MEASUREMENT AND GEOMETRY 35_INVESTIGATIONS AND REFLECTIONS
(Year 3) ACMMG061, NSW MA2 11MG
Measure volume and capacity in cubic centimetres, millilitres and litres.
GUIDED AND INDEPENDENT INVESTIGATIONS and REFLECTION
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.
Children investigate and explain independently over many lessons at just beyond their current level of understanding, informing
both themselves and the teacher of their current level of understanding. It is during independent investigation that deep understanding and
metalanguage develops.
As they investigate, allow children to experience confusion (problematic knowledge) and to make
deep understanding, If children knew what it was they were doing, it wouldn’t be called learning!
mistakes to develop resilience and
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Children DISCUSS then RECORD their response to the REFLECTION question.
Teaching Segment and Video 1:
Cubic centimetre.
These investigations and reflections are directly linked to Explicit Teaching, and also appear on the Explicit Teaching Plan. Instructions for
students appear on this PDF, on the corresponding Video and on the Explicit Teaching PowerPoint.
 In pairs, children draw a metric length chart, for example,
They draw a line 1 centimetre in length. They explain their line has one dimension – left to right.
They add a second dimension, to draw a square with dimensions 1 centimetre, explaining its a square centimetre.
They explain their square has two dimensions – left to right, and up and down. They add a third dimension, to draw
a cube with dimensions 1 centimetre, explaining it is a cubic centimetre.
They explain their cube has three
dimensions - left to right, and up and down, and front to back. They explain that their unit to measure length has
been turned into a square to measure area, and then turned into a cube to measure volume and capacity.
Reflection: How are metric cubic units to measure volume and capacity related to metric length and area units?
What is a cubic centimetre?
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1
Teaching Segment and Video 2:
Models in cubic centimetres.
Volume and capacity of objects
with faces and edges in cubic
centimetres.
Teaching Segment and Video 3:
Litre and millilitre.
Teaching Segment and Video 4:
Volume and capacity in
millilitres.
Volume and capacity in litres and
millilitres.
 In pairs, children use cubic centimetres to make models. They work out the volume of their model. They record
their models and their model’s volume. Reflection: How can we measure volume and capacity in cubic
centimetres?
 In pairs, children investigate how many cubic centimetres can be packed in rows and layers into a small box.
Children record the box packed with cubic centimetres in rows and layers Children then work out the number of
cubic centimetres in each layer and the number of layers to work out the volume and capacity of the box.
Reflection: How can we measure volume and capacity in cubic centimetres?
 In pairs, children select a litre jug. They record a unit of measurement, litre.
 They divide their litre by 10, and record decilitre.
They identify that if they multiply their decilitre by 10, they will have a litre.
 They divide their decilitre by 10, and record centilitre.
They identify that if they multiply their centilitre by 10, they will have a decilitre.
 They divide their centilitre by 10, and record millilitre.
They identify that if they multiply their millilitre by 10, they will have a centilitre.
Reflection: How is metric measurement for measuring volume and capacity in liquid units related to multiplicative
place value? What is a litre? What is a millilitre?
 In pairs or small groups, children use a measuring jug to measure the capacities of small containers (less than 1
litre) in millilitres. They fill the container to capacity with water, then measure the volume of water. They label the
container's capacity in millilitres. Reflection: How can we measure volume and capacity in millilitres?
 In pairs or small groups, children use a measuring jug to measure the capacities of large containers (more than 1
litre) in litres and millilitres. Measure the volume of water, by either: pouring the water into the measuring jug to 1
litre, emptying the measuring jug, then pouring the remaining water from the container into the measuring jug.
Adding the volumes of water together. OR filling the measuring jug to 1 litre, pouring the 1 litre of water into the
container, filling the measuring jug to 1 litre again, pouring water from the measuring jug into the container until it
is filled to capacity. Subtracting the volume of water left in the measuring jug from 1 litre to work out the volume
poured into the container. Adding the volumes of water poured into the container together. They label each
container's capacity in litres and millilitres. Reflection: How can we measure volume and capacity in litres and
millilitres?
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Email: [email protected]
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More investigations.
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
Compare and order models.
 In groups of 3, children each use cubic centimetres to each make a model. They each work out the volume of their
model. They compare the models, placing them in order of volume. They explain that if model A has a smaller
volume than model B, and model B has a smaller volume than model C, then model A also has a smaller volume
then model C. They explain that if model C has a greater volume than model B, and model B has a greater volume
than model A, then model C also has a greater volume then model A. They each record the models and their
volumes. Reflection: How can we measure, compare and order volume and capacity in cubic centimetres?
Same volume, different models.
 In pairs, children use the same number of cubic centimetres to each make a model. They swap models and each
work out the volume of one of their partner's model. They compare the models, identifying that different models
can have the same volume. They each record all three models and their volumes. Reflection: Can different models
have the same volume?
Computer generated threedimensional models in cubic
centimetres.
 Children use a computer program, for example, Microsoft Word, to construct two-dimensional representations of
three-dimensional models using cubic units. Reflection: How can we measure volume and capacity in cubic
centimetres?
Compare and order capacities.
 In pairs or small groups, children use a measuring jug to measure the capacities of small containers (less than 1
litre) in millilitres. They fill the container to capacity with water, then measure the volume of water. They label
each container's capacity in millilitres, and place them in order of capacity. They explain that if container A has a
smaller capacity than container B, and container B has a smaller capacity than container C, then container A also
has a smaller capacity then container C. They explain that if container C has a greater capacity than container B,
and container B has a greater capacity than container A, then container C also has a greater capacity then
container A. Reflection: How can we measure volume and capacity in millilitres?
Same volume and capacity,
different dimensions.
 In pairs or small groups, children use a measuring jug to measure the capacities of containers with the same
volume but different dimensions, for example, margarine containers. They fill the container to capacity with water,
then measure the volume of water. They label each container's capacity in millilitres, identifying that a container
may have the same volume but different dimensions. Reflection: Can different containers have the same capacity?
Short and wide, tall and narrow.
 In pairs, children select 2 containers – one short and wide, one tall and narrow. They predict which container will
have greater capacity, then measure their capacities. Reflection: Can different containers have the same capacity?
 Children investigate containers at home with capacities measured in millilitres and litres. (European and Arabic
liquid bottles and containers are often measured in centilitres - cL)
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PROBLEM SOLVING directly linked to explicit teaching, investigations and reflections
Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort
– that’s why they’re called problems!
Problems are designed to develop and use higher order thinking. Allowing children to grapple with problems, providing minimal
support by asking strategic questions, is key. Differentiating problems allows children to solve simpler problems, before solving
more complex problems on a concept.
Problems may not always be solved the first time they are presented – or at all. The focus of problem solving is the development
of problem solving understanding and capacity – not mastery! Returning to a problem after further learning, develops both
resilience and increased confidence as children take the necessary time and input the necessary effort.
After solving problems, children also create their own problems.
Create 3 levels of a problem. GUIDE children through the first level using the problem solving steps. Allow children to investigate the second level
with friends, with minimal guidance. Allow children to investigate the third level INDEPENDENTly. Children create their own problem.
These problems are directly linked to Explicit Teaching, are embedded in the Explicit Teaching Plan, and appear on the Explicit Teaching PowerPoint.
These, and more problems, appear as blackline masters on the Problem Solving PDF and are differentiated on the Problem Solving PowerPoint.
Teaching Segment and Video 1:
Cubic centimetre
Teaching Segment and Video 2:
Model
Box
Teaching Segment and Video 3:
Litre and millilitre
Teaching Segment and Video 4:
Volume and capacity in millilitres

Annie constructed a cube where each dimension was 1 centimetre long. What is the volume of Annie’s cube?
(1 cubic centimetre)

What is the volume of this model?

What is the capacity of the box?

Annie filled a measuring jug with water to 1 litre. How many millilitres of water does Annie have?
(1000 millilitres)

Jody filled a container to capacity with water.
She poured water into a measuring jug.
What was the capacity of the container? (600 millilitres)
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Email: [email protected]
Twitter: @learn4teach
= 1 cubic centimetre (5 cubic centimetres)
= 1 cubic centimetre
YouTube: A Learning Place A Teaching Place
(20 cubic centimetres)
Facebook: A Learning Place
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Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Draw a metric measurement chart for length.
Draw a line 1 centimetre in length.
How many dimensions does your line have?
Add a second dimension, to draw a square with dimensions 1 centimetre.
What is the area of your square?
How many dimensions does your square have?
How has your 1 centimetre line been turned into a square centimetre to measure
area?
Add a third dimension, to draw a cube with dimensions 1 centimetre.
What is the volume of your cube?
How many dimensions does your cube have?
How has your 1 square centimetre been turned into a cube to measure volume and
capacity?
Reflection: How are metric cubic units to measure volume and capacity related to
metric length and area units? What is a cubic centimetre?
Problem Solving
Annie constructed a cube where each dimension was
1 centimetre long.
What is the volume of Annie’s cube?
Hint: Change the volume, and allow children to solve again!
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Use cubic centimetres to make a model, for example,
Work out the volume of your model by counting the cubic centimetres.
Record both model and its volume.
Reflection: How can we measure volume and capacity in cubic centimetres?
Problem Solving
What is the volume of this model?
= 1 cubic centimetre
Hint: Change the volume, and allow children to solve again!
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Have a small box and some cubic centimetres.
Investigate how many cubic centimetres can be packed into the small box, either
 by completely packing the box, for example,
or
 by packing 1 layer and working out how many
layers you need, for example,
Record the box packed with cubic centimetres in rows and layers.
Work out the volume of the box, either
 by working out the number of cubic centimetres in each row and adding, for
example, 12 + 12 = 24
or
 by working out the number of cubic centimetres in each row, and multiplying
by the number of rows, for example, 12 x 2 = 24
Record the volume of the box, for example, volume = 24 cubic centimetres.
Reflection: How can we measure volume and capacity in cubic centimetres?
Problem Solving
What is the capacity of this box?
= 1 cubic centimetre
Hint: Change the capacity, and allow children to solve again!
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Select a litre jug.
Record a unit of measurement, litre.
Divide the litre by 10, and record decilitre.
If you multiply the decilitre by 10, will you have a litre?
Divide the decilitre by 10, and record centilitre.
If you multiply the centilitre by 10, will you have a decilitre?
Divide the centilitre by 10, and record millilitre.
If you multiply the millilitre by 10, will you have a centilitre?
Reflection: How is metric measurement for measuring volume and capacity in liquid
units related to multiplicative place value? What is a litre? What is a millilitre?
Problem Solving
Annie filled a measuring jug with water to 1 litre.
How many millilitres of water does Annie have?
Hint: Change the liquid, and allow children to solve again!
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Have a measuring jug marked in millilitres, and a small container.
Fill the container to capacity with water.
Measure the volume of water, by pouring the water into the measuring jug.
Record the container's capacity in millilitres.
Reflection: How can we measure volume and capacity in millilitres?
Problem Solving
Jody filled a container to capacity with water.
She poured water into a measuring jug.
What was the capacity of the container?
Hint: Change the capacity, and allow children to solve again!
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Have a measuring jug marked in millilitres, and a large container.
Fill the container to capacity with water.
Measure the volume of water, by either:
 pouring the water into the measuring jug to 1 litre, emptying the measuring
jug, then pouring the remaining water from the container into the measuring
jug. Add the volumes of water together.
OR
 filling the measuring jug to 1 litre, pouring the 1 litre of water into the
container, filling the measuring jug to 1 litre again, pouring water from the
measuring jug into the container until it is filled to capacity. Subtract the
volume of water left in the measuring jug from 1 litre to work out the volume
poured into the container. Add the volumes of water poured into the
container together.
Record the container's capacity in litres and millilitres.
Reflection: How can we measure volume and capacity in litres and millilitres?
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Sit in a group of 3.
Each of you use cubic centimetres to make a model.
Each of you work out the volume of your model.
Compare the volumes of your models.
Place your models in order of volume.
Each of you record the models and their volumes.
Is the first model’s volume smaller than the second model’s volume?
Is the second model’s volume smaller than the third model’s volume?
So is the first model’s volume also smaller than the third model’s volume?
Is the third model’s volume larger than the second model’s volume?
Is the second model’s volume larger than the first model’s volume?
So is the third model’s volume also larger than the first model’s volume?
Reflection: How can we measure, compare and order volume and capacity in cubic
centimetres?
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Sit with a friend.
Each use the same number of cubic centimetres to make different models.
Swap models and each work out the volume of one of your friend's model.
Do both models have the same volume?
Each record all three models and their volumes.
Reflection: Can different models have the same volume?
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Use a computer program, to construct two-dimensional representations of threedimensional models using cubic units, for example,
Reflection: How can we measure volume and capacity
in cubic centimetres?
http://www.alearningplace.com.au
Investigating measuring volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Sit in a group of 3.
Each of you have a small container.
Each of you work out the capacity of your container.
Compare the capacities of your container.
Place your containers in order of capacity.
Each of you record the containers and their capacities.
Is the first container’s capacity smaller than the second container’s capacity?
Is the second container’s capacity smaller than the third container’s capacity?
So is the first container’s capacity also smaller than the third container’s capacity?
Is the third container’s capacity larger than the second container’s capacity?
Is the second container’s capacity larger than the first container’s capacity?
So is the third container’s capacity also larger than the first container’s capacity?
Reflection: How can we measure, compare and order volume and capacity in
millilitres?
http://www.alearningplace.com.au
Investigating Measure volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Sit with a friend.
Each of you have a different margarine, cream or ice cream
container labelled with the same volume, for example,
500mL
500mL
Each of you use a measuring jug to measure the capacity of your container by filling
each container to capacity with water and measuring the volume of water.
Label each container's capacity in millilitres or in litres and millilitres.
Do both containers have the same capacity?
Each of you record both containers and their capacities.
Reflection: Can different containers have the same capacity?
http://www.alearningplace.com.au
Investigating Measure volume and capacity in cubic centimetres, millilitres and
litres.
MEASUREMENT AND GEOMETRY 35 Measure volume and capacity in cubic centimetres, millilitres and litres.
Select 2 containers – one short and wide, one tall and narrow,
for example, a 1L drink bottle and a 1L ice cream container.
Measure the containers’ capacities.
Reflection: Can different containers have the same capacity?
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