MEASUREMENT and GEOMETRY
Concept Development
The world is full of two-dimensional shapes and three-dimensional objects. People began to
measure the length - one dimension - of these shapes and objects. A line is one-dimensional
because it takes up space along one direction
Length
Names for specific lengths grew out of necessity and began using body parts, for example foot,
hand and el (elbow). Multiple units were used to measure longer lengths and yards, furlongs, miles
etc were created. Units were divided to measure shorter lengths and inches etc were created
Around 300 years ago, the French decided to create a new system for measuring length, which
they called the metric system. They based the metric system on place value - multiplying and
dividing by 10 to make longer or shorter units
They began with the metre. A metre was designed to be one-ten-millionth of a quarter of a
meridian - A meridian is a circular line around the Earth passing through both North and South
Poles - how amazing is that? The word metre means to measure
To measure shorter lengths, the metre was divided by 10 to make a decimetre (used in Europe).
To measure even shorter lengths, the decimetre was divided by 10 to make a centimetre. To
measure even shorter lengths, the centimetre was divided by 10 to make a millimetre. The
prefixes 'deci', 'centi' and 'milli' are used for all units of measurement in the metric system. Deci
means tenth - a decimetre is a tenth of a metre (10 of them are as long as a metre so one is a
tenth as long as a metre). Centi means hundredth - a centimetre is a hundredth of a metre (100 of
them are as long as a metre so one is a hundredth as long as a metre). Milli means thousandth - a
millimetre is a thousandth of a metre (1000 of them are as long as a metre so one is a thousandth
as long as a metre)
To measure longer lengths, the metre was multiplied by 10 to make a decametre (used extensively
in Europe). To measure even longer lengths, the decametre was multiplied by 10 to make a
hectometre. To measure even longer lengths, the hectometre was multiplied by 10 to make a
kilometre. The prefixes 'deca', 'hecto' and 'kilo' are used for all units of measurement in the metric
system. Deca means ten - decametre literally means ten metres. Hecto means 100 - hectometre
literally means 100 metres. Kilo means 1000 - kilometre literally means 1000 metres
This means that we can name really long lengths or really short lengths using words rather than
fractions to name the lengths!
Because the metric system is based on a decimal
system, learning to convert between units of
measurement makes sense when relating it to
multiplicative place value
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Area
Area is amount of space a two-dimensional shape takes up. A shape is two-dimensional because it
takes up space along 2 directions - that means it has length in two directions. Name we give the
lengths include length, width, depth, height, breadth ...
When children first begin to investigate area, they investigate tessellation and shapes. By the end
of Year 2, they find that the best shape to measure area is the square because it takes up the same
space no matter which way it is oriented (a word which has the same meaning as orientated!)
In Year 3, they begin to investigate measuring the dimensions of their square and find that a
square with dimensions of 1cm is a square centimetre. There is a huge difference between a
square centimetre and a centimetre square(d) as this example demonstrates:
This shape is 2 square centimetres and has an area of 2 square centimetres
This 2 centimetre square(d) describes a square with sides 2cm in
length and has an area of 4 square centimetres!
A square centimetre is a unit of measurement for measuring area
The units of measurement for measuring area grew out of the units of measurement used to
measure length. Squares are created from metres (square metres), centimetres (square
centimetres), hectometres (hectares), kilometres (square kilometres)
As children develop their understanding of the features and properties of shapes, they use these
understandings to measure and calculate area. Children investigate the relationship between the
area of rectangles and triangles. This then allows them to investigate dividing straight-sided
shapes into rectangles and triangles to find the area - no need to rote learn formulas!
Children investigate the relationship between the circumference (perimeter) of a circle and the
radius of the circle (pi) allows children to find the area of circles
Volume and Capacity
Volume is amount of space something three-dimensional takes up. An object is three-dimensional
because it takes up space along 3 directions - that means it has length in three directions. Name
we give the lengths include length, width, depth, height, breadth ...
Volume includes capacity. Capacity is the total amount of space inside a container - think of a
container of water 'filled to capacity'. If the container of water is not filled to capacity, the volume
of water (amount of space the water takes up) will be less than the capacity of the container
Volume and capacity can be measured in cubic units or in liquid units
When children first begin to investigate volume and capacity, they investigate tessellation and
objects. By the end of Year 2, they find that the best shaped object to measure volume and
capacity is the cube because it takes up the same space no matter which way it is oriented (a word
which has the same meaning as orientated!)
In Year 3, they begin to investigate measuring the dimensions of their cube and find that a cube
with dimensions of 1cm is a cubic centimetre. There is a huge difference between a cubic
centimetre and a centimetre cube(d) as this example demonstrates:
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This object is 2 cubic centimetres and has a volume of 2 cubic centimetres
This 2 centimetre cube(d) describes a cube with sides 2cm in length
and has a volume of 8 cubic centimetres!
A cubic centimetre is a unit of measurement for measuring
volume and capacity
The units of measurement for measuring volume and capacity grew out of the units of
measurement used to measure length and area. Cubes are created from metres (cubic metres),
centimetres (cubic centimetres), hectometres (cubic hectometres), kilometres (cubic kilometres)
As children develop their understanding of the features and properties of objects, they use these
understandings to measure and calculate volume and capacity.
Objects and containers with straight edges and 90⁰ vertices can be measured using cubic units.
Objects and containers without straight edges and 90⁰ vertices need to be measured using a liquid
measure
The creators of the metric system created a liquid unit of measure that had the same volume as a
cubic centimetre - and called it a millilitre. Liquid units of measurement for measuring volume and
capacity are the millilitre (cubic centimetre), litre (1000 cubic centimetres - visualise a MAB block =
1/1000 cubic metre), kilolitre (1 000 000 cubic centimetres = 1 cubic metre)
Using this fabulous relationship, we can work out the volume and capacity of any threedimensional object in both cubic and liquid units!
When the creators of the metric system multiplied a millilitre by 1000 to get a litre - they used the
mass of a litre of water to create a unit of measurement of mass
Mass
Mass is a measure of the amount of matter. We often use the terms mass and weight
interchangeably. They are different: The amount of matter does not change if gravity changes. For
example the amount of matter in a person is the same on Earth or on the Moon. Weight changes if
gravity changes. For example a person's weight is greater on Earth than on the Moon, because the
Earth's gravity is greater
When children first begin to investigate mass, they investigate through hefting and equal-arm
balances
The units of measurement for measuring mass grew out of the units of measurement used to
measure length, area and volume and capacity.
The creators of the metric system called the mass of a litre of water, a kilogram. This means that
the mass of a millilitre of water is 1 gram. (Technically water at 4⁰C - the temperature water is at
its densest) Kilograms were then divided by 10 to create decigrams, the decigram divided by 10 to
create centigrams. Kilograms were multiplied by 1000 to create tonnes
So 1 litre of water has a mass of 1 kilogram - no wonder 'heavy' rain can cause so much damage!'
The Scope and Sequences, Teaching Programs, Teaching Plans, Teaching Videos and Learning
Videos develop the concepts of Measurement and Space from K-6
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