rounding to different amounts

a ppt is here

usually rounding to a finer amount (5p or 5c) will provide a more accurate estimate to the true cost than rounding to e.g. the nearest 10p or 10c
but not always...

for three addends:
rounding to the nearest 5p is more accurate in 123 cases
rounding to the nearest 10p is more accurate in 28 cases
and for the remaining 69 cases, both methods of rounding are equally accurate

for four addends:
nearest 5p = 417 cases
nearest 10p = 105 cases
equally accurate = 193 cases

for five addends:
nearest 5p = 1210 cases
nearest 10p = 321 cases
equally accurate = 471 cases

[thanks to the National Mathematics Project team, published in the UK in 1989, Eon Harper et al for these solutions and the suggestion for this task]

estimating sums

giant chairs

possibly using the average height graph (in feet)
1 foot = 0.3048 metres (30.48 cm)

state how high off the ground you think the seats of these chairs are

approximate square roots

this isn't too helpful a technique, but does practice some useful skills

compare some actual square roots with the approximations, using the formula

elephants per whale

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

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

size of a million

1, 000, 000
Students can estimate answers, then calculate them.

1 million cm = 10 km, roughly 6.25 miles
1 million pence = £10, 000
1 million grains of salt = half a cup
1 miilion seconds = 11.57 days, less than two weeks
1 million burghers = 600 cows
1 million words is around 4000 pages of an average book
1 million cm^3 = 1 m^3 (a neat model for a million)

The Daily Mirror contains around 125, 000 words so a million words would be roughly 8 copies of this newspaper.

The Independent has around 130, 000 words (so 7.5 of these).

Man Utd attendance is around 76, 000. How many games to make a million?

Terry Pratchett's 'Johnny and the Bomb' (1996, with 272 pages) contains around 70, 500 words. How many readings of this to make a million words?

JK Rowling's 'Harry Potter and the Goblet of Fire' (2000, sales exceed 6.6 million and the book has 636 pages) has around 258, 600 words. How many readings of this to make a million words?

Stomach fluids have a million times as much hydrogen as water.

Molecules rotate at a million revolutions per second.

And the sheep?
There is a 1 in a million chance of a ewe having 5 lambs apparently.