MEASUREMENT – THIRD LEVEL
Significant Aspect of Learning
Use knowledge and understanding of measurement and its application.
Learning Statements
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Relationships between measurements;
Formulae;
Degree of accuracy;
Interpret questions;
Select and communicate processes and solutions;
Justify choice of strategy used.
Experiences & Outcomes
MNU 3-11a:
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.
MTH 3-11b:
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 3-03a:
I can use a variety of methods to solve number problems in familiar contexts, clearly
communicating my processes and solutions.
MNU 3-07a:
I can solve problems by carrying out calculations with a wide range of fractions, decimal fractions
and percentages, using my answers to make comparisons and informed choices for real-life
situations.
Learning Intention
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Through investigation, we are learning how to apply our knowledge of measurement to
solve real-life problems.
Success Criteria
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I can calculate the perimeter and area of a 2D shape.
I can calculate the volume of a 3D object.
I can use formula appropriately.
I can convert between measurements.
I can interpret the problem and solve appropriate calculations accurately.
ASSESSMENT
EVIDENCE
The learner first of all worked
out all possible areas of the
enclosure (in whole metres)
and then realised that there
was a more efficient method.
Learner Conversation:
“I halved 82, which is 41. Working in whole metres, I then multiplied the
highest length by the smallest breadth, that is 40m by 1m, to give an area
of 40 square metres. I then took 5 from the length and added 5 to the
breadth and I realised that the area had increased to 210m². So I kept
doing that and I realised that the answer was around 20m by 21m. I then
narrowed down my working and took 0.5m from the length and added
0.5m to the breadth. A square of side 20.5m gives the maximum area.”
Learner Conversation:
“Since the existing wall was 50m long, I decided to make the opposite
side 50m long too. I took 50 away from the 82m of fencing and divided
the answer by 2, which is 16. A rectangular enclosure 50m by 16m gives
an area of 800m². To see if the area could be bigger or smaller, I took 1m
from the length. An enclosure 49m by 16.5m gives an area of 808.5m²,
which is bigger. I kept going until 41m by 20.5m gave me the biggest
area. After that, the area got smaller.”
Teacher’s Reflections:
Our learner coped very well
with this problem,
immediately recognising
the value of translating the
given information into a
diagram.
However, the difficulties
encountered by the rest of
the class, caused by the
deliberate limiting of
information, highlighted the
need, in future, for more
exposure to realistic
problems which have to be
tackled from scratch.
Learner Conversation:
“I drew a diagram of the paddock using the information
provided and split it into a triangle and rectangle. Using two
formulae, I worked out the areas of the triangle and the
rectangle and added them together. I multiplied the result by
15, which gave us the amount of seed needed in grams. I
then converted my answer to kilograms.”
Learner Conversation:
“To start with, I split the floor plan into two
rectangles. I then worked out the volumes of the
cuboids that sit on these rectangles using the
formula. I then added them together to give me the
overall volume of the barn in cubic metres.”
The learner also used an alternative strategy for
calculating the volume of the barn. He calculated
the volume of the barn as if it was a cuboid and
then subtracted the volume of the part that was
‘missing’.
Many learners immediately divided the volume of the barn by the volume of
a hay bale. After class discussion, the pupils then realised that this would
just give a high estimate to the number of hay bales that could be put in the
barn. For simplicity, we decided to stack the hay bales in columns in a
particular way (length 110cm x breadth 45cm x height 35cm). However, it
was noted that hay bales would not be stacked in this way in real-life for
safety reasons (stability) and this would again just give us an estimate.
On reflection, we could have
further challenged our learner
by asking him to investigate
how many bales could be
stored using different
stacking methods to improve
stability, eg. joints staggered
as in a brick wall.
Learner Conversation:
“I took the volume of the old tank away from the volume of
the new tank. This told me that there would be 2620 litres of
milk in the old tank after it was filled the second time. I
changed this volume into cubic centimetres and also
changed the length and breadth of the old tank into cm. I then
substituted into the formula for the volume of a cuboid, which
gave me an equation to solve to find the missing height.”
The learner also used an alternative strategy to
find the height of the milk in the old tank when it
was filled the second time.
Learner Conversation:
“I used the formula to find the volume of the old tank. I changed this into
cubic centimetres and then into litres. To find out how many times the
milk from the new tank would fill the old tank, I divided the volume of the
new tank by the volume of the old tank, which gave me 1.90972. So I
knew that the milk would fill the old tank once and about nine tenths of
the tank the second time. To find the height of the milk the second time
the old tank is filled, I changed 2m to 200cm and found 0.90972 of 200,
which gave me 181.944. So the milk would be about 182cm high.”
On completion of the investigation,
pupils were put into groups to
discuss how they approached the
tasks, strategies used and their
conclusions. These discussions were
observed by the teacher.
I really thought that
there was not
enough information
in the paddock
question.
I thought that too,
but once we drew a
diagram the
problem was much
clearer.
The milk tank problem was
interesting. I thought that you
were heading in the wrong
direction because you used a
different method to me. I was
surprised when our answers
were the same. I then tried your
method so that I could
understand it. And it worked!