A Question of Scale

Age 14 to 16 Challenge Level:

Why do this problem?

This activity gives practice in working with powers of 10 and tests awareness of relative sizes of physical objects encountered in scientific contexts. The numbers are given in scientific notion, such as 1.2e3 for 1200 or 26e-3 for 0.026, the familiarity with which is essential in the sciences.

You can print out this activity for use on cards if you wish.

Possible approach

The activity could work well as a starter activity with students working individually on computers or working collaboratively to try to place the objects on the scale with as few wrong answers as possible. Alternatively, it could be played competitively with pairs of students taking it in turns to place the objects and checking to see if they are right. There is the opportunity for lots of discussion to justify where students wish to place things on the scale, referring to sizes they know and deciding whether the named objects are smaller or larger.

The activity generates a variety of questions so could be used over a series of lessons with students trying to beat their best scores, helping them to build up a fluency with powers of 10 and a better awareness of the size of things.

There are various levels at which the activity could be used. First students could look at the list of scientific quantities and disentangle which of them they first of all recognise and, secondly, which of them they could place on the scale. Once the easier ones are placed students could take it in turns to take sensible guesses with the harder ones, adjusting the answers in turn until the cards are correctly placed. Finally, the numbers could be revealed to allow the placement of the most difficults cards. This is still non-trivial because quantities are given in standard forms such as 260e-9 (260 nanometres) which would correspond to 2.6e-7.

Key questions

Are there any objects in the list whose size I am fairly sure about?
Is this object bigger or smaller than a metre? How much bigger or smaller?

Possible extension

Big and Small Numbers in Biology and Big and Small Numbers in Physics are two problems which give practice in estimation and calculations using very large and very small numbers.

Possible support

Start by arranging the objects whose size is well known, and use the checking facility to see how many are right so far. Then gradually add in the others.