Mathematics

  

3D shape and volume

This unit focuses on students' ability to visualise and conceptualise shape and space effectively. Students will develop the ability to describe and draw 3D objects from different points of view including top view, side view and front view. We will then move on to develop students understanding of how we can measure space, building on from the concepts of area and perimeter into volume. Students begin with concrete experiences with cubic cm and move into the abstract by using formulae to calculate the volumes of various rectangular prisms.

Key understandings:

• How does the shape of an object change when viewed from different sides?

• What does volume measure and how is this useful?

• How are volume and area connected?

• What is a formula and how is it connected to the concept of volume?

What are they?

How can we view them?

How does the perspective change them?

Drawing 3D shapes in two dimensions is made easier by using isometric grid paper...

Developing stronger mathematical understanding of the volume of objects is best done through problem-solving activities. The sorts of mathematical discussions involved in interpreting 3D shapes using formulae strengthen mathematical reasoning and knowledge. One such task might be to calculate how many laptops it would take to fill an empty cupboard. Establishing the volume taken up by one laptop may be found by stacking a few laptops in a drawer of known size and volume. From here, it becomes a question of measuring the cupboard and performing some calculations to work out how many drawers would fill the cupboard and then how many laptops that would be altogether.

Manipulating 3D shapes is possible on a computer using something like Google SketchUp.

Here's the Grade 5 pod...

Students may be using this tool to explore the 3 dimensions of a solid shape. This activity will reinforce the idea that we measure 3D shapes in cubic units. Alternatively, pieces of cardboard cut to the same sizes as our base ten manipulatives can be added to create interesting compound shapes where the value of the length, breadth and height dimensions can easily be seen and their relationship to overall volume clearly understood.

How perimeter and area are related...

How area and volume are related...

Next unit... Adding and subtracting fractions