Measurement and Geometry 63_Explicit Learning Plan
(Year 6) ACMMG140, NSW MA3 14MG
Construct Solid and Skeletal Models of Three-dimensional Objects.
THIS IS A SUMMARY OF THE LEARNING PLAN, DESCRIBING THE SEQUENCE OF LEARNING WHICH WILL OCCUR OVER MULTIPLE LESSONS. COMPLETE LEARNING PLAN STARTS ON THE NEXT PAGE.
Children:
Construct
solid and
skeletal
models.




Draw
models
from
different
viewpoints.

Children:
 ask one another questions about Constructing Solid and
Skeletal Models of Three-dimensional Objects, for
example:
►
How could we test this net?
►
Is this net a pyramid or a prism? How do you
know?
construct a three-dimensional object
from a net, for example,
fold to test if it is the net of a square
prism, for example,
measure and cut straws to a
corresponding length
join the straws with chenille sticks,
for example,
draw the front, side, top view of a Three-dimensional model, for
example,
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►
Are bases on prisms at opposite ends of the
prism?
►
How could we join these edges together at a
vertex, to make a skeletal model of the square
pyramid?
►
Are the flat surfaces and straight lines, faces and
edges?
►
Are the faces that are not bases, quadrilaterals?
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Measurement and Geometry 63_Explicit Learning Plan
(Year 6) ACMMG140, NSW MA3 14MG
THIS IS THE FULL LEARNING PLAN, WITH DETAILS OF ACTIONS AND QUESTIONS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Construct prisms and pyramids from plasticine, nets and connecting cubes, including from drawings of different views, identifying faces and bases then
sketch top, front and side views.
Construct skeletal models of prisms and pyramids, identifying edges and vertices.
Resources: prisms, pyramids, card, tape, straws, chenille sticks, connecting cubes, plasticine, pencil, paper
What could we do?
Children think about, talk and listen to a friend about, then have the
Focuses
opportunity to share what they already know.
children’s
thoughts on the
concept, exposing
current
understanding and
any
misconceptions.
Reviews
dimensions.
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►
Today brings an investigation about three-dimensional
objects.
►
What do you know about three-dimensional objects?
►
Talk about three-dimensional objects with a friend.
►
Is anyone ready to share what they are thinking about
three-dimensional objects?
►
We’ve been investigating three-dimensional objects.
►
And we found that they have 3 dimensions.
►
We found they go up and down, left to right, and front to
back.
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Reviews
the properties of
prisms, pyramids,
cones, cylinders
and spheres.
(Measurement
and Geometry
54)
Display some cones, cylinders and spheres, for example,
Point to the flat and curved surfaces
and curved lines.
►
We found that prisms, pyramids, cylinders, cones and
spheres are all three-dimensional objects.
►
We found that a surface on a three-dimensional object
can either be flat or curved.
►
And we found that the lines a three-dimensional object
can either be straight or curved.
►
We found that the flat and curved surfaces, with curved
lines on three-dimensional objects are just called flat or
curved surfaces, and the lines are just called curved lines.
►
We found that cones, cylinders and spheres have flat or
curved surfaces and curved lines.
►
We found that a cylinder has 2 bases, and 1 curved
surface.
►
And we found that a cone has 1 base, and 1 curved
surface.
►
And we found that a sphere 1 curved surface.
►
We found that flat surfaces and straight lines on threedimensional objects are called faces and edges.
►
And we found that a vertex is a point where 2 or more
edges meet.
►
We called three-dimensional objects with faces, edges
and vertices, prisms and pyramids.
►
We found that a prism has 2 bases, and the faces that
are not bases are quadrilaterals.
Display some prisms and pyramids, for example,
Point to the flat surfaces and
straight lines.
Point to the 2 bases and the
quadrilateral-shaped faces on prisms.
Point to the 1 base and the triangular faces on pyramids.
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Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
►
And we found that a pyramid has 1 base, and the faces
that are not bases are triangles.
►
We found that prisms and pyramids are named by the
shape of their bases.
►
We’ve investigated cross-sections on prisms and
pyramids.
►
And we found that a cross-section is a cut made parallel
to the base.
►
We found cross-sections on prisms are uniform, because
they always the same shape and size as the base.
►
We found cross-sections on pyramids are non-uniform,
because they are the same shape but different sizes to
the base.
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►
Display some prisms and pyramids, for example, cubes, square
prisms, rectangular prisms, triangular prisms, square pyramids and
triangular pyramids
►
Which of these three-dimensional objects are pyramids?
►
How do you know?
►
What are the properties of pyramids?
►
Do all pyramids have 1 base?
►
Are the faces that are not the base on all pyramids,
triangular?
What is the shape of this pyramid's base?
Is the base square?
Because the base of this pyramid is square, what is the
pyramid’s name?
Is it a square pyramid?
►
►
Display a square pyramid, for example,
►
►
►
Display a prism, for example, a square prism,
►
►
►
►
Trace the faces of the square prism onto card, for example,
►
►
►
►
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Today we’re going to investigate how we can construct
models of prisms and pyramids, identifying faces, edges
and vertices.
Which of these three-dimensional objects are prisms?
How do you know?
What are the properties of prisms?
Do all prisms have 2 bases?
Are the faces that are not bases on all prisms,
quadrilaterals?
What is the shape of this prism's base?
Is the base square?
If the base of this prism is square, what is its name?
Is it a square prism?
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Introduces
constructing nets
of prisms and
pyramids, then
testing to see if
they make the
prism or pyramid
when folded. top
Children join the faces together to make a net, then fold to see if it is
the net of a square prism again, for example,
Children identify the nets that did
make a square prism, for
example,
►
Let’s trace the faces of the square prism onto card.
►
If we join the faces together, we will have made a net.
►
Let’s join the faces together in different ways, then fold
to test to see if we have made the net of a square prism.
►
Did every net make a square prism?
►
Let’s look at the nets that did make a square prism.
►
Do the faces that are not bases need to be stuck in a
row?
►
Do the bases need to be on opposite edges of the faces
that are not bases?
►
Why?
►
Are bases on prisms at opposite ends of the prism?
►
Let’s trace the faces of the square pyramid onto card.
Display a pyramid, for example, a square pyramid,
Trace the faces of the square pyramid onto card, for example,
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Children join the faces together to make a net, then fold to see if it is
the net of a square pyramid again, for example,
►
If we join the faces together, we will have made a net.
►
Let’s join the faces together in different ways, then fold
to test to see if we have made the net of a square
pyramid.
Children identify the nets that did
make a square pyramid, for
example,
►
Did every net make a square pyramid?
►
Let’s look at the nets that did make a square pyramid.
►
Does the base need to be on the same edge of each face
that is not a base?
Allow children time now to engage in guided and independent
investigation of making nets of prisms and pyramids by tracing the
faces, cutting them out, and sticking them back together. Children
identify whether their net will make the prism / pyramid again or not,
and why.
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Introduces
constructing
skeletal models of
prisms and
pyramids. top
►
We’ve investigated constructing nest of prisms and
pyramids.
►
And we found that we are tracing the faces to construct
nets.
►
Display some prisms and pyramids, for example, cubes, square
prisms, rectangular prisms, triangular prisms, square pyramids and
triangular pyramids.
►
To do that, we need to look at the edges and vertices.
►
Which of these three-dimensional objects are prisms?
How do you know?
What are the properties of prisms?
Do all prisms have 2 bases?
Are the faces that are not bases on all prisms,
quadrilaterals?
►
►
►
►
Display a prism, for example, a square prism,
Today we're going to investigate skeletal models of
prisms and pyramids.
►
What is the shape of this prism's base?
►
Is the base square?
►
If the base of this prism is square, what is its name?
►
Is it a square prism?
Display some straws.
►
Let’s make the edges out of lengths of straw.
Children measure the length of each
edge of the square pyramid and cut
their straws the corresponding
lengths, for example,
►
What length are the edges of the bases?
►
What length are the edges of the faces that are not
bases?
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►
Have we made all of the edges of the square prism?
►
How could we describe the edges of a square prism?
►
Do we have 8 short edges and 4 long edges?
►
Do we have 12 edges altogether?
Display some chenille sticks.
►
How could we join these edges together at a vertex, to
make a skeletal model of the square pyramid?
Children place a chenille stick inside 2 straws to join them at a vertex,
for example,
►
Could we use these chenille sticks in each vertex, to join
the edges together?
Place 2 chenille sticks inside 2 straws to join them at a vertex, for
example,
►
Is one chenille stick going to allow us to make a sharp,
strong vertex?
►
Might we need to use more than 1 chenille stick?
Children may experiment to determine the optimum number of
chenille sticks to use to join edges at vertices to ensure the vertices
will remain sharp, strong and the skeletal model will keep its shape.
►
You could experiment to see how many chenille sticks
you need to make the skeletal model.
Children join their straw edges together to make an example, or a
non-example, of a skeletal model of the square prism, for example,
►
If we join the edges together, we will have made a
skeletal model.
►
Let’s join the edges together in different ways, then test
to see if we have made the skeletal model of a square
pyramid.
Allow children to describe the edges of the square prism.
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Display the skeletal models of square prisms, for example,
►
Which skeletal models are the skeletal model of a square
prism?
►
Let's place skeletal models of a square prism in a group.
►
Do the edges of the bases need to be opposite ends of
the faces?
►
Why?
►
Are bases on prisms at opposite ends of the prism?
►
What do you notice about the example of skeletal
models of square prisms?
►
Are the base edges at the ends of the face edges?
Allow children time now to engage in guided and independent
investigation of making skeletal models of prisms and pyramids by
measuring and making edges from straws and vertices from chenille
sticks. Children identify whether their skeletal model is the prism /
pyramid or not, and why.
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Reviews
►
nets and skeletal
models of prisms
and pyramids.
(Measurement
and Geometry 34,
44)
Introduces
constructing
models of prisms
from connecting
cubes, identifying
bases and faces.
►
Display a prism, for example, a square prism,
Make the square base of the square prism using connecting cubes,
for example,
Add 4 layers to the base, for example,
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We’ve investigated constructing models of prisms and
pyramids using modelling clay, nets and skeletal models.
Today we’re going to investigate constructing prisms
using connecting cubes.
►
How could we construct a square prism using connecting
cubes?
►
What shape is the base?
►
Is the base square?
►
Could we start by making a square base?
►
Could we add some layers of the base?
►
How many layers could we add?
►
Could we add 4 layers?
►
Have we constructed a square prism?
►
How many bases?
►
Are there 2 bases?
►
What shape are the bases?
►
Are the bases square?
►
What shape are the faces that are not bases?
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►
Are the faces that are not bases, quadrilaterals?
►
What prisms could we make using connecting cubes?
►
Is this a prism?
►
What are the properties of a prism?
►
Does a prism have flat surfaces and straight lines?
►
Are the flat surfaces and straight lines, faces and edges?
►
Do edges meet at a vertex?
►
Are there 2 bases?
►
Are the faces that are not bases, quadrilaterals?
►
How could we describe this prism?
►
How many faces?
►
Is there a top face, a bottom face, a front face, a back
face, a right face, a left face, and 2 more faces in each
corner?
►
Are there 2 bases and 12 faces that are not bases?
►
Are there 14 faces?
Construct a prism using connecting cubes, for example,
Allow children to identify the properties of the prism.
Allow children to count the faces, for example, top, bottom, right,
left, back, front, plus 8 more for the ‘missing’ cube at each corner.
Allow children time now to engage in guided and independent
investigation of making models of prisms using connecting cubes.
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Reviews
Display a prism, for example, a square prism,
►
drawing prisms.
(Measurement
and Geometry 34,
44)
Introduces
drawing models of
prisms from
different
viewpoints. top
►
Children draw the top view, for example,
Children draw the front view, for example,
Children draw the side view, for example,
Children draw the opposite side view, for example,
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Email: [email protected]
Twitter: @learn4teach
We’ve investigated drawing prisms and pyramids using a
viewpoint, and using isometric dot paper.
Today we’re going to investigate drawing prisms and
pyramids from different viewpoints.
►
What would this prism look like from the top?
►
From the top, would it look like a rectangle?
►
Let’s draw the top view.
►
What would this prism look like from the front?
►
From the front, would it look like a rectangle?
►
Let’s draw the front view.
►
Are the front and top views, the same?
►
Are the top and front both faces that are not bases?
►
What would this prism look like from the side?
►
From the side, would it look like a square?
►
Let’s draw the side view.
►
What would this prism look like from the opposite side?
►
From the opposite side, would it look like a square?
►
Are both side views, a base?
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Construct a prism using connecting cubes, for example,
Allow children to identify the properties of the prism.
Distribute some 1 square centimetre grid paper.
Children draw the top view on grid paper, for example,
Children draw the front view, for example,
Children draw the side view, for example,
►
Is this a prism?
►
What are the properties of a prism?
►
Does a prism have flat surfaces and straight lines?
►
Are the flat surfaces and straight lines, faces and edges?
►
Do edges meet at a vertex?
►
Are there 2 bases?
►
Are the faces that are not bases, quadrilaterals?
►
What would this prism look like from the top?
►
Let’s draw the top view.
►
What would this prism look like from the front?
►
Let’s draw the front view.
►
What would this prism look like from the side?
►
Let’s draw the side view.
►
What would this prism look like from the opposite side?
►
Let’s draw the opposite side view.
Children draw the opposite side view, for example,
Allow children time now to engage in guided and independent
investigation of making models of prisms using connecting cubes, then
drawing them from different viewpoints.
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