# Orders of Magnitude

Students will be expected to make order of magnitude calculations. For example, in cell biology, students will need to demonstrate an understanding of size and scale. When looking at topics on the atmosphere, pollution and climate change, students should be able to use orders of magnitude to evaluate the significance of data. An understanding of orders of magnitude is also expected when looking at road safety and stopping distances for example. In some cases as part of the physics course, students will be expected to be able to give estimated values of particular quantities such as typical speed for wind, the speed of sound and various transportation methods (e.g. walking and cycling).

The biggest challenge in this area of mathematics when used in the science classroom is the basic difference between mathematics as an abstract subject and its use as a tool for science. Mathematicians are quite happy to talk about exact numbers however big or small, but in science a measurement stated as part of the results of a scientific experiment can NEVER be exact.

Students are often insecure or lack confidence in making their own decisions about what accuracy to use and when. Use a range of scientific contexts to give them opportunity to explain and justify their choices. Students are often more likely to trust the output of a calculator, even if the sum has been entered incorrectly, than to ask whether it is reasonable based on the context and their estimate.

Practice with the use of numbers is a crucial scientific skill. This list of interesting questions will allow students to practice these skills whilst developing awareness of orders of magnitude in scientific contexts.

These resources help prepare students for this by reviewing place value when multiplying and dividing by 10 and the use of powers of 10 in scientific contexts. It then goes on to suggest some areas for investigation focusing on climate change.

You may find this orders of magnitude and standard units table helpful.

## Links and Resources

### Nrich - A Question of Scale

This activity will test your knowledge of powers of 10 in scientific contexts. There are hints that can be used by students if they need some help understanding the notation.

This resource will need flash player

### Multiplication and Division by Powers of 10: Follow Me Cards

Two sets of follow me cards, the first of which requires students to multiply a whole number by 10 or 100 to find the next card. The second set requires students to divide whole numbers by 10 or 100.

### Units of measurement

A detailed description of different types of measurement

### Orders of magnitude and standard units

A quick guide from the Royal Society

### Powers of Ten

Perhaps the most famous video designed to help guide students (and adults) gain a sense of the scale of the universe on a relative level comparing object and sizes to each other. Moving from a 1mx1m picnic blanket up to the whole universe and then back down to an electron in steps of x10 each time. Whist dated in some senses, this video is still really helpful in helping gain a sense of perspective.

The same idea was updated in 2009 with a film called COSMIC VOYAGE narrated by Morgan Freman with higher production values.

THIS website has a similar interactive simulation you can scroll through

### Relative size activity

A set of 25 downloadable cards featuring objects of various sizes. Some of the objects are very small indeed, such as the width of DNA, while others are very very large, such as the distance from the Earth to the Andromeda galaxy

### The Scale of the Universe

Probably the best interactive animation on scale and relative size available. This scrollable resource allows you to see object of similar size (Asia is bigger than Mercury!) and differences (The star Betelgeuse is bigger than the distance between the Sun and the Earth!). I’ve never known a student or adult not been rather amazed by this.

### Universcale

An interactive. flash based animation that allows you to scroll through various objects to see their relative size, ranging from subatomic particles up to the universe. As mentioned above, helping students to get a sense of relative or comparative sizes can be more useful that trying to apply meaning to absolute numbers.

### Biology Measurement Challenge

These interesting questions will allow students to practise using different units of measurement whilst developing awareness of orders of magnitude in scientific contexts. Some also require students to find additional information. As with any problems involving approximation, they offer opportunity for classroom discussion and justification.

Resources include solutions and teachers resources that include possible approaches in the classroom, key questions and ideas to support and challenge student. This could be used to demonstrate number, size and scale and the quantitative relationship between units in cell biology.

### PLUS - Mathematics of Climate Change

*Plus* is an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics. This set of resources look at the mathematics of climate change.

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Last updated | 15 December 2015 |

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URL | https://www.stem.org.uk/lxpxd |

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