FIRST LEVEL
Significant Aspect of Learning
Use knowledge and understanding of the number system, patterns and relationships.
Experiences and Outcomes
Having explored fractions by taking part in practical activities, I can show my understanding of:
- how a single item can be shared equally
- the notation and vocabulary associated with fractions
- where simple fractions lie on the number line
MNU 1-07a
Through exploring how groups of items can be shared equally, I can find a fraction of an amount by applying my
knowledge of division.
MNU 1-07b
Through taking part in practical activities including use of pictorial representations, I can demonstrate my
understanding of simple fractions which are equivalent.
MTH 1-07c
Learning Statements
- Relative size of fractions
- Connections between operations and fractions
- Use mathematical vocabulary and notation
- Select and communicate processes and solutions
- Justify choice of strategy used
- Interpret questions
1
EVIDENCE
TASK – Which is bigger, one half or one third? Use different resources and materials to help you complete
this task.
Using a fractions wall is an easy
way to see the size of the
fractions. Like, one third is
bigger than one quarter.
Let’s start by drawing
a whole. But how are
we going to draw an
accurate half? I know,
I’ll draw another
whole under the first
one and then split it in
half.
If we fold the
paper we can get
half. And then fold
it again to get
quarters.
From my fractions wall I
can see that two quarters is
the same as one half. I can
see that 20 cubes split in
half is 10. I can also see that
20 cubes split into quarters
is 5.
Listen to: Learner Voice - Fractions Wall
“If this was a cake I think I would rather have one half because one
quarter is smaller. But from my fractions wall I can see that two
quarters is the same as one half. I might use this to trick people.”
“What went well was comparing the halves, quarters and eighths
because I could see that they were halved each time.”
Teacher Voice
The learner decided that using a fractions wall would be a good tool in order to see the size of fractions as it would be easy to compare. He then used
different materials and resources and was able to share equivalent fractions with a peer. He used the strategy of folding the paper in order to divide it equally
into halves, quarters and eights. He continued this further by explaining that, in order to create quarters, the whole must be cut into 4 sections because the
denominator is 4.
2
TASK – We have been asked to design a logo for the new local garden centre. The logo has to consist of the colours green, red
and purple. ½ green, ¼ red and ¼ purple.
I had to split one square in half
because ½ of 25 is 12 and a half. So
I had to colour 12 and a half
squares red.
I have 20 squares
in my logo. So to
find a quarter I
divide by 4. What
is 20 divided by 4?
My logo has 180 squares
altogether. I divide by 2 to get
green. I divide 180 by 4 to get the
red and then the purple. I know I
had to divide by 2 and 4 because
they’re the denominators.
Listen to: Learner Voice - Logo task
“First of all, I chose 20 squares for my logo but then I wanted the logo to be
bigger so I made it 52 squares. I used an even number because I knew it would
be easier to divide by 2. I checked that half of my squares were green. I knew
that to find a half I had to divide by 2 and I checked my answer by doing a
multiplication sum.”
half of 52 is 26 and 52 ÷ 2 = 26 and 26 x 2 = 52
Teacher Voice
The learner described a half as splitting a whole into 2 and a quarter as splitting a whole into 4. He thought carefully about the type of paper he used for his
logo, chose squared paper and was able to justify his choice. He checked his work using multiplication strategies and made the link between fractions and
operations. When discussing his work with a peer he realised he had to divide the total number of squares and not the number of squares left to ensure he had
¼ red and ¼ purple. The learner was then able to justify the choice of strategy he used when designing his logo and shared this with others.
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TASK - Primary 7 are having a toy sale to raise money for school charities. The toys will be sold for a discounted price
because they are second hand. Display the original price and the sale price.
The guitar is £4 and I want to make
it quarter of the original price. £4 is
There is a difference between taking a quarter
the same at 400 pence so the sum is
off the original price and having a toy quarter
of
the original price. I need to take away when
400 ÷ 4 (the
denominator).
The new
TASK - The garden centre
is going
to order
lots of stock to sell. Using
the floor plan to help, decide
finding
a quarter off. I knew from when I have
price is £100, no wait, 100 pence so
been in the shops that I can say 25% off
which plants they should order and
£1. where they should be stored at the shop. The total number of
instead of a quarter off.
plants must be 100.
Lots of shops use
fractions in their
discounts to make it
look like you are
getting a good deal.
I chose to have 10
trees in my Garden
Centre. I then worked
out the fraction. The
numerator is the
number of trees I have
and the denominator
is the number of
plants I have
altogether.
I put all of the
trees into the
outdoor area. I
split the total
amount of trees
in half so that 5
were in one red
space and 5 were
in another.
have to put 10 on each shelf so 20 ÷ 2 = 10.”
Teacher Voice
The learner began by exploring and discussing what was meant by the word ‘sale’. He understood that many shops display offers such as buy one, get one free,
half off, 10% off etc. He then chose the toys for the shop, created the original price and estimated the sale price. He was able to use division and subtraction to
create the new sale price. He explained that to find the sale price of £1, it is important to know that £1 is equal to 100 pence. The learner made links between
fractions and percentages through a discussion with an adult. Although this was not part of the task, this link will be the learner’s next step.
4
TASK – Create a real life fractions word problem and explain your answer.
I have 20 flowers and 5 vases. How many flowers
would be in each vase?
I split the flowers five groups and this is fifths. I
thought it was quarters first but it’s 4 in each group,
not four groups.”
Answer: 4
I chose to use 20 flowers in my word
problem because I knew it could be divided,
it was an even number. I then thought that
I could divide 20 into 5 groups equally. I
wanted to check my work so I asked if I
could use cubes to make sure I was right. If
tried to split the 20 cubes into 6 groups, so
sixths, but the cubes that were shared were
unequal. I knew my word problem had to
use dividing because you needed to split
objects into groups.
I created a word problem with 10
sweets. I gave 5/10 to John and
3/10 to Nicole. I know I have 2/10
lengths because I use my
subtraction skills.
Answer: 2 tenths
Teacher Voice
The learner was given word problems linked to fractions and he was able to justify his answers as well as the strategies he used. He was able to look at the
relative size of fractions, use vocabulary and notation as well as the connections that fraction have to multiplication, division, addition and subtraction. He then
created word problems for a peer. When his peer made a mistake, he explained where his friend had gone wrong and appropriate strategies to get the answer.
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TASK – Create a game board or poster to show your understanding of fractions. You can use as many
different resources as you would like.
Learner Voice
“I played my board game with my friends. One person got
the wrong answer but I explained what they had done
wrong. They got their next answer right!”
Teacher Voice
The learner used this opportunity to showcase his
learning to others. He demonstrated a sound knowledge
of the links fractions have to operations as he was able to
share his strategy of completing the calculation, what is
one half of 60. He created a poster linking fractions into
his own life and confidently shared these with others.
This task was a great way for me to assess what the
learner knew about fractions as he had to create
questions and justify his answers.
In my board game you have to move around
the board answering questions about fractions.
If you get an answer wrong you go to jail. To
get out of jail you need to answer another
question about fractions. The questions can be
sums like what is a half of 10 or they can be,
‘name the fraction’. There is a square on the
board game and if you land on it you need to
match fractions cards (the words to the
notation).
Next steps:
The learner is now ready to extend his
learning by investigating the links
between fractions, decimal fractions
and percentages. He should now
investigate the everyday contexts
where these occur. The learner should
now begin to look at fractions in the
simplest forms including equivalent
fractions.
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