FRACTIONS, DECIMAL FRACTIONS AND PERCENTAGES –
SECOND LEVEL
Significant Aspect of Learning
Use knowledge and understanding of the number system,
patterns and relationships.
Experiences and Outcomes
I have investigated the everyday contexts in which simple fractions,
percentages or decimal fractions are used and can carry out the necessary
calculations to solve related problems.
MNU 2-07a
I have investigated how a set of equivalent fractions can be created,
understanding the meaning of simplest form, and can apply my knowledge
to compare and order the most commonly used fractions.
MTH 2-07c
I can use the terms profit and loss in buying and selling activities and can
make simple calculations for this.
MNU 2-09c
Learning Statement
 Relationship between fractional numbers, decimal fractions
and percentages
 Interpret questions
 Determine the reasonableness of a solution
 Use mathematical vocabulary and notation
 Select and communicate processes and solutions
 Justify choice of strategy
Task
The learners were given an enterprise challenge to set up a small
business selling Candy Cane Reindeer at the school Christmas
Fair. I wanted them to use their knowledge of fractions and
percentages to consider all the costs involved and compare the
profits that could be made.
The learners had been learning about equivalent fractions and
simplifying fractions and I wanted them to apply this knowledge
to carry out calculations to compare costs.
They were given this table and asked to compare the different
costs.
Information for making 6 reindeer.
Material
Amount
Cost
Comment
1 box of Candy Canes
1 packet of goggly eyes
12
12
£1.00
£0.50
30 assorted eyes
1 ball of wool
1
£1.00
1 packet of pom-poms
1
£2.50
Total:
We discussed that one reindeer would have two
antlers, two eyes and one nose. This meant that
we could make 15 reindeer from one packet of
eyes and one hundred reindeer from one packet
of noses. We also measured that we would need
2m of wool for each reindeer. As one ball
contained 150m metres of wool, this would be
all the wool that we needed.
100 assorted pom-poms
Evidence
The learner’s first task was to find the costs of the materials involved
and determine the most expensive.
Teacher Voice The learner showed that
he was able to write the amounts as
fractions of the whole cost and that he
could simplify the fractions and order
them. He was able to explain why pompoms were the biggest cost for 6
reindeer, but also extended this learning
further by noticing that for more
reindeer this cost would not change as
there were 100 pom-poms in a bag.
Pupil Voice Pom-poms are the biggest cost for 6 reindeer
1
because 2 is bigger because it takes 2 halves to make a
whole, but it takes 10 tenths to make a whole. It won’t
always be the biggest cost, candy canes will, because there
are 100 pom-poms in a bag.
The learner was then asked how many boxes of candy canes would
be needed to make 60 reindeer if they allowed for
1
10
Watch: Pupil Voice- Reindeer task
1
A 10 is the same as dividing by 10 so
I divided 120 by 10 to find out how
many candy canes. We needed to
buy extra for those that might be
broken.
Pupil Voice My friend used a different strategy.
He simplified the fractions, but realised that it
would have been much quicker to divide like I did.
wastage.
Teacher Voice The learner
needed to understand the
terminology and apply his
learning of finding
fractions of amounts. The
learner demonstrated that
he could interpret the
question and apply his
skills to find the cost. He
shared his learning with
other pupils. He was able
to justify his choice of
method and help his friend
understand why his
method was quickest.
The learner was then asked to find the total cost of 60 reindeer.
Please refer to table at the start for information.
Evidence continued in next photo.
Teacher Voice The learner needed to use
skills to find the cost of each material
item, reading the table to interpret the
information and apply knowledge of
finding fractions of amounts and
simplifying them. The learner
successfully found the cost of ‘goggly
eyes’ by simplifying a fraction.
Pupil Voice I noticed that one ball of wool
would make 75 reindeer because I needed
2m for each reindeer and each ball was
150m. Half of 150 is 75, so one ball would
do. I used my fractions to work out the
other materials. From this I learned my
costs for making 60 reindeer.
Pupil Voice I used my fractions skills to work out how many packets of each material I
would need and then added up the cost. It was £16.50, but then we found out that the
shop had reduced pom-poms by 50p so our total cost for 60 reindeer was £16.00.
The learner was then asked: How much will you sell each reindeer
for if you are to make a profit of 25%?
Teacher Voice In the starter task the learner
demonstrated that he could match simple
percentages with the equivalent fractions,
including
1
’s. This showed that he could
100
simplify fractions and that he understood that
percent was a fraction meaning out of 100.
The learner demonstrated that he understood
1
that making a profit of 25% meant finding 4 of
the total amount and adding it on. The learner
applied his understanding to work out 25% of
the total cost, before dividing it by 60 to find
the cost of one reindeer. This challenged the
learner and he worked collaboratively to solve
the problem.
Pupil Voice I found this really
challenging. I knew that 25%
of £16 was £4 because 25% is
the same as
1
, so I then added
4
it to the £16 because it was the
cost price and the £4 was the
profit. The teacher helped us
realise that we now needed to
divide this amount by 60 to
find the cost of one reindeer. It
1
came to 333 𝑝 so I rounded this
up to 34p because people
1
3
don’t have p.
Teacher Voice The learner showed that he understood the terms ‘profit’ and ‘cost’ in working on this
problem and immediately realised that he needed to round up the price. I gave the learner a further
challenge which was to come up with other amounts that could be charged and asked the learner to
find what profit could be made. The learner initially made a mistake because he assumed that as 40p
was 50% profit then 80p would be 100% profit. When he calculated 120p as being 350% profit, the
learner realised that 100% for 80p might not be correct. This demonstrated that the learner was using
knowledge of estimation to check answers and assessing the reasonableness of the answer.
Pupil Voice I thought that 40p would be good to start with because it was the next multiple of 10 after
34p. Then I doubled it to get 80p which I thought would make 100%, but I realised I was wrong when I
worked out 120p and it was a much bigger percent. So I worked out 80p using fractions and found that
3200
2
the percentage was really 200% because it was 1600 which is equal to 1 which is 2 wholes which is 200%.
I think customers would pay 80p for our reindeer and it would make 200% profit.
Teacher Voice The learner
changed the percentage for
80p after realising his
mistake.
Teacher Voice The learner demonstrated an understanding between fractional number and
percentage. The learner clearly demonstrated that he understood the first solution was not
reasonable and used his skills to find a reasonable solution.
It was decided to sell each reindeer for 80p. The learner was asked to
explain which would be the better deal for the customer; 2 for £1.50
or 25% off?
Teacher Voice Using doubling skills, the learner quickly worked out that the customer would save
10p with the first deal. For the second deal, the learner converted 25% into a fraction to establish
that the saving was 20p and was able to identify the better deal demonstrating an understanding of
the knowledge and skills required to solve the problem. This showed that the learner was able to
link the relationship between percentage and fractions and apply it to interpret ‘real life’ questions.
Pupil Voice It was easy to double
the 80p and find the difference
between the answer and £1.50. I
1
4
knew that 25% was the same as so
I found a
1
of 80 by dividing by 4. It
4
made 20p which is a better deal
because you get more money off.
We decided to offer our customers
‘2 for £1.50’ as this would make us
more money than the other deal.
Teacher Voice The learner demonstrated that he could select and communicate processes and
solutions in realising which deal was better for the seller. The learner showed that he understood how
to use the correct mathematical notation for percentage and fractional number in this example.
Finally the pupils were asked to design packaging.
For the packaging we need a card background to stick the candy
canes onto. This has to be a suitable Christmas themed design that
1
3
2
10
has; of the colouring green,
colouring blue and
1
20
of the colouring yellow,
1
20
of the
of the colouring red. The rest is left blank. How
much is blank? Can you express it as a fraction? What type of paper
would help you create your design?
Teacher’s Voice The learner suggested that we used squared paper to make our design and
changed all of the fractions into percentages. This demonstrated that the learner was making a link
with the previous activity and knew the link between fractional numbers and percentage. A second
learner suggested using the 100 square on the interactive board. This was met with much approval
from the other learner, as he could easily adapt his design through trial and error. This
demonstrated that the learner could select and communicate the process and solutions. The learner
quickly realised that 10% would be blank, re-enforcing that he understood that percent meant out
of 100, as the other amounts added up to 90. The learner reinforced that he had interpreted the
question successfully and was able to justify his choice of strategy.
Pupil Voice We had been using
fractions in the other task so I just
saw that I could turn the fractions
into percentages and if we used a
100 square then it would be easy to
design because percent means per
100. Using the Paint on the Smart
board made it easy to change my
design. When I was happy with it, I
coloured it onto squared card.
Teacher’s Voice The learner realised how important accuracy was to ensure each colour was a true
fraction of the design. Through reflection on learning, the learner demonstrated that he
understood the relationship between equivalent fractions and simplified fractions as well as the
relationship between fractions and percentage. Through successfully completing the tasks, the
learner demonstrated that he could apply knowledge of simple fractions and percentages to solve
‘real life’ problems involving comparing and ordering fractions. This demonstrates that the learner
is confident at second level in this aspect.
We met our target of making a 200% profit of £32, which along with other money raised, funded
the purchase of new technology for the school.