Scottish Survey of Literacy &
Numeracy
Support material for Measurement
Second Level - Area
Produced by Education Scotland
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Scottish Survey of Literacy and Numeracy 2011
Performance in Measurement at Second Level
Based on the recent SSLN 2011 survey, evidence indicates that
over half of P7 pupils answered correctly, questions based on the
measurement organiser.
I can use my knowledge of the sizes of familiar objects or places to assist me
when making an estimate of measure.
MNU 2-11a
I can use the common units of measure, convert between related units of the
metric system and carry out calculations when solving problems MNU 2-11b
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
Scottish Survey of Literacy and Numeracy 2011
Evidence from this survey also suggests that pupils
have difficulty with other aspects of measurement at
P7:
• Calculating volumes
• Where fractions, decimal fractions and percentages was a
secondary organiser
• Area and perimeter
• Conversion of units, especially those involving decimal
fractions.
This presentation will:
• Explore aspects of measurement pupils find
challenging
• Consider why these aspects cause particular
difficulties
• Identify strategies to support learning with the aim
of promoting deeper understanding
Second Level - Experiences & Outcomes
I can use the common units of measure, convert
between related units of the metric system and carry
out calculations when solving problems.
MNU2-11b
Common units of measure
• Length : mm, cm, m and km
• Area: mm2, cm2, m2 and km2
• Volume: mm3, cm3, m3 and km3
• Mass: mg, g, kg and tonne
2011 Scottish Survey of Literacy and Numeracy
Based on evidence from the survey, less than half of pupils gave
the correct response to this question.
Question
How many grams are there in 4.75 kg?
“I can use the common units of measure, convert between related units of
the metric system.”
MNU 2-11b
Pupil responses include:
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•
•
•
A
B
C
D
4750 g
475 g
4500 g
4075 g
Reflective question
How would you plan learning and teaching to resolve the
‘common errors’?
Support for multiplication at Second Level can be found on the Education
Scotland website.
Units
Why do learners find the conversion of units so challenging?
Is it the unit conversion or the inability to multiply and divide by
10, 100 and 1000 that causes difficulty?
Exploring the language of units could enhance learners’
understanding.
Through learners understanding the significance of the prefixes
‘centi-’, ‘milli-’ and ‘kilo-’ , converting between units becomes
easier.
Language of Measure
Building on language from the Es and Os in First level
For example:
I have discussed the important part that numbers play in the
world and explored a variety of systems that have been used by
civilisations throughout history to record numbers.
MTH 1-12a
Metric system ~ milli
•
•
•
•
Latin for thousand ( mille)
Millennium
millipede
milliamp
Metric system ~ centi
•
•
•
•
French for hundred
Century
Centurion
U.S. currency
Metric system ~ kilo
•
•
•
•
•
Ancient Greek for thousand
kilograms
kilobytes
kilocalories
kilohertz
Scottish Survey of Literacy and Numeracy 2011
Based on evidence from the survey, less than half of pupils gave
the correct response to this question.
Question
Which of the following is the most likely to be nearest to the
weight of an average man?
Tick () one box.
A
8.5 kg
B
85 kg
C
185 kg
D
850 kg
E
1850 kg
Pupil responses
Reflective question
What real life contexts could you include, when planning
learning and teaching, to enable pupils to select appropriate
units for length, area and weight?
Second Level - Experiences & Outcomes
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.
MNU2-11c
Building on First Level area
The following Es and Os contribute to progression
in learning within MNU 2-11c
MNU 1-11a
MNU 1-11b
MNU 1-01a
MNU 1-02a
MNU 1-03a
MTH 1-16a
Units and Area
Here is an example of a question that has been
shown to be problematic for learners.
Question: Find the area of the rectangle
0.25m
50cm
• Why does a question like this cause difficulty?
• Does over reliance on using a formula reinforce the
difficulty?
• How do we enable learners to interrogate a question to
extract the relevant information?
50 cm
25 cm
1m
0.25 m
25 cm
0.5 m
25 cm
1m
25 cm
100 cm = 1 m
25 cm
50 cm
50 cm
Scottish Survey of Literacy and Numeracy 2011
Based on evidence from the survey, a quarter of pupils gave the
correct response to this question.
Question:
A 4 cm square is cut from a piece of card which is 8 cm by 6 cm.
8 cm
4 cm
6 cm
What is the area of the card remaining after the square is cut?
Pupil responses
Reflective question
How would you plan learning and teaching to improve the
number of pupils, who can successfully answer this type of
question?
Reflective questions
Consider the following questions:
How often do you:
• Emphasise the part units play in area calculations?
• Plan rich learning tasks which consolidate learning
of area?
• Consider other shapes where the product of
length and breadth is not applicable?
• Plan tasks which involve conversion of units?
Different methods to find the area of 2D
shapes: Area of a triangle
It is important that learners consider the relationship
between rectangles and triangles. They should be
encouraged to investigate why the area of a triangle is
half the area of the corresponding rectangle.
Through an investigative approach, learners should
establish that the area of a triangle is one half that
of the corresponding rectangle, a formula can then
be discussed.
Consider this triangle . . .
12 cm
16 cm
12 cm
16 cm
Developing numeracy
Calculating the area of the type of triangle in the
previous slide, discussion could support the
development of incorporating a secondary organiser
eg fraction or decimal fraction.
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Is the area ½ of 12 multiplied by 16?
Is the area ½ of 16 multiplied by 12?
Is the area 12 multiplied by 16 and then halved?
Do we need to half both?
What could determine which number we should
half, to simplify the number calculation?
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