whiteboard as examples, emphasising that shapes with curved surfaces cannot be constructed with this method and that the shapes with a large number of faces (i.e. icosahedron and dodecahedron) would require detailed planning to work out how to construct them.

Provide students with the 3D Shapes Design Sheet and allow time for them to complete it.

Step 4.

As students complete their design sheet, check their work and allow them to move on to create their shapes. Encourage students to support and assist each other as needed if they have difficulty manipulating the straws and string.

Step 5.

Once all students have completed their shapes, invite them to form pairs to discuss their design.

Encourage students to share the following information with their partner:

What shape they made.
How many edges it has.
How many vertices it has.
What went well when constructing it.
What challenges were faced?

Take Action: Analysing 3D Shapes

Step 1.

Explain to students that now that the shapes are finished, they will be completing a more specific analysis of some of the shape features, thinking about both maths and art.

Step 2.

Show the class the following clip:

All About Lines (https://www.youtube.com/watch?v=tos2et_JEgA)

Step 3.

Once the clip has finished, invite students into a discussion about lines, asking the following questions:

What did we learn about lines from the clip?
How are lines important in our geometric mobiles?
What kinds of lines have been used in the creation of our geometric mobiles?
What part of a three-dimensional shape do the lines in our geometric mobiles represent?

Step 4.

Explain to students that they will now be reflecting on the use of line in their 3D shape constructions. Hand out and explain the 3D Shape Analysis Sheet and provide students with time to complete this task.

Note: Students only need to complete the art analysis side at this point.

Step 5.

Explain that the next step is a maths analysis. Using the 'Think-Pair-Share' approach, invite students to respond to the following question:

What is area?

When you reach the ‘Share’ stage, use the discussion to ensure students understand that area refers to the amount of flat space inside a shape and that it can be measured in centimetre squares.

Think Pair Share
Think pair share is a collaborative learning strategy in which students work together to solve a problem or answer a question.
Think - students independently think about an issue or question and record their thoughts.
Pair - students work in pairs to discuss their ideas and record new thoughts.
Share - students share their thoughts with the whole group or with other pairs to reach consensus.

Step 6.

Now show the following clip:

Find the Shaded Area of A Grid (https://www.youtube.com/watch?v=soDzRFYi6UI)

Upon completion of the clip, invite students to share new learning and respond to any questions or misunderstandings they may have.

Step 7.

Explain to students that in the next activity they will be drawing the 2D shape that forms one ‘face’ of their geometric shape, and then finding the area.

Model this process, completing the following steps:

Trace one ‘face’ of your 3D shape onto grid paper, lining up at least one edge with a straight side of the shape.
Count the number of whole squares (centimetre squares) within the shape and write it down.
Match up parts of squares that you think would form a whole square together and count them.
Note any remaining parts that cannot be combined with another.
Add the numbers of squares to work out the total area in cm².

Step 8.

Provide students with grid paper and allow time for them to complete the task, recording their findings on the maths side of the 3D Shape Analysis Sheet.

Reflection

Step 1.

Invite students into a class circle to reflect on the lesson. Provide time for each student to complete the following sentence starter:

Two new things I learnt in this lesson are...

Differentiated Learning

Extension

Construction of Shapes: Students with strong visual-spatial skills and/or a thorough understanding of shape can be encouraged to design and construct a more complex shape such as the icosahedron. Keep in mind that creating these shapes will require students to be able to visualise/create the net of the shape in order to determine how straws should be joined.

Finding Area: Students who have designed shapes with a greater number of faces (e.g. dodecahedron or icosahedron) will consequently have a variety in the fractions of centimetre squares they will need to combine to calculate the area. They will therefore have to think more specifically about the fractions of the centimetre squares.

Provisions for Learning Support

Construction of Shapes: Students who you anticipate may find the construction element of this task challenging can be encouraged to make a tetrahedron. They can re-watch the DIY video (up until 2:20) to view the steps for this shape.

Finding Area: Invite any students finding it difficult to calculate area into a focus group so that you can support them.

STEAM - Geometric Models

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Summary

Learning intentions:

Students will...

Success criteria:

Students can...

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