Data Handling – SECOND LEVEL
Significant Aspect of Learning
Research and evaluate data to assess risks and make informed choices
Learning Statements
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Appropriate collection of data and graphical representations
Reliability of data and graphical presentation
Probability
Relationship between fractional numbers, decimal fractions and percentages
Determine the reasonableness of a solution
Use mathematical vocabulary and notation
Experiences & Outcomes
I can conduct simple experiments involving chance and communicate my predictions and
findings using the vocabulary of probability. MNU 2-22a
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 can show the equivalent forms of simple fractions, decimal fractions and percentages and can
choose my preferred form when solving a problem, explaining my choice of method. MNU 2-07b
I have carried out investigations and surveys, devising and using a variety of methods to gather
information and have worked with others to collate, organise and communicate the results in an
appropriate way. MNU 2-20b
I can display data in a clear way using a suitable scale, by choosing appropriately from an
extended range of tables, charts, diagrams and graphs, making effective use of technology. MTH
2-21a
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Learning Intention

To be able to use the language of probability
Success Criteria
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
order the vocabulary of probability on a scale using numerical values.
list possible outcomes of simple experiments.
The teachers’ version of the probability game show involved a host asking a contestant to stand on
a line of probability according to how likely the event was to happen. Events grew increasingly
more subjective and ‘tricky’ to give a definitive answer to.
After watching the teachers’ version of the probability game show the learner was then encouraged
to use the game show question cards within small groups. Firstly he was asked to group them into
Possible and Impossible. This led to discussion using other vocabulary such as ‘certain’,
‘uncertain’, ‘likely’, and
‘unlikely’.
EXAMPLE CARD:
You toss a 6-sided die
and it doesn’t land on
2.
Teacher Comment
This task gave me the opportunity to assess how much the learner had learned
from watching the teacher version of the probability game show. At each stage
of these card sorting activities the group aspect of this task encouraged the
learner to use the language of probability in order to justify his sorting of the
cards. The learner was not only having the chance to use the mathematical
language but also give solutions and justify the reasonableness of his answers
to both peers and teachers.
Learner Voice
“I liked getting to discuss these cards in a group because at first I was worried
we would be the contestants and I wouldn’t know where to stand. This way I got
to talk to my friends about what I thought was most likely to happen first.
This was good practice at telling each other what we thought was impossible or
certain or likely. And we also had a good argument about what an ‘equal
chance’ was.
Some of the cards were really hard because you don’t know if there is really a
right or wrong answer or just a very good explanation.
It has made me think that probability is all about educated guesses and how
well you can explain your answer.”
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The learner was then asked to sort these onto a probability numerical scale.
IMPOSSIBLE
CERTAIN
The learner once again used
listening and talking skills to
discuss and justify his placing on
the scale. The learner appeared
more keen to place his cards
down as he was more
comfortable with the idea of
probability on a ‘scale’ as
opposed to definitive boxes such
as in the previous tasks. This
showed his developing
understanding of the possibility
that answers are subjective and
require clear justification.
Learner Voice
“I liked using the scale because it felt like you could get the answer right more
easily…I think this is because some of these cards, there is not an exact right
answer, or no one can ever know what the answer will be for definite so you
have to place it on the line as closely to the right answer as you can.”
3
Learning Intention

Create a visual representation of my
information
Success criteria
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


choose the best type of diagram to show
my results clearly
diagram contains title, labels, axes and
scale
software is used to create my graph
interpret the data and draw conclusions
Teacher Comment
After the initial 'Probability' task, I asked the learner to
continue throwing the dice to extend this experiment
and test the hypothesis that seven would be the most
common outcome. The learner knew that a bar
graph would be the best way to represent this data.
He gave the graph a title and labelled the axes
without any prompting.
These experiments allowed the learner to begin to
assign numerical language to the possible outcomes
of an event.
Through exploring the possibilities of totals throwing
1 and 2 dice and recording answers the learner soon
noticed the patterns and was able to independently
explain his findings. He then applied this to similar
experiments such as using a spinner, flipping coins
and playing ‘races’ with die.
Learner Voice
“Learning about probability is really helping my discussion
skills. I have to be able to give reasons for my answer and
not just write the answer down.
I noticed that when I did the extra task seven became the
most popular total from the two dice. I chose a bar graph
rather than a pie chart or a line graph because I thought it
was easier to see the information.”
Learner Conversation
“These experiments were really
fun. Now I can see how much
probability has to do with
games.
I found it really easy to name all
the outcomes on the dice
because you could see them all.
It was more tricky with two but
not after you had added them all
up.
After we had recorded all the
possibilities when you roll 2 dice,
it was really obvious to see how
car number 7 was the most
likely to win!” (Referring to
wacky races game)
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Learning Intention
To apply our knowledge and understanding of fractions, decimal fractions and percentages to
situations involving probability.
Success Criteria
 describe the probability of an event happening within a zero to one scale.
 explain how the implications of chance are used in daily routines, decision making and the
media.
 use the difference between the predictions and actual outcomes and explain results.
‘A prediction is what you think will happen based on
something that you already know.’
The learner was asked to take his experiments a little
further by designing his own spinners to suit certain criteria,
e.g. make a spinner with a 25% chance of spinning a prime
number. This allowed him to demonstrate and predict the
outcomes in an experiment, using numerical values of
probability. He was then asked to use his spinners, make a
frequency table and charts to explore the probability of
scoring different totals. This then gave the learner accurate
actual results and allowed him to display and explain the
results.
Learning Intention

Create a visual representation of my information
Success criteria




choose the best type of diagram to show my results clearly
diagram contains title and keys
use software to create my chart
interpret the data, draw conclusions and make predictions.
Number
on
spinner
8
7
5
4
10
15
21
1
Number
of times
landed
on
4
3
2
1
6
3
0
1
Learner Voice
I can see from my pie chart that the spinner landed on number 10 the most. I know
because the number 10 has the biggest piece of the pie. The smaller the piece of
pie then the less often the spinner landed on that number. I can predict that if I kept
playing this game then my spinner would probably land on a number that was not a
prime number because the prime numbers have the smallest pieces of the pie.
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After watching various educational clips the learner took part in group discussions about the everyday
implications of probability on his life. He discussed daily routines, decision making and the media.
The video clip used to fuel this discussion was:
http://www.nationalstemcentre.org.uk/elibrary/resource/7327/lucky-numbers
This gave the learner an excellent insight to all three of these real life uses for probability. The learner
then completed “Exit” cards for the lesson explaining how the implications of chance are used in
either daily routines, decision making or the media. These sparked a lot of interest and resulted in the
learner having a clearer understanding of the way in which data could be misleading.
Learner ‘Exit Card’ answers:
“The weather. This is predicted by meteorologists, who are special weather scientists. They
look at the patterns in the clouds and also what has happened in previous years to make very
educated guesses about what the weather will be.”
“Lifeguards at the seaside make decisions based on the weather about what the sea will be
like. That is how they decide what flag to put up at the beach to say it is safe.”
“Running. You can say who will be most likely to win a race based on who goes to running
club and who doesn’t.”
“Plant growth: People growing things in their gardens may experiment with what kind of
plants grow best and also where to put them as some areas might get more light so
different plants will be more likely to grow better and some might be certain to die.”
“Animal Breeding. Breeders will have to predict whether or not the animals will be a good
match, and if the baby will have a good nature.”
“Gambling with cards; you have a 1/52 chance of getting a specific card however you have
a 1/13 chance of getting one of say…the Queens or Kings” - much higher!”
Learner Voice: “This really made me think about how I will use maths in the future not just
now.”
The learner had now had many opportunities to discuss probability in a real life context and to use
the vocabulary of probability, relating the chance of an event happening to a scale of 0-1 (impossible
– certain, or by using fraction/percentage/decimal fraction notation)
The learner then completed a set of questions which aimed to demonstrate his understanding of
these learning intentions and success criteria together.
Teacher Comment
These diagnostic questions gave an excellent picture of how the learner was able
to really apply his knowledge and understanding of probability that he had
gathered over several lessons. Not only did he have to use the language but he
had to think very carefully back to his experiments and what he learned from
those. The learner applied his knowledge of multiplication, fraction and
percentage skills to complete the majority of this task with ease.
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As a class we watched a clip
of a quiz show where the
contestant is faced with three
doors. Behind one door is a
new car and behind the other
two are turnips. The
contestant chooses a door and
wins whichever prize is behind
that door.
The host of the show knows
where the car is hiding and
when the contestant chooses
a door he then opens one of
the two remaining doors to
reveal a turnip. The contestant
must then decide whether to
stick with his original choice,
or to switch to the other door.
Being careful to stop the clip at
a certain point the learner was
posed the question - How
should the contestant answer
in order to maximise his
chances of winning a car, and
what is the reason for this
decision?
The solution is that they
should change their original
choice of door to the other
door which has not been
opened. Originally their
chosen door had only a 1 in 3
chance of winning and a 2 in 3
chance of losing, i.e. they are more likely to have chosen a losing door initially, so should change
their choice of door to increase their chances of winning.
Teacher Comment
This problem is good for discussing the vocabulary, e.g. a 1 in 3 chance and also when faced
with the remaining two doors pupils assume incorrectly that they then have a 50/50 chance of
winning. An excellent discussion followed and it was good to explore why this is not the case.
Pupil Voice
“Waw! That problem really made you think! After you hear the answer and why it all made sense!
But before, your instincts tell you to stick with it. But probability really makes you understand
chance.”
The learner was then set with the task to come up with his own ‘game show’ based on probability
questions which would demonstrate his own achievement of the success criteria ‘describe the
probability of an event happening within a zero to one scale.’
Most groups chose to do a very similar version of the teacher led probability game show. One group
chose to do this as a ‘Who Wants to be a Millionaire?’ Style game show. All learners chose to do a
‘Monty Hall’ style problem as their final bonus round.
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Teacher Comment:
As a teacher assessing the learner’s knowledge of the probability of an event happening this
gave an excellent opportunity for me to see the pupil think this through from start to end. He
not only had to come up with his own event, he had to decide as part of a group what they
thought the answer was and verbalise his justification as an ‘expert on probability’. This
developed his own questioning skills and aptitude to determine the reasonableness of a
solution. The leaner had to communicate his solutions, using mathematical vocabulary and
notation.
The learner started his game show
by asking the audience to organise
themselves into a human
probability line. The learner
described this as ‘Perfect
numeracy warm up for any chance
lesson’. He was very engaged with
his learning.
Example of probability game show questions from one learner:
“Our teacher will let us have 15 minutes extra break if you get all the answers right”
“Your Mum will make you fish and chips for tea tonight”
“Every member of the class owns a dog”
“Every member of this class has a purple jumper”
“Our teacher will give us all 20/20 on our Friday Mental Maths”
“There is a 1/12 chance I can guess the month a stranger’s birthday is on”
Learner comment:
“This was a really fun way of demonstrating my skills. I had to work well as a group and
make some good decisions as an expert before we did our game show.”
“This was the best part about probability – inventing your own ideas. Even some of the
craziest ideas when you really think about it…they are still possible…but with a very low
percentage.”
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