average-with-spread

if I gave you just the average height of two people you wouldn't know whether they were roughly the same height or whether one was tall and the other short

Bethan Copeland's theorem

if you start with a square number,
add the next square number,
then subtract the next square number,
you always end up with a number that's 4 away from the square number before the one you started with

e.g. 16 + 25 - 36 = 5 and 9 - 4 = 5



Bethan discovered and proved this when in y10

elephants per whale

how many average elephants weigh the same as an average blue whale?

tables practice

given a pair of numbers, (a, b) find the smallest number, c so that
when you add this to one of the pair the other will divide (exactly) into this total

b is a factor of (a + c)
and
a divides into (b + c)

(3, 8) is 13 because
13 + 3 divides by 8 and
13 + 8 divides by 3

(5, 7) is 23
5 + 23 divides by 7 and
7 + 23 divides by 5

(6, 8) is 10
6 + 10 divides by 8
8 + 10 divides by 6

what if the pair are co-prime?

otherwise you need to divide by the hcf first and then what?

(10, 15) is 5
(12, 18) is 6

(1, anything) needs special consideration...

why do these rules work?

estimating II

please estimate:

1. the area of the Sahara desert in square miles?
2. a maximum speed for a Cheetah to run?
3. the number of litres in an average bath?
4. words to a daily newspaper (one with quite a few words in)?
5. the length of the largest recorded whale?
6. a very hot oven's temperature?
7. times a spot on a car tyre touches the ground in a km?

answers:

1. 3 million (area of UK = 94, 251 sq miles, Sahara = 31.83 UK)
2. 70 mph
3. 140 litres
4. 100, 000 words
5. 29m
6. 260 degrees C
7. 500 (an interesting calculation, diameter seems to be around 73.5cm)

estimating things (I)

• how many peas do you think will fit on a tablespoon (not teaspoon)?
• how many students in this school?
• how many pages in an average novel?
• how far do you think it is from London to Athens?
• how many bricks in an average house?

they do say that if you ask for the lowest and highest anyone thinks it could reasonably be, then calculate the geometric mean of these two values, you get a pretty good estimate

it might be worth testing ....

some answers:

• about 50 peas per tablespoon
• it depends
• about 300 to 400 pages per novel
• 1,500 miles from London to Athens
• 15,000 bricks per house

it's all relative

if an average sort of a cow is 132 cm high, how high would you estimate the girl is?