Measurement and Geometry 54_Guided and Independent Investigations
(Year 5) ACMMG111, NSW MA3 14MG
Properties of three-dimensional objects, sections and cross-sections.
GUIDED INVESTIGATION
Children learn
how to investigate the concept by following teacher’s instructions until they are
ready to investigate the concept independently.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their
current level of understanding informing both themselves and the teacher of their current
level of understanding
Resources: prisms, pyramids, modelling clay (plasticine, not play dough), plastic knife or fishing line, pencil, paper
What could we do?
Children:
1. sit in pairs
2. construct prisms and pyramids from
modelling clay as guided by the teacher
3. describe the prism's or pyramid's
base/s and faces
4. cut and describe a section from the
prism or pyramid
5. cut and describe a cross-section from
the prism or pyramid
6. record and label the prism or pyramid
and the sections and cross-sections
7. identify whether the cross-sections are
uniform or non-uniform and why
What language could we use to ask
questions and explain?
What could we do?
 How could we construct a prism
or pyramid from this modelling
clay?
 Is this a prism or a pyramid?
 How could we cut a section from
this prism / pyramid?
 What shape is the section / crosssection?
 Is this a cross-section?
 Is the cross-section the same size
as the base/s?
 Is this a uniform or non-uniform
cross-section?
 Why?
REFLECTION Before, during and after lessons,
children discuss then record responses to reflection
questions to inform themselves and the teacher of their
current level of understanding
•
•
•
•
•
What language could we use
to explain?
Children:
 I constructed a prism /
1. sit in pairs or small groups
pyramid by …
2. construct prisms and pyramids from
 I cut a section from the
modelling clay that are neither too easy nor
prism / pyramid
too challenging
 The shape of the section
3. describe the prism's or pyramid's base/s and
is ...
faces
 This is / is not a cross4. cut and describe a section from the prism or
section because ...
pyramid
 The cross-section is / is
5. cut and describe a cross-section from the
not the same size as the
prism or pyramid
base/s
6. record and label the prism or pyramid and
 This cross-section is
the sections and cross-sections
uniform / non-uniform
7. identify whether the cross-sections are
because ...
uniform or non-uniform and why
What is a three-dimensional object?
• What is a uniform cross-section?
What is a prism?
• What is a non-uniform cross-section?
What is a pyramid?
• Why do prisms have uniform cross-sections?
What is a section?
• Why do pyramids have non-uniform crossWhat is a cross-section?
sections?
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Email: [email protected]
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1
CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative assessment
data for both the child and the teacher.
‘Doing’ mathematics is not enough and is not a good indicator of understanding.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,

In pairs, children each construct the same prism from modelling clay, for example, a square prism. They identify and describe the
properties of the square prism, for example, 6 faces including 2 bases, faces that aren’t bases are quadrilaterals, bases are
squares. One child cuts sections from their square prism. The other child cuts cross-sections from their square prism. They each
describe the sections and the cross-sections, identifying that cross-sections are cut parallel to the bases, and therefore are the
same shape and size as the bases. They identify the cross-sections of the prism are uniform because they are the same shape and
size as the bases.

In pairs, children each construct the same pyramid from modelling clay, for example, a square pyramid. They identify and
describe the properties of the square pyramid, for example, 5 faces including 1 base, faces that aren’t bases are triangles, base is
squares. One child uses a plastic knife or fishing line to cut sections from their square pyramid. The other child uses a plastic knife
or fishing line to cut cross-sections from their square pyramid. They each describe the sections and the cross-sections, identifying
that cross-sections are cut parallel to the bases, and therefore are the same shape. They identify the cross-sections of the
pyramid are non-uniform because they are the same shape but different sizes to the base.
In pairs, children have transparent fill-able containers in the shape of prisms and pyramids and coloured water. They pour in a
small quantity of the coloured water and tilt the container to make a section or cross-section. They record the section or crosssection, identifying that the cross-section is parallel to the base.

Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Investigating Sections and Cross-sections of Prisms and Pyramids
MEASUREMENT AND GEOMETRY 54 Describe the properties of prisms and pyramids, identifying that prisms have 2
bases and their faces that are not bases are quadrilaterals and pyramids have 1 base and their faces that are not bases
are triangles, explaining that prisms and pyramids are named by the shape of their base/s, Identify sections and crosssections on prisms and pyramids, identifying cross-sections are parallel to the base/s and prisms have uniform crosssections and prisms have non-uniform cross-sections
Sit with a friend.
Each of you construct the same prism from modelling clay, for example, a square prism.
Identify and describe the properties of the prism, for example, 6 faces including 2 bases, faces that
aren’t bases are quadrilaterals, bases are squares.
One of you cut sections from your square prism while your friend cut cross-sections from their
square prism.
Describe the sections and the cross-sections, identifying that cross-sections are cut parallel to the
bases, and therefore are the same shape and size as the bases.
Identify the cross-sections of the prism are uniform because they are the same shape and size as
the bases.
http://www.alearningplace.com.au
Investigating Sections and Cross-sections of Prisms and Pyramids
MEASUREMENT AND GEOMETRY 54 Describe the properties of prisms and pyramids, identifying that prisms have 2
bases and their faces that are not bases are quadrilaterals and pyramids have 1 base and their faces that are not bases
are triangles, explaining that prisms and pyramids are named by the shape of their base/s, Identify sections and crosssections on prisms and pyramids, identifying cross-sections are parallel to the base/s and prisms have uniform crosssections and prisms have non-uniform cross-sections
Sit with a friend.
Each of you construct the same pyramid from modelling clay, for example, a square pyramid.
Identify and describe the properties of the square pyramid, for example, 5 faces including 1 base,
faces that aren’t the base are triangles, base is square.
One of you cut sections from your square pyramid while your friend cut cross-sections from their
square pyramid.
Describe the sections and the cross-sections, identifying that cross-sections are cut parallel to the
bases, and therefore are the same shape as the base.
Identify the cross-sections of the pyramid are non-uniform because they are the same shape as
the base but different sizes.
http://www.alearningplace.com.au
Investigating Sections and Cross-sections of Prisms and Pyramids
MEASUREMENT AND GEOMETRY 54 Describe the properties of prisms and pyramids, identifying that prisms have 2
bases and their faces that are not bases are quadrilaterals and pyramids have 1 base and their faces that are not bases
are triangles, explaining that prisms and pyramids are named by the shape of their base/s, Identify sections and crosssections on prisms and pyramids, identifying cross-sections are parallel to the base/s and prisms have uniform crosssections and prisms have non-uniform cross-sections
Sit with a friend.
Have transparent fill-able containers in the shape of prisms and pyramids and coloured water.
Pour in a small quantity of the coloured water and tilt the container to make a section or crosssection.
Record the section or cross-section, identifying that the cross-section is parallel to the base.
http://www.alearningplace.com.au