MEASUREMENT AND GEOMETRY 52_INVESTIGATIONS AND REFLECTIONS
(Year 5) ACMMG108, ACMMG109 NSW MA1 10MG
Area of hectares and square kilometres, calculate area of rectangles by multiplying lengths of adjacent sides, compare metric and imperial systems.
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:
Metric length units have been
turned into squares to measure
area.
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 explain the distinction between square centimetres and centimetres square/d, reading cm 2 as square
centimetre not centimetre square/d. Children explain the distinction between square metres and metres
square/d, reading m2 as square metre not metre square/d. Reflection: What is a square centimetre? What is a
square metre?
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Teaching Segment and Video 2:
Hectare as 100m x 100m square.

Children go to the playground or local park with a measuring device (for example, a trundle wheel or an app)
and markers, (for example, cones), to mark out the area of a hectare as a square with sides 1 hectometre (100
metres) in length. Reflection: What is a hectare?
Square kilometre as 1000m x
1000m square.

Children have a map of the local area. They use the scale to work out a length of 1 kilometre (1000 metres).
They turn the kilometre into a square with sides 1 kilometre long, to make a square kilometre. They visualise the
size of a square kilometre. Reflection: What is a square kilometre?
Measure, calculate area in
square metres.

In pairs or small groups, children measure the length of the adjacent sides of the room in metres. Children work
out the area by multiplying the number of square metres in each row by the number of rows. Children calculate
area by multiplying the lengths of the adjacent sides. Children explain they are multiplying ‘length’ by ‘width’.
Reflection: How can we calculate area?

Children investigate the Imperial measurement system, including the history and units of measurement used to
measure area. Reflection: What is the Imperial measurement system?
Teaching Segment and Video 3:
Imperial system.
More investigations.
Hectares using scale in maps.
Hectares using scale in maps
with different dimensions.
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching
PowerPoint.
 Children have a map of the local area which includes a local park. They use the scale on the map to work out a
length of 1 hectometre (100 metres) in the park. They turn the hectometre into a square to make a hectare.
They go to the park with a measuring device (for example, a trundle wheel or an app) and markers, (for example,
cones), to mark out the area of a hectare as a square with sides 100 metres / 1 hectometre in length. Reflection:
How can we measure the area of a hectare?

Children have a map of the local area which includes a local park. They use the scale on the map to draw
hectares in shapes other than squares. They go to the park with a measuring device (for example, a trundle
wheel or an app) and markers, (for example, cones), to mark out the area of a hectare in shapes other than
squares. For example, they may make hectares as 50 metres by 200 metres (half a hectometre by 2
hectometres), or 25 metres by 400 metres (quarter of a hectometre by 4 hectometres). They explain that the
shapes all have an area of a hectare. They explain that a hectare need not be square. Reflection: How can we
measure the area of a hectare?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
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Square kilometres with different
dimensions.

Children have a map of the local area. They use the scale on the map to draw square kilometres in shapes other
than squares. For example, they may make square kilometres as 500 metres by 2000 metres (half a kilometre by
2 kilometres), or 250 metres by 4000 metres (quarter of a kilometre by 4 kilometres). They explain that the
shapes all have an area of a square kilometre. They explain that a square kilometre need not be square.
Reflection: How can we measure the area of a square kilometre?
Measure, calculate area in
square centimetres.

Children have a rectangle. Children measure the area of the shape in square centimetres. Children measure the
length of one side. They measure the length of the adjacent side. They calculate the area by multiplying the
number of square centimetres on one side with the number of rows. Children calculate the area by multiplying
the lengths of 2 adjacent sides. They call one side ‘length’ and the other side ‘width’ and calculate the area by
multiplying length by width. Reflection: How can we measure and calculate area in square centimetres?
Use scale to measure, calculate
area in square metres.

In pairs, children have square centimetre grid paper. They use the scale 1 square centimetre:1 square metre to
draw areas of a specific number of square metres on the square centimetre grid paper, for example, shapes that
have areas of 12 square metres. Multiply the lengths of adjacent sides of the rectangle to calculate the area.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the rectangle to calculate the area.
Reflection: How can we measure and calculate area in square metres?
Use scale to measure, calculate
area in square hectares.

In pairs, children have square centimetre grid paper. They use the scale 1 square centimetre:1 hectare to draw
areas of a specific number of hectares on the square centimetre grid paper, for example, shapes that have areas
of 12 hectares. Multiply the lengths of adjacent sides of the rectangle to calculate the area. Explain that you
multiplied the ‘length’ of the rectangle by the ‘width’ of the rectangle to calculate the area. Reflection: How can
we measure and calculate area in hectares?
Use scale to measure, calculate
area in square kilometres.

In pairs, children have square centimetre grid paper. They use the scale 1 centimetre:1 square kilometre to draw
areas of a specific number of square kilometres on the square centimetre grid paper, for example, shapes that
have areas of 12 square kilometres. Multiply the lengths of adjacent sides of the rectangle to calculate the area.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the rectangle to calculate the area.
Reflection: How can we measure and calculate area in square kilometres?

In pairs, children roll a die twice to determine the length of adjacent sides of a rectangle in square centimetres,
square metres, hectares or square kilometres They explain they calculated the area of the rectangle by
multiplying the number of rows by the number of squares in each row. Children explain they are multiplying
‘length’ by ‘width’. Reflection: How can we calculate area in square centimetres, square metres, hectares and
square kilometres?
Dice areas.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
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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:
Metric length units have been
turned into squares to measure
area.

Harold drew a shape with an area of 2 square centimetres.
Julie drew a shape that is 2 centimetres square/d.
Which shape is Harold’s and which shape is Julie’s?
(Julie’s
Harold’s
)
Teaching Segment and Video 2:
Hectare as 100m x 100m square.

Ally’s sheep field was a square with dimensions 1 hectometre by 1 hectometre. What is the area of the field? (1
hectare which is 10 000 square metres)
Square kilometre as 1000m x
1000m square.

Ally’s sheep field was a square with dimensions 1 kilometre by 1 kilometre. What is the area of the field? (1
square kilometre which is 1 000 000 square metres)
Measure, calculate area in square
metres.

Wilma painted one rectangular wall of her room.
The diagram shows the wall.
What area did Wilma paint? (8 square metres)
Teaching Segment and Video 3:
Imperial system.

2 metres
4 metres
Ally’s sheep field has an area of 1 hectare. Robbie’s sheep field has an area of 1 acre. Whose sheep field has the
larger area? (Ally’s – an acre is less than half as big as a hectare)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Explain the distinction between square centimetres and centimetres square/d.
Does cm2 say square centimetre or centimetre square/d? Why?
Explain the distinction between square metres and metres square/d.
Does m2 say square metre or metre square/d? Why?
Reflection: What is a square centimetre? What is a square metre?
Problem Solving
Harold drew a shape with an area of 2 square
centimetres.
Julie drew a shape that is 2 centimetres square/d.
Which shape is Harold’s and which shape is Julie’s?
Hint: Change the area, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Go to the playground or park a measuring device (for example, a trundle wheel or
an app) and markers, (for example, cones).
Mark out the area of a hectare as a square with sides 100 metres / 1 hectometre in
length.
Reflection: What is a hectare?
Problem Solving
Ally’s sheep field was a square with
dimensions 1 hectometre by 1 hectometre.
What is the area of the field?
Hint: Change the object, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Select a map of the local area.
Use the scale to work out a length of 1 kilometre (1000 metres).
Turn the kilometre into a square with sides 1 kilometre (1000 metres) long, to make
a square kilometre.
Visualise the size of a square kilometre using local landmarks.
Reflection: What is a square kilometre?
Problem Solving
Ally’s sheep field was a square with
dimensions 1 kilometre by 1 kilometre.
What is the area of the field?
Hint: Change the object, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Measure the length of the adjacent sides of the room in metres.
Work out the area by multiplying the number of square metres in each row by the
number of rows.
Calculate area by multiplying the lengths of the adjacent sides.
Did you calculate area by multiplying length by width?
Reflection: How can we calculate area?
Problem Solving
Wilma painted one rectangular wall of her room.
The diagram shows the wall.
2 metres
What area did Wilma paint?
4 metres
Hint: Change the area, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Investigate the Imperial measurement system, including:
•
•
the history and
units of measurement used to measure area.
Reflection: What is the Imperial measurement system?
Problem Solving
Ally’s sheep field has an area of 1 hectare.
Robbie’s sheep field has an area of 1 acre.
Whose sheep field has the larger area?
Hint: Change the object, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Have a map of the local area which includes a local park.
Use the scale on the map to work out a length of 1 hectometre (100 metres) in the
park.
Turn the hectometre into a square to make a hectare.
Go to the park with a measuring device (for example, a trundle wheel or an app) and
markers, (for example, cones), to mark out the area of a hectare as a square with
sides 100 metres / 1 hectometre in length.
Reflection: How can we measure the area of a hectare?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Select a map of the local area which includes a local park.
Use the scale on the map to draw hectares in squares, and in shapes other than
squares.
Go to the park with a measuring device (for example, a trundle wheel or an app) and
markers, (for example, cones), to mark out the area of a hectare in squares and in
shapes other than squares.
For example, you may make hectares as 50 metres by 200 metres (half a hectometre
by 2 hectometres), or 25 metres by 400 metres (quarter of a hectometre by 4
hectometres) etc.
Explain that the shapes all have an area of a hectare.
Explain that a hectare need not be square.
Reflection: How can we measure the area of a hectare?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Select a map of the local area.
Use the scale on the map to draw square kilometres in shapes other than squares.
For example, you may make square kilometres as 500 metres by 2000 metres (half a
kilometre by 2 kilometres), or 250 metres by 4000 metres (quarter of a kilometre by
4 kilometres).
Explain that the shapes all have an area of a square kilometre.
Explain that a square kilometre need not be square.
Reflection: How can we measure the area of a hectare?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Have a rectangle.
Measure the area of the rectangle in square centimetres.
Measure the length of one side.
Measure the length of the adjacent side.
Calculate the area by multiplying the number of square centimetres on one side
with the number of rows.
Calculate the area by multiplying the lengths of 2 adjacent sides.
Did you multiply ‘length’ by ‘width’ to calculate the area?
Reflection: How can we measure and calculate area in square centimetres?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Have square centimetre grid paper.
Use the scale 1 centimetre:1 metre to draw rectangles with areas of a specific
number of square metres on the square centimetre grid paper.
For example, rectangles that have areas of 12 square metres.
Multiply the lengths of adjacent sides of the rectangle to calculate the area.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the
rectangle to calculate the area.
Reflection: How can we measure and calculate area in square metres?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Have square centimetre grid paper.
Use the scale 1 centimetre:1 hectare to draw rectangles with areas of a specific
number of hectares on the square centimetre grid paper.
For example, rectangles that have areas of 12 hectares.
Multiply the lengths of adjacent sides of the rectangle to calculate the area.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the
rectangle to calculate the area.
Reflection: How can we measure and calculate area in hectares?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Have square centimetre grid paper.
Use the scale 1 centimetre:1 kilometre to draw rectangles with areas of a specific
number of square kilometres on the square centimetre grid paper.
For example, rectangles that have areas of 12 square kilometres.
Multiply the lengths of adjacent sides of the rectangle to calculate the area.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the
rectangle to calculate the area.
Reflection: How can we measure and calculate area in square kilometres?
http://www.alearningplace.com.au
Investigating Measuring Area using Hectares and Square Kilometres
Measurement and Geometry 52 Hectares and square kilometres
Roll a die twice to determine the lengths of adjacent sides of a rectangle.
Decide on a unit of measurement for area, for example, square centimetre or
square metre or hectare or square kilometre.
Calculate the area by multiplying the number of square centimetres or square
metres or hectares or square kilometres in each row with the number of rows.
Calculate the area by multiplying the lengths of the adjacent sides.
Explain that you multiplied the ‘length’ of the rectangle by the ‘width’ of the
rectangle to calculate the area.
Reflection: How can we calculate area in square centimetres, square metres,
hectares and square kilometres?
http://www.alearningplace.com.au