Category Archives: Handling Data

23. Coffee overload

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I was sat in a coffee shop when I overheard the barista say to a customer ‘Take your time, there are about 20,000 different drinks available’.

Sounded like a mathematical challenge to me.

image

If the menu below was real, how many different drinks could made?

How many would be drinkable?

Size: S, M, L

Drink: Filter, Americano, Cappucinno, Machiatto, Latte, Espresso, Hot chocolate.

Coffee type: Decaf or caffeinated

Flavour: Vanilla, Mint, Hazelnut, Ginger, Caramel, None

Milk: None, whole, skimmed, soya

Hint: Be methodical, work out the hot chocolate options first.

Solution
Hot choc
Size *Flavour*Milk = 3*6*4 = 72

Coffee
Size*Drink*Type*Flavour*Milk =
3*6*2*6*4 = 864

Total number of drinks
864 + 72 = 936

This doesn’t consider extra shots of coffee or syrup. Imagine how many variations there are in a big coffee shop!

Me … I’ll have a black filter, no milk, no sugar.

14. JDs Tree Diagram

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My friend JD came up with this visual way of explaining tree diagrams. I’m reproducing it here with permission (Thanks!). It helps if you have a school uniform with a tie and jumper, however this could easily be done with coats and hats.

Set Up
You need 6 volunteers, dressed as listed:
1. (No jumper, no tie) x 2
2. (No jumper, tie) x 2
3. Jumper, tie
4. Jumper, no tie

(This can be adapted for listing multiple outcomes too)

Activity
Draw a V shape on the ground.
Explain that in the morning you have choices when you get dressed. Each branch represents a choice.
Choice 1: Do you put your tie on or not?
Get a student wearing a tie to stand at the end of one branch and one without a tie to stand at the end of the other

Draw a V from each student.
Choice 2: Do you put your jumper on or not?
Get the class to decide who stands where

Discussion
If all the choices are equally likely, what is the probability of getting in trouble with your teacher over uniform?
Can you prove this by looking at the probabilities of the individual events?
What would happen if the outcomes were not equally likely?

It’s a good idea to try and take a picture of what this looks like to display in class. You could also annotate it with fractions and overall probabilities.

9. Scrabble maths

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Check out this link I found on Pinterest:
Printable scrabble tiles

You could practice basic numeracy skills or even pose averages questions like find me a five letter word with a range of 3 and a median of 2 (QUOTH, 41132 is one possible solution).

tiles

3. Class Averages

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This is my favourite activity for introducing different measures of average. You can do this in a corridor or outside, no special equipment required.

Set Up
Line up the class in height order

Range
Ask the shortest and tallest students to stand back to back. The difference in height is the range.

Median
Tell the first and last student to make a half turn. Ask the second and second to last student to make a half turn. Repeat until only one or two students are facing forward.
One pupil = median height.
Two pupils = halfway between their heights is the median.

Mean
Imagine everyone is the same height. Tell the students to try to be the same height by bending knees or standing on tiptoes. Explain the mean is about sharing out equally.

Mode
Ask students to put themselves into groups of the same height. The biggest group is the mode.

This activity links a numerical calculation with a physical activity, which makes it more memorable.

2. Human pie chart

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The main problem students have with drawing pie charts is working out the angles. Barcharts are easy, but as soon as protractors are involved the shutters go down.

How about using the whole class to turn a barchart into a pie chart using nothing more than a playground and a piece of chalk?

1. Pick a topic eg How did you get to school today?
2. Get pupils to move into the correct groups eg Automobile (car), Bus, Walk, Cycle
3. Create a human barchart eg
AAAAAA
BBBB
WW
CCC
4. Move the bars in order into a line
AAAAAABBBBWWCC
5. Move the bars into a circle
(You’ve just turned a barchart into a circle)
6. Mark the centre of the circle, mark in the lines between each section (4 sectors)
7. Ask how many degrees one person represents.
8. Ask how many degrees each sector is worth.
Note: If you have a low ability group or no calculators you may wish to edit the number involved to be a factor of 360. Extra pupils can be keeping notes on a mini whiteboard.
9. To consolidate this you can repeat this with a different question.
10. To extend this task you can split up the class into two groups and ask a different question. They must create two pie charts and compare the data.

This activity is a great task as it makes for a memorable lesson and good discussion point. If you take pictures for a wall display it can make a nice revision prompt.