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How many different combinations of two
ice-cream flavours are possible on a double
cone?
Answer: 3 (Flavours used are strawberry
and vanilla)
2 scoops
of vanilla
1 scoop of vanilla
1 scoop of strawberry
2 scoops
of strawberry
1
How many different combinations of three ice-cream
flavours are possible be on a double cone?
Answer: 6 (Flavours used
strawberry and chocolate.)
2 scoops
of vanilla
2 scoops
of strawberry
1 scoop of vanilla
1 scoop of strawberry
are
vanilla,
1 scoop of vanilla
1 scoop of chocolate
1 scoop of strawberry
1 scoop of chocolate
2 scoops of
chocolate
Your task today is to investigate how many combinations
there would be for 4, 5 and 6 different flavours of icecream.
Record all of your working out on the sheets
provided.
2
Name:
School:
Ice-Cream Up Investigation
In the space below, describe the investigation
that you are being asked to do.
Introduction:…………………………………………………………
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Put your results into a table.
3
Name:
Number of IceCream Flavours:
1
2
3
4
5
6
School:
Number of
combinations on a
double cone:
1
3
6
10
15
21
Can you see a pattern or rule? Yes / No
Describe this pattern or rule in your own
words.
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4
Name:
School:
How many combinations would be possible for
7 flavours ?
Predict your answer:…………………………………………..
How many combinations would be possible for
10 flavours ?
Predict your answer:………………………………………….
Can you find a quick way to work out how many
combinations would be possible for 20
flavours ?
Predict your answer:……………………………………………
Explain what your quick way is:
…………………..…………………………………………………………….
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5
Answers:
The numbers
1, 3, 6, 10, 15, 21, 28, 36, etc
are called the Triangular Numbers.
In this sequence, the difference between
the consecutive numbers gets bigger by 1
each time.
e.g. 1 and 3 ………the difference is 2
3 and 6 ………the difference is 3
6 and 10 ………the difference is 4
and so on…………………………
1
3
6
10
15
6
Formula:
A quick way to work out the number of
possible flavour combinations on a double
cone can be made using this formula:
Possible combinations = 0.5n2 + 0.5n
Where
n is the number of ice-cream flavours
E.g. for 20 flavours (n = 20)
Possible combinations = 0.5 x 20 x 20 + 0.5 x 20
= 200
+ 10
= 210
7
Name:
School:
8