Introduction to standard index form

Lesson idea. 4

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	Introduction to 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]]
Format / structure	5
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]]

Teacher Notes Topic: Introduction to Standard Index Form

Original Author: Mark Dawes

Type of Lesson/length: Investigation and Discussion. Work in pairs. 45 minute lesson

Age/Level/Key Stage: Years 7-9, KS3

Learning objectives

By the end of this lesson students should be able to:

a

b

c

Pedagogical rationale/strategy

This needs to be written...

Resources required

This was originally written for use with TI-82 Graphical Calculators, but nowadays new scientific calculators can also be used.

Differentiation/student ability/sets

State them here if known/identified

Background

This is for pupils who haven’t yet been introduced to standard index form and is a way for them to be intrigued by it and to work out for themselves how it works.

Important facts

On modern scientific calculators numbers that are too big or too small for the 10-digit display are shown in standard index form. Most such calculators now use ×10ⁿ but older calculators might use ‘E’ in the display instead.

If a calculator is in ‘scientific mode’ it will display all numbers in standard index form.

About the lesson Plan

Display the first slide and ask the pupils what each of the sets of numbers have in common.

The first set all have 1 significant figure, the second have 2 sig figs, etc. The pupils are likely to find this difficult.

Then ask them to put their calculator into Scientific Mode. If the school has sets of scientific or graphical calculators then these can be set up in the right mode in advance.

The pupils should start only with numbers with 1sf and should type them in and then press ‘=’. They should then choose other 1sf numbers, should predict what the calculator will show and then type them in. At this stage they are probably best to stick to big numbers.

In the discussion that follows there are likely to be lots of ways to explain what is going on.

Common misconceptions

Next, ask what they think might happen if they type a number with 2sf. Usually they assume that it will have two digits and that the index will denote the number of zeroes. They should now try some on their calculators and produce a new theory.

The pupils can then move on to other numbers of significant figures, until they have got a way of describing how to predict what the calculator will do with any big number.

Extension/follow up lesson

I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.

Resources

The worksheet of solar system data allows the pupils to write some numbers in standard index form, to do some conversions and to see the point of using standard index form.

The worksheet has some other interesting features for the pupils to discover/wonder about. For example, Pluto is included even though it is no longer regarded as a planet (by definition it is now a ‘Plutoid’). The distances of the objects from the sun are averages: why? [They do not have circular orbits – which is a common misconception.] The moon does not have a distance given – because its average distance from the sun is the same as that of the earth (why?).

Maths issue

There is only one rational number that cannot be written in standard index form – that is zero (why?).

There is then a definition to show the pupils at the end of the lesson.

Resource set up

• Graphical Calculator Investigative Introduction [OHT] Working in pairs (with one calculator or two), turn on, press mode (top left), the right arrow (so that sci is flashing) and enter, followed by quit (press 2nd and then mode). The calculator will now change all numbers into standard form (using 4E7 notation to stand for 4 x 10⁷ ).

• Can they predict what certain numbers put up on the w/b will be displayed as?

• Calculator uses 4E7 – this is because it can’t write them properly as 4 x 10⁷ - we have to write them this way.

• Write some of the numbers on the w/b using correct notation.

Solar System Worksheet: Fill in empty columns and put the masses in ascending order.

Assessment/ homework opportunities

Follow up/ where to next?

Links to other resources

Other methods of teaching the same topic