Introduction to standard index form

Working out the rules according to which a calculator displays large numbers

Lesson idea. Numbers that are too big for the calculator's 10-digit display are shown in standard index form. Many calculators now use ×10n but older calculators may use ‘E’ in the display instead. This activity is for secondary school pupils who are unfamiliar with standard index form. It is an intriguing one hour investigation where pairs of students explore the way a calculator converts numbers. They may well find out how it works for themselves.

Teaching approach. The Standard Index Form is a key idea for mathematicians and scientists. The notion that we choose to write numbers in this way requires some explanation. So in this activity, pupils take part in an investigation^(ta) on how standard index form works. This is a higher order^(ta) problem solving context where students are encouraged to engage in mathematical thinking^(ta). They may be involved in whole class^(ta) or small group work^(ta) discussion^(ta), so they have a good opportunity to practice using mathematical language^(ta) and questioning^(ta). This means that students do not need to be able to explain their ideas in full: they can use the calculator's feedback to discover whether their ideas are correct or not. This is also an exciting way for pupils to realise an initial idea that fits the data may need to be extended when new data arises. This resource therefore aims to develop investigative skills, as well as introduce pupils to standard index form in a memorable way. The pupils can later use their knowledge of indices in discussion^(ta) and group talk^(ta) as they explain what is happening.

Resource details
Title	An Introduction to the Standard Index Form
Topic	[[Topics/Standard Index Form|Standard Index Form]]
Teaching approach	[[Teaching Approaches/Investigation|Investigation]],  [[Teaching Approaches/Group talk|Group talk]],  [[Teaching Approaches/Higher order|Higher order]],  [[Teaching Approaches/Questioning|Questioning]],  [[Teaching Approaches/Whole class|Whole class]],  [[Teaching Approaches/Mathematical thinking|Mathematical thinking]],  [[Teaching Approaches/Language|Language]],  [[Teaching Approaches/Group work|Group work]],  [[Teaching Approaches/Discussion|Discussion]]
Learning Objectives	Students should be able to: convert numbers between standard index form and ordinary form, recognise whether a number is in standard index form or not.
Subject	[[Resources/Maths|Maths]]
Age of students / grade	[[Resources/Age 12-16|Age 12-16]],  [[Resources/6th form as a recap|6th form as a recap]],  [[Resources/Secondary|Secondary]],  [[Resources/KS4|KS4]],  [[Resources/KS3|KS3]]
Additional Resources/material needed	This was written for use with TI-82 Graphical Calculators, but new scientific calculators can also be used.
Other (e.g. time frame)	This activity will take at least an hour.
Files and resources to view and download	The Introduction to standard index form/Teacher Notes contains teacher notes, a PowerPoint presentation and an Excel worksheet to be used for an activity on numbers in the solar system. All three files are also available to download: File:Introduction to standard index form - teacher notes.doc, File:Standard index form.ppt, File:Solar system data.xls.
Acknowledgement	This resource was adapted from resources contributed by Mark Dawes