5. averages and range mr barton maths.com venn diagrams
TRANSCRIPT
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5. Averages and Range
mr barton maths .com
Venn Diagrams
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About Venn Diagrams
• I began to see the huge potential for the use of Venn Diagrams as a rich task from my constant source of inspiration – the amazing Median Maths Blog, by Don Steward. He created a lovely Straight Line Graphs Venn Diagrams task that you can access here
• Here is why I love Venn Diagram activities so much– 1) Students can always make a start. If they can think of a number/expression/object
or whatever it might be, it has to go in one of the regions on the diagram, so they are up and running
– 2) The more regions student find, the more challenging the task gets, which adds a nice element of differentiation
– 3) They are incredibly versatile, and can be used for almost all maths topics for all ages and abilities
– 4) They are very quick to create and require no special resources– 5) Students can create their own
• Give them a go, and if you or your pupils cannot resist the urge to create your own Venn Diagram tasks, please let me know
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Instructions• The diagram below shows how triple Venn Diagrams work• Try to find an example of a number/expression/object to go
into each of the 8 regions• If you think it is impossible to find an example for one or more
of the regions, try to explain why
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Median = 5
Range > Mean
Mode = 4
Think of a list of 5 numbers that could belong in each region
b d
f
c
hg
e
a
Task 1
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Range < Mean
Median = Mean
No mode
Think of a list of 5 numbers that could belong in each region
b d
f
c
hg
e
a
Task 2
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Median > Range
Mode = Mean
Mean > Median
b d
f
c
hg
e
a
Think of a list of 5 numbers that could belong in each region
Task 3
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Venn Diagrams Challenges• Which was the easiest region to complete, and which was the hardest?
• Which region has the most possible examples, and which has the fewest?
• If you think it is impossible to find an example for a particular region, convince me why
• Describe your strategy for filling in the regions
• Create your own Venn Diagram on this topic where it is possible to fill in all the regions
• Create your own Venn Diagram on this topic when it is impossible to fill in just 1 of the regions. How about one where it is impossible to fill in 2, 3, 4, etc regions?
• Can you create a quadruple Venn Diagram for this topic?
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Venn Diagrams Challenges (adapted)• Which was the easiest region to complete, and which was the hardest?
• Describe your strategy for filling in the regions
• If you think it is impossible to fill in a region, identify and change one of the categories to make it possible
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1. Create your own Venn Diagram on this topic when it is impossible to fill in just 1 of
the regions. How about one where it is impossible to fill in 2, 3, 4, etc regions?
2. Can you create a quadruple Venn Diagram for this topic?
Venn Diagrams Ultimate Challenges!
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Exemplar Material (Wiles) – Task 1
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Exemplar Material (Wiles) – Task 2
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Exemplar Material (Wiles) – Task 3
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