# Little Man

##### Stage: 1 Challenge Level:

Alara from FMV Erenkoy Primary School sent us a very full solution to this problem:

Estimation of how tall he is : - It is not possible to say an exact number or measurement for his height. There could only be some estimations. However, I can make an estimation using the ratio of the man's height to the mug's height.

Something at school or at home which is approximately twice as tall as the Man : - It depends on the mug's height; for example according to my milk mug's height when I checked, my big dictionary and my cd box is approximately twice as tall as the Man.

Something which is about half as tall? And again, as I have written above, according to my milk mug's height, my post-it papers and small address note book are about half as tall as the Man.

How tall the Man's mug might be? My mug's height is 10 cm and I am 150 cm tall. The ratio between me and my mug is 10/150, that is to say 1/15. The Man's mug might be 15 times smaller than his height.

How many "Man Mugs" of tea might fill one of my mug? There is a way to answer this question, if we take into considerationthe "ratio principles". Above, I identified that I'm 15 times as tall as my mug. So, let's assume the Little Man is as tall as my mug, so he is 10 cm tall. If we consider the same ratio between the Little Man and his mug, the Man Mug is 15 times smaller than him. 15 "Man Mugs" of tea might fill my mug.

Sam from Farndon Primary School and Harri from Pilgrim's School also estimated similar heights for the Man, although Sam thought that 79 "Man Mugs" of tea would fill one of our mugs. Do you agree with Alara or Sam? Can you explain why?