MEASUREMENT AND GEOMETRY 64_INVESTIGATION AND REFLECTION
(Year 6) ACMMG135, ACMMG136, ACMMG137, ACMMG138, NSW MA3-11MG
Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and litres, litres and kilolitres, kilolitres and megalitres.
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:
Millilitres and cubic centimetres.
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.

Children sit in pairs or small groups with a moisturiser box and jar to measure volume and capacity in cubic
centimetres and millilitres. They measure the volume of the box in cubic centimetres. They convert the cubic
centimetres to millilitres. They measure the volume of the jar in millilitres using displacement. They convert
the millilitres to cubic centimetres. They explain relationship between the volume of the box and the volume of
the jar. They measure the capacity of the jar in millilitres. They convert the millilitres to cubic centimetres. They
fill the jar with water to the stated volume of moisturiser. They explain the relationship between the volume of
the box, the volume of the jar, the capacity of the jar and the volume of moisturiser. Reflection: What is the
relationship between cubic centimetres and millilitres?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
Teaching Segment and Video 2:
Convert between millilitres and
litres.

In pairs, children select numbers of millilitres or litres. They record a metric measurement chart and a place
value chart as necessary. They convert between millilitres and litres, by multiplying / dividing by 1000.
Reflection: How can we use multiplicative place value to convert between litres and millilitres?
Convert between litres and
kilolitres.

In pairs, children select numbers of litres or kilolitres. They record a metric measurement chart and a place
value chart as necessary. They convert between litres and kilolitres by multiplying / dividing by 1000.
Reflection: How can we use multiplicative place value to convert between litres and kilolitres?
Convert between kilolitres and
megalitres.

In pairs, children select numbers of kilolitres or megalitres. They record a metric measurement chart and a
place value chart as necessary. They convert between kilolitres and megalitres by multiplying / dividing by
1000. Reflection: How can we use multiplicative place value to convert between kilolitres and megalitres?
Convert between millilitres, litres,
kilolitres and megalitres.

In pairs, children select numbers of millilitres, litres, kilolitres or megalitres. They record a metric measurement
chart and a place value chart as necessary. They convert their number of millilitres, litres, kilolitres or
megalitres to another unit of measurement by multiplying / dividing by 1000 or 1 000 000. Reflection: How can
we use multiplicative place value to convert between millilitres and litres and kilolitres and megalitres?
More Investigations
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching
PowerPoint.
Relationship between cubic
centimetre and millilitre.

Children have a medicine measuring cup of about 30 millilitres. They fill the medicine measuring cup to 25
millilitres. They select 5 cubic centimetres and make a model to submerge. They submerge the model and note
the volume of water displaced – 5 millilitres - as the volume of the volume of the model - 5 cubic centimetres.
They then identify that 1 millilitre has a volume of 1 cubic centimetre. Reflection: What is the relationship
between cubic centimetres and millilitres?
Volume and capacity of boxes and
jars.

In pairs, children select boxes and jars to measure volume and capacity in cubic centimetres and millilitres.
They measure the volume of the box in cubic centimetres. They convert the cubic centimetres to millilitres.
They measure the volume of the jar in millilitres. They convert the millilitres to cubic centimetres. Reflection:
What is the relationship between cubic centimetres and millilitres?
Volume of a fish tank.

In pairs, children calculate the volume of water needed to fill a fish tank, for example, 1 metre by 50
centimetres to a depth of 70 centimetres. Children calculate the capacity in cubic centimetres, then convert to
millilitres. They convert their volume of water between kilolitres, litres and millilitres using multiplicative place
value. Reflection: What is the relationship between cubic centimetres and millilitres? How can we use
multiplicative place value to convert between millilitres and litres and kilolitres and megalitres?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Volume of water flushed.

Children research to find the volume of water used in one flush of a toilet (or use the average volume of 6 litres
per flush). They count the number of times they flush a toilet in one day / week. They convert the amount
between millilitres and litres. They calculate the total volume of water flushed by the whole class and convert
between millilitres, litres and kilolitres. They calculate the total volume of water flushed by the whole school
and convert between millilitres, litres, kilolitres. They calculate how many days it would take before the school
has flushed a megalitre of water. Reflection: How can we use multiplicative place value to convert between
millilitres and litres and kilolitres and megalitres?
Volume of water in a pool.

Children calculate the volume of water needed to fill a swimming pool, 3 metres by 7 metres by 1.5 metres.
They convert between millilitres, litres, kilolitres and megalitres. Reflection: How can we use multiplicative
place value to convert between millilitres and litres and kilolitres and megalitres?
Capacity vs volume of water in a
fish tank.

In pairs, children investigate the capacity of a large fish tank and the volume of water a large fish tank would
hold if filled to an appropriate depth. For example, the tank's dimensions may be 1 metre by 50 centimetres by
75 centimetres. Children calculate the volume of water in cubic centimetres, then convert to millilitres.
Children mark an appropriate water level and repeat. Reflection: What is the relationship between cubic
centimetres and millilitres? How can we use multiplicative place value to convert between millilitres and litres
and kilolitres and megalitres?
Time to fill a fish tank.

In pairs, children investigate how long it would take to fill a fish tank, after measuring the capacity of a large
fish tank and the volume of water a large fish tank would hold if filled to an appropriate height. They measure
the rate of flow of water from the tap in appropriate units, for example, … millilitres per 10 seconds.
Reflection: What is the relationship between cubic centimetres and millilitres?
1 litre in different containers.

In pairs, children have rectangular containers with different dimensions. They calculate, then measure, the
depth of 1 litre of water in containers with different dimensions. Reflection: What is the relationship between
cubic centimetres and millilitres?
Volume of water in a shower.

Children keep a diary of their shower times for a week. They also measure the flow of water from their shower
in 10 seconds. They add together the total volume of water used. They convert to cubic centimetres. They
draw a scale model of rectangular container that would have that volume. Reflection: What is the relationship
between cubic centimetres and millilitres?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Volumes of containers of different
dimensions.

Children draw the containers and calculate the depth of 1 litre of water in containers with different dimensions
for example:
►
a container with a base of 5 cm x 10 cm and height 40 cm
►
a container with a base of 20 cm x 10 cm and height of 15 cm
►
a container with a base of 30 cm x 7 cm and height of 10 cm
Reflection: What is the relationship between cubic centimetres and millilitres?
Mulch

Children sit in pairs or groups. They have a price list from a garden centre that sells mulch by the cubic metre.
They work out the volume of mulch needed in a garden of specified size, for example, 10 square metres, to a
depth of 10 centimetres. Reflection: How large is a cubic metre?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
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.
Teaching Segment and Video 1:
Cubic centimetres and millilitres.
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 2:
Convert millilitres litres.
I had 300mL of water in a container. I placed an object in the water and the level rose to 320mL. What was the
volume of the object in cubic centimetres? (20 cubic centimetres)

Toni recorded the capacity of a container as 1770 millilitres and Gary recorded it as 1.77 litres. Are these
capacities the same? How do you know? (yes, because there are 1000 times as many millilitres as litres to measure the
same volume, we divide the number of millilitres by 1000 to get the number of litres, 1770 ÷ 1000 = 1.77)
Convert litres kilolitres

A water tank has a capacity of 6.25 kilolitres. How many litres does the water tank hold when it is filled to
capacity? (6250 litres)
Convert kilolitres megalitres

A dam has a capacity of 6.25 megalitres. How many kilolitres does the dam hold when it is filled to capacity?
(6250 kilolitres)
Convert megalitres litres

A dam has a capacity of 6.25 megalitres. How many litres does the dam hold when it is filled to capacity? (6 250
000 kilolitres)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
5
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Sit in pairs or small groups.
Have a moisturiser box and jar.
Measure the volume of the box in cubic centimetres.
Convert the cubic centimetres to millilitres.
Measure the volume of the jar in millilitres using displacement.
Convert the millilitres to cubic centimetres.
Explain relationship between the volume of the box and the volume of the jar.
Measure the capacity of the jar in millilitres.
Convert the millilitres to cubic centimetres.
Fill the jar with water to the stated volume of moisturiser.
Explain the relationship between the volume of the box, the volume of the jar, the
capacity of the jar and the volume of moisturiser.
Reflection: What is the relationship between cubic centimetres and millilitres?
Problem Solving
I had 300mL of water in a container.
I placed an object in the water and the level rose to
320mL.
What was the volume of the object in cubic
centimetres?
Hint: Change the volumes, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Select a number of millilitres or litres.
Record a metric measurement chart and a place value chart.
Convert between millilitres and litres by multiplying or dividing by 1000.
Reflection: How can we use multiplicative place value to convert between litres and
millilitres?
Problem Solving
Toni recorded the capacity of a container as 1770
millilitres and Gary recorded it as 1.77 litres.
Are these capacities the same? How do you know?
Hint: Change the volumes, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Select a number of litres or kilolitres.
Record a metric measurement chart and a place value chart.
Convert between litres and kilolitres by multiplying or dividing by 1000.
Reflection: How can we use multiplicative place value to convert between litres and
kilolitres?
Problem Solving
A water tank has a capacity of 6.25 kilolitres.
How many litres does the water tank hold when it is
filled to capacity?
Hint: Change the volume, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Select a number of kilolitres or megalitres.
Record a metric measurement chart and a place value chart.
Convert between kilolitres or megalitres by multiplying or dividing by 1000.
Reflection: How can we use multiplicative place value to convert between kilolitres
and megalitres?
Problem Solving
A dam has a capacity of 6.25 megalitres.
How many kilolitres does the dam hold when
it is filled to capacity?
Hint: Change the volume, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Select a number of millilitres, litres, kilolitres or megalitres.
Record a metric measurement chart and a place value chart.
Convert your number of millilitres, litres, kilolitres or megalitres to another unit of
measurement by multiplying or dividing by 1000 or 1 000 000.
Reflection: How can we use multiplicative place value to convert between millilitres,
litres, kilolitres and megalitres?
Problem Solving
A dam has a capacity of 6.25 megalitres.
How many litres does the dam hold when it is
filled to capacity?
Hint: Change the volume, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Have a medicine measuring cup of about 30 millilitres.
Fill the medicine measuring cup to 25 millilitres.
Select 5 cubic centimetres and make a model.
Submerge the model and note the volume of water displaced as the volume of the
volume of the model.
Identify the volume of 5 millilitres in cubic centimetres.
Identify the volume of 1 millilitre in cubic centimetres.
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Select boxes and jars to measure volume and capacity in cubic centimetres and
millilitres.
Measure the volume of the box in cubic centimetres.
Convert the cubic centimetres to millilitres.
Measure the volume of the jar in millilitres.
Convert the millilitres to cubic centimetres.
Explain the relationship between the volume of the box and the volume of the jar.
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Calculate the volume of water needed to fill a fish tank 1 metre by 50 centimetres to
a depth of 70 centimetres.
Convert between cubic centimetres and millilitres.
Convert the volume of water between kilolitres, litres and millilitres using
multiplicative place value.
Reflection: What is the relationship between cubic centimetres and millilitres? How
can we use multiplicative place value to convert between millilitres and litres and
kilolitres and megalitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Research to find the volume of water used in one flush of a toilet (or use the
average volume of 6 litres per flush).
Count the number of times you flush a toilet in one day / week.
Convert the volume between millilitres and litres.
Calculate the total volume of water flushed by the whole class.
Convert between millilitres, litres and kilolitres.
Calculate the total volume of water flushed by the whole school.
Convert between millilitres, litres, kilolitres.
Calculate how many days it would take before all of the children in the school have
flushed a megalitre of water.
Reflection: How can we use multiplicative place value to convert between millilitres
and litres and kilolitres and megalitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Calculate the volume of water needed to fill a swimming pool, 3 metres by 7 metres
by 1.5 metres.
Convert from cubic centimetres and millilitres.
Convert between millilitres, litres, kilolitres and megalitres.
Reflection: How can we use multiplicative place value to convert between millilitres
and litres and kilolitres and megalitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Investigate the capacity of a large fish tank and the volume of water a large fish tank
would hold if filled to an appropriate depth.
For example, the tank's dimensions may be 1 metre by 50 centimetres by 75
centimetres.
Calculate the capacity in cubic centimetres, then convert to millilitres.
Mark an appropriate water level and calculate the volume of water in cubic
centimetres, then convert to millilitres.
Reflection: What is the relationship between cubic centimetres and millilitres? How
can we use multiplicative place value to convert between millilitres and litres and
kilolitres and megalitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Investigate how long it would take to fill a fish tank, after measuring the capacity of
a large fish tank and the volume of water a large fish tank would hold if filled to an
appropriate height.
Measure the rate of flow of water from the tap in appropriate units, for
example, …millilitres per 10 seconds.
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Have large rectangular containers with different dimensions.
Calculate, then measure, the depth of 1 litre of water in the containers with
different dimensions.
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Keep a diary of your shower times for a week.
Measure the flow of water from your shower in 10 seconds.
Calculate the total volume of water used in the week.
Convert to cubic centimetres.
Draw a scale model of rectangular container that could contain that volume of
water.
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Visualise large rectangular containers with different dimensions.
Draw the containers and calculate the depth of 1 litre of water in the containers
with different dimensions for example:
 a container with a base of 5 cm x 10 cm and height 40 cm
 a container with a base of 20 cm x 10 cm and height of 15 cm
 a container with a base of 30 cm x 7 cm and height of 10 cm
Reflection: What is the relationship between cubic centimetres and millilitres?
http://www.alearningplace.com.au
Investigating Converting Between Cubic and Liquid Units of Measurement, and
Between Millilitres, Litres, Kilolitres and Megalitres
MEASUREMENT AND GEOMETRY 64 Relationship between cubic and liquid units – convert millilitres and cubic centimetres, millilitres and
litres, litres and kilolitres, kilolitres and megalitres.
Sit in pairs or groups.
Have a price list from a garden centre that sells mulch by the cubic metre.
Work out the volume of mulch needed in a garden of specified size, for example, 10
square metres, to a depth of 10 centimetres.
Reflection: How large is a cubic metre?
http://www.alearningplace.com.au