Area and volume - Education Scotland

```Scottish Survey of Literacy &amp;
Numeracy
Support material for Measurement
Third Level - Area and Volume
Produced by Education Scotland
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Scottish Survey of Literacy and Numeracy 2011
Performance of Measurement at Third Level
Based on the recent SSLN 2011 survey, evidence indicates that
over a third of S2 pupils answered correctly, questions based on
the measurement organiser, which involves the following Es and
Os.
I can solve practical problems by applying my knowledge of measure,
choosing the appropriate units and degree of accuracy for the task and using
a formula to calculate area or volume when required.
MNU 3-11a
Having investigated different routes to a solution, I can find the area of
compound 2D shapes and the volume of compound 3D objects, applying my
knowledge to solve practical problems.
MNU 3-11b
Scottish Survey of Literacy and Numeracy 2011
Evidence from this survey also suggests that pupils
have difficulty with other aspects of measurement at
S2 :
• Calculations involving perimeter, area and volume as well as
how to use one value to calculate the other
• Problem solving in context of length, perimeter, area and
volume
• Where smaller items do not fit exactly into larger items
relating to volume and area.
• Fractions, decimal fractions and percentages as a secondary
organiser
• Conversion of units for length, weight and volume ( also
second level).
Prior Learning from Second Level
Building on prior learning from second level experiences and outcomes
relating to measurement:
Pupils should be confident and competent with…
• Identifying shapes in and around their environment
• Using an appropriate measuring device and then apply them for use in
real life situations.
• Making an estimate of measure
• Finding the perimeter and area of a simple 2D shape or volume of a
simple 3D object
• Converting between related units of the metric system
• Using the vocabulary associated with the metric system.
Building on prior learning from Es and Os relating to number processes:
Pupils should be confident in using whole numbers, fractions and decimal
fractions using a range of methods in a range of contexts.
Scottish Survey of Literacy and Numeracy 2011
Measurement at Third Level
Based on the recent SSLN 2011 survey, evidence indicates that
over a third of S2 pupils answered correctly, questions based on
the measurement organiser, which involves the following Es and
Os.
I can solve practical problems by applying my knowledge of measure,
choosing the appropriate units and degree of accuracy for the task and using
a formula to calculate area or volume when required.
MNU 3-11a
Having investigated different routes to a solution, I can find the area of
compound 2D shapes and the volume of compound 3D objects, applying my
knowledge to solve practical problems.
MNU 3-11b
Scottish Survey of Literacy and Numeracy 2011
In particular, a question focusing on a practical problem
involving perimeter :
Less than a fifth of pupils answered this question correctly.
Question: Perimeter problem solving
Farmer Brown wants to make a rectangular chicken run. He bought
18 meters of fencing wire and fixes the wire to posts 1 meter apart.
What is the longest run that he can make for his chickens?
Learners’ responses include
A
8m
B
9m
C
17m
D
18m
E
16m
Scottish Survey of Literacy and Numeracy 2011
In a similar question from the 2011 SSLN survey, one tenth of
pupils gave the correct response of 3cm.
Question
A cube has a volume of 27 cm3.
What is the length of one side of the cube?
Reflective questions
• What other response(s) do you think pupils would have given?
• Why do you think this type of question causes difficulties for
pupils?
• When planning learning and teaching, how could you help pupils
overcome any difficulties with this type of question?
Third Level - Experiences &amp; Outcomes
I can solve practical problems by applying my knowledge of
measure, choosing the appropriate units and degree of
accuracy for the task and using a formula to calculate area or
volume when required.
MNU 3-11a
Having investigated different routes to a solution, I can find the
area of compound 2D shapes and the volume of compound 3D
objects, applying my knowledge to solve practical problems.
MTH3-11b
Volume
Area
Length
Area: Applying my knowledge to
solve practical problems
A new business has taken over an existing floor space and
wishes to replace the existing floor covering.
Area : Strategy 1
“Having investigated different routes to a solution, I can find the area of
compound 2D shapes”
3m
5m
8m
9m
A
B
12m
Area A = (8 x 3)m&sup2; = 24m&sup2;
Area B = (9 x 3)m&sup2; = 27m&sup2;
Total Area = 51m&sup2;
3m
Strategy 2
3m
A
5m
9m
8m
B
12m
Area A = (5 x 3)m&sup2; = 15m&sup2;
Area 2 = (12 x 3)m&sup2; = 36m&sup2;
Total Area = 51m&sup2;
3m
Strategy 3
3m
9m
5m
8m
3m
12m
Area of large rectangle = (12 x 8)m&sup2; = 96m&sup2;
Area of yellow rectangle = (9 x 5)m&sup2; = 45m&sup2;
Area of blue shape = (96 – 45)m&sup2; = 51m&sup2;
How could this problem have been differentiated to
meet the needs of all learners?
For example, omit some of the lengths…
5m
6m
7m
10m
4m
12m
Some alternative compound shapes…
Extract from explanations in Principles and Practice paper for
Numeracy states that :
‘for young people, with well developed understanding, problems involving
circular properties could be introduced and investigated’
MTH 3-11b
Perimeter: Prior learning at Second Level
I can explain how different methods can be used to find the perimeter and
area of a simple 2D shape or volume of a simple 3D object. MNU 2-11c
10m
7m
4m
12m
Perimeter =(7 + 4 + 12 + 10 + 5 + 6 )m = 44m
Perimeter: Building on from second to third level
Should the strategy adopted to calculate the perimeter be different
if…
• Some of the lengths were omitted?
• Varying units of length were used?
• More ‘complicated’ numbers were used e.g. decimal fractions or
fractions?
• The problem also involves algebraic expressions.
For example, how could this problem have been
Use varying units of length…
350cm
5m
500cm
8m 50cm
8m
3m
1m
50
12m
100cm
1000mm
How could this problem have been made more
challenging?
Use decimal fractions (or fractions)…
2.5m
5m
9.5m
8m
3m
12m
Perimeter: Building on from Second to Third Level
• Can you provide opportunities for young people to create
their own floor coverage ?
• Why is calculating area important?
• Can you identify any other examples where calculating area is
used in real life?
How could this problem have been made more
challenging?
Omit some of the lengths…
5m
6m
7m
4m
12m
Perimeter
7m
10m
4m
12m
Perimeter =(7 + 4 + 12 + 10 + 5 + 6 )m = 44m
Numeracy across learning
Tasks which involve the integration of techniques from across
the Numeracy Experiences and Outcomes are found to be more
challenging by learners than those which require the application
of a direct fact.
Consider these projects on NAR which link numeracy across
learning
Carleith primary: (prior learning for perimeter and area)
https://www.narscotland.org.uk/virtual_file_path/68/20110628092647/inde
x.html
Westhill Academy: Area of compound 2D shapes
https://www.narscotland.org.uk/virtual_file_path/171/20110812133016/ind
ex.html
Key features to consider when planning CPD for
learning and teaching
• There is a clear developmental sequence throughout the
lesson, learners recognise links with earlier work, build on
prior learning in numeracy and confidently use their
knowledge within familiar and unfamiliar contexts.
• An appropriate balance between developing and
synthesising/using key facts
• Programmes of study and practitioners’ lesson plans make
effective use of prior learning to build on learners’ numeracy
knowledge and skills including second and third level
interface
• Learners confidently use mental strategies.
Key features to consider when planning CPD for
learning and teaching
• Learners give explanations of their reasoning as well as their
methods
• Non-routine problems, open ended tasks and investigations
are often used by learners to develop their problem solving
skills to develop their problem solving skills including
reasoning and generalising
• Staff introduce new numeracy terms, vocabulary and symbols
meaningfully and expect and encourage correct use.
The Numeracy Principles and Practice Paper is essential reading
for everyone and can be used to prompt discussion amongst
staff.
www.educationscotland.gov.uk
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