Year Five - Thinking in Cubes
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About this Big Idea
In this Big Idea students explore volume and representations of three-dimensional shapes. Students use blocks to explore shapes and two-dimensional representations of these as they solve problems.
Understanding Goals:
Students will understand:
- relationships between two-dimensional and three-dimensional shapes.
- multiple representations of three-dimensional objects.
- the concept of volume as it applies to rectangular solids
Background:
In geometry, a three-dimensional object is called a solid. The three-dimensional object may in fact be hollow, but it is still defined as a geometrical solid.
Core Content from the Syllabus:
Working Mathematically
Three Dimensional Shapes
- visualise and sketch three-dimensional objects from different views, including top, front and side views
- show simple perspective in drawings by showing depth
- create prisms and pyramids using a variety of materials, eg plasticine, paper or cardboard nets, connecting cubes
- construct three-dimensional models of prisms and pyramids and sketch the front, side and top views
- describe to another student how to construct or draw a three-dimensional object (Communicating)
- construct three-dimensional models of prisms and pyramids, given drawings of different views
- recognise that the order of coordinates is important when locating points on the number plane, eg (2, 3) is a location different from (3, 2) (Communicating)
Volume
- measure the volumes of rectangular containers by packing them with cubic-centimetre blocks
- explain the advantages and disadvantages of using cubic-centimetre blocks as a unit to measure volume (Communicating, Reasoning)
- describe arrangements of cubic-centimetre blocks in containers in terms of layers, eg 5 layers of 8 cubic-centimetre blocks (Problem Solving)
- recognise the need for a formal unit larger than the cubic centimetre • construct and use the cubic metre as a unit to measure larger volumes
- explain why volume is measured in cubic metres in certain situations, eg wood bark, soil, concrete (Communicating, Reasoning)
Language:
- object, shape, three- dimensional object (3D object), prism, cube, pyramid, base, uniform cross-section, face, edge, vertex (vertices), top view, front view, side view, net
- capacity, container, volume, layers, cubic centimetre, cubic metre, measure, estimate. Note: The abbreviation m3 is read as 'cubic metre(s)' and not 'metre(s) cubed'.
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students build connections between two- and three-dimensional representations of solids by using views of a rectangular solid to construct a model with cubes. Students investigate what the inside looks like and compare results. - See page 25
Questions for reflection:
- How did you figure out how to build your solid? What did you have to think about?
- How are the insides of our solids similar? Different? Why?
- What surprised you about building rectangular solids from cubes and views?
Play
Students use multiple views of block towers to construct cities of cubes that match those views. Students learn that the number of cubes used to build the city is its volume, and develop their own City of Cubes puzzles, which support students in learning how to record complex three-dimensional figures on paper and interpret those representations. - See page 61
Questions for reflection:
- Is there more than one way to build a city that matches the views given? If there is more than one way, what is the fewest number of cubes it could take to build it? What is the greatest number of cubes you could use to build it?
- What was challenging about making your own? What was challenging about creating the drawings? How did you address these challenges?
- What makes a city hard to build? What images make it easier to build?
- What strategies did you use? How did you figure out the volume of the city?
Investigate
Students investigate the volume of rectangular solids by packing little boxes into larger boxes of their own design, while trying to minimize the volume of empty space. - See page 67
Questions for reflection:
- What are the dimensions of your box? What is its volume? How much empty space will be left in your box?
- What strategies did you come up with for minimizing the empty space? How can we be sure that we, as a class, have found the smallest packing box possible?
- What interesting things did you discover when trying to pack boxes?
- How does thinking about volume help you design a packing box?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
