Scottish Survey of Literacy &
Numeracy
Support material for Measurement
First Level - Area
Produced by Education Scotland
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Scottish Survey of Literacy and Numeracy 2011
Performance in Measurement in P4
Based on the recent 2011 Survey of Literacy and Numeracy,
evidence indicates that more than half of P4 pupils answered
correctly, questions based on the measurement organiser.
I can estimate how long or heavy an object is, or what amount it holds, using
everyday things as a guide, then measure or weigh it using appropriate
instruments and units.
MNU 1-11
I can estimate the area of a shape by counting squares or other methods.
MNU 1-11b
Scottish Survey of Literacy and Numeracy 2011
Evidence from this survey suggests that pupils have difficulty
with the following aspects of measurement at P4:
• Reading scales where the value of an intermediate
graduation needs to be deduced
• Counting squares to measure area of irregular shapes
involving whole and half square centimetres.
• Multi-step and word problems, particularly those without a
diagrammatical representation
• Measuring lengths and weights involving every-day objects,
particularly when involving halves or quarters.
Scottish Survey of Literacy and Numeracy 2011
Evidence also suggests that learners are more
successful with the following aspects of measurement
at P4.
• Ordering objects in weight and length when they
have a visual representation
• Finding the area of regular shapes which only involve
whole square centimetres.
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, most learners answered
correctly.
Question
A box of apples is put on a scale
What did the box of apples weigh?
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, around two fifths of
learners answered correctly.
Question
How much do the apples weigh?
A
153 grams
B
150 grams
C
180 grams
D
190 grams
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, around a third of learners
answered correctly.
Question
Angus is 1m 19 cm tall.
Mark is 14 cm shorter than Angus.
Sam is 10 cm taller than Mark.
How tall is Sam?
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, about a third of learners
answered correctly.
Question
Jill pours milk into a measuring jug.
3 litres
2 litres
1 litres
How much milk is in the jug?
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, about a third of learners
answered correctly.
Question
Camilla is growing cress seeds.
She measures the height of the tallest
seedling.
Measure the height of the drawing of the
cress seedling in millimetres.
How often are learners given the opportunity to
work with millimetres.
Measurement at First level
I can estimate how long or heavy an object is, or what
amount it holds, using everyday things as a guide, then
measure or weigh it using appropriate instruments and
units.
MNU 1-11a
Scottish Survey of Literacy and Numeracy 2011
In the Scottish Survey of Literacy and Numeracy, in a question
similar to this, almost a third of learners answered correctly.
Question
Which unit of length would you use to measure the distance
between Edinburgh and Glasgow?
Tick () one box.
A
centimetre
B
millimetre
C
kilometre
D
metre
Pupil responses
•
•
•
•
A
B
C
D
4%
8%
66%
21%
1% of pupils did not attempt this question.
Scottish Survey of Literacy and Numeracy 2011
A question focusing on reading a scale to measure length:
About half of pupils answered this question correctly.
Question
What is the length of this paper clip to the nearest centimetre?
0
5
10 cm
First Level - Experiences & Outcomes
I can estimate the area of a shape by counting
squares or other methods.
MNU1-11b
First Level - Area
Recent surveys, including 2011 Scottish Survey of
Literacy and Numeracy, show that children find it
difficult to estimate the area of a shape.
What strategies would be appropriate to develop this
concept with learners?
First Level – Initial understanding
Building on prior learning from early level Es and Os
I am developing a sense of size and amount by observing, exploring, using and
communicating with others about things in the world around me.
MNU 0-01a
I have experimented with everyday items as units of measure to investigate and
compare sizes and amounts in my environment, sharing my findings with others.
MNU 0-11
It is crucial that before children try to estimate the area of a
shape, they first understand what the term area relates to.
Children must understand that area is the amount of surface
enclosed within the boundaries of a two-dimensional shape.
Before engaging in the measurement of shapes
children should be
• encouraged to look at objects in their environment
• able to discuss surface coverage and size
• able to compare e.g. the floor surface of the gym
hall, playgrounds or sports field, the top of the
dining tables or classroom tables, or the surface of
display boards….
Scottish Survey of Literacy and Numeracy 2011
Exemplars
For example
Based on evidence from this survey, almost half of pupils
achieved the correct answer for this question.
Question
Each square has an area of 1 square centimetre.
What is the area of the shaded shape (in square centimetres)?
Reflective questions
• By inspection, how do learners compare the amount of
surface for different shapes?
• Can they always make this judgement through inspection?
• If inspection is not appropriate, what other methods could be
used to compare the area of two different shapes?
First Level – Introducing the concept of Area
(direct and indirect comparisons)
Using a variety of non standard units of measurement e.g.
hands, bottle tops, counters etc, children should be given the
opportunity to explore how to compare the area of 2 shapes or
objects such as jotters/books/tables.
Encourage children to discuss the problems associated with
using such a variety of different measuring units.
Using non standard units for estimating the
area of regular shapes
Estimating the area of irregular shapes
Having developed the understanding of measuring area using
squares:
What learning activities will support estimating the area of
irregular shaped objects?
What part will rounding play in the process?
Square Units
Through discussion, children should understand the
• inconsistencies and gaps caused by using non-standard units
of measurement (counters/hands etc)
• that area is always measured in square units.
People often use square centimetres, square metres or square
kilometres for measuring area.
In the 2011 Scottish Survey of Literacy and Numeracy,
in a question similar to this, almost a third of learners
answered correctly.
Question
Donald draws a triangle on a grid.
What is the area of the triangle?
Each square = 1 square centimetre
(cm2).
Reflective questions
How can we ensure that children understand what a square
centimetre or square metre looks like?
Can they think of situations when a square metre would be a
better unit of measurement than square centimetres?
Square Unit of Measurement
Allow children the opportunity to measure, draw or identify square units (cm
or m) using rulers, measuring tapes, metre sticks or trundle wheels ensuring
they understand that all sides must measure 1.
1
1
1
1
Children should then explore laying squares over a surface to enable them to
calculate the area through the counting of squares.
For example, children can use square centimetre pieces of paper to calculate
the area of their reading book. Do they think that using these square
centimetres would be a suitable way of measuring a classrooms or
playgrounds area? What could they use instead? (introduce square metres of
paper)
1 cm2
1 m2
1 km2
Progressing from estimating to calculating
For regular shapes, the progression from estimating to
calculating involves counting squares
Can you support children to link their learning of repeated
addition to multiplication using area?
3
3 + 3 + 3 + 3 + 3 is the same as….
3
5 sets of 3 =
3
3
3
5 x 3 = 15
Practical exploration
By allowing children to use practical materials they can explore
making the possible combinations of length and breadth e.g.
• laying out 24 building blocks or 24 paper squares in different
ways.
• relating practical activities to costs of materials, carpets etc.
using whole numbers.
Some practical ideas for AREA – considering
Bloom’s Taxonomy
The following activities are ideas to
promote HIGHER ORDER THINKING
skills in children.
Creating
Evaluating
Analysing
ANALYSING – breaking information into
parts to explore understanding and
relationships
(organising/comparing/deconstructing)
•
•
Calculate the areas of these compound
shapes in square centimetres (breaking
into rectangles).
Which has the greatest area?
Applying
Understanding
Remembering
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