Introduction to standard index form/Teacher Notes

This page is also available as a .doc download File:Introduction to standard index form - teacher notes.doc It refers to a number of resources, which are available (and linked below)

• File:Standard index form.ppt - which includes opportunities for questioning⁽ⁱ⁾ and guides the lesson
• File:Solar system data.xls - which provides an opportunity for some more in depth thinking

Teacher Notes Introduction to Standard Index Form

Type of Lesson/length: Investigation and Discussion. Work in pairs. At least one hour of lesson time.

Age/Level/Key Stage: Years 7-12, KS3, KS4, 6^th form (as a recap)

Learning objectives

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

• Convert numbers between standard index form and ordinary form
• Understand whether a number is in standard index form or not

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

Pupils work together to explore the way the calculator converts numbers. This means it is accessible to large numbers of pupils.

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. Alternatively, it could be used by Sixth Form students as a recap and review of the topic.

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 from File:Standard index form.ppt 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 excel worksheet of solar system data (File:Solar system data.xls 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

Homework could involve pupils writing up the ideas they have discovered during the lesson. This will give them an opportunity to revisit the topic a while after they have first explored it and will provide evidence of what they have taken from the lesson. The teacher can then use this to assess their understanding.

Follow up/ where to next?

To use standard index form with small and large numbers in different contexts.

Links to other resources

Other methods of teaching the same topic