Introduction to standard index form/Teacher Notes: Difference between revisions

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This page is also available as a .doc download [[introduction to standard index form - teacher notes.doc]]
'''Teacher notes on Introduction to Standard Index Form'''
It refers to a number of resources, which are available (and linked below)
* resource1
* resource2


'''<center>Introduction to Standard Index Form – Mark Dawes</center>'''
[[File:introducingstandardform.jpg|link=]]


This was originally written for use with TI-82 Graphical Calculators, but nowadays new scientific calculators can also be used.
'''What you need:'''
* Teacher's notes - read below or download [[file:introduction to standard index form - teacher notes.doc]]
* A lesson guide including opportunities for {{teachtag|questioning}} - PowerPoint [[file:standard index form.ppt]]
* Solar system data is an opportunity for in-depth thinking - Excel [[file:solar system data.xls]]
* Calculators - this lesson was written for use with TI-82 Graphical Calculators but other calculators can also be used.


'''Background'''
'''Learning objectives:'''
* Being able to convert numbers between standard index form and ordinary form.
* Knowing whether a number is in standard index form or not.


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.
'''About:'''<br />
Numbers that are too big or too small for the calculator 10-digit display are shown in standard index form. Many calculators now use ×10<sup>''n''</sup> but older calculators may use ‘E’ in the display instead. If a calculator is in ‘scientific mode’ it will display all numbers in standard index form. This activity is for secondary school pupils who are unfamiliar with standard index form. It is an intriguing investigation (one hour) when pairs of students explore the way a that calculator converts numbers. They find out how it works for themselves - the pairing-up helping to make the task accessible to more pupils.


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 ×10<sup>''n''</sup> but older calculators might use ‘E’ in the display instead.
[[Image:StdIndexFormE.png]]


If a calculator is in ‘scientific mode’ it will display all numbers in standard index form.
'''Lesson Plan:'''
* Ask the pupils what each of the sets of numbers have in common on the first slide of the PowerPoint [[file:standard index form.ppt]]. They are likely to find this difficult (the first set all have 1 significant figure, the second set have 2 significant figures).


'''The lesson'''
* Ask the pupils to put their calculator into Scientific Mode. If you own the calculators then they can be set up in advance. Starting with '1 significant figure' numbers, pupils should enter them in turn and press ‘<nowiki>=</nowiki>’. They should then enter other '1 significant figure' numbers but as they do, predict what the calculator will show. It is probably best to use only big numbers at this stage. In the discussion that will follow, you may hear many explanations of what is happening.


Display the first slide and ask the pupils what each of the sets of numbers have in common.
* Ask pupils what they think would happen if they enter a number with 2 significant figures. A common misconception is that they assume the result will also have two digits and that the index will denote the number of zeroes. They should now try some examples on their calculators and improve the theory. Ask them to enter increasing numbers of significant figures, until they can predict how the calculator will display '''any''' big number.


The first set all have 1 significant figure, the second have 2 sig figs, etc. The pupils are likely to find this difficult.
* There is only one rational number that cannot be written in standard index form. It's zero, but why? The PowerPoint presentation has a definition to show to the pupils at the end of the lesson.


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.
'''Using standard form on the calculator: '''


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.
* Graphical calculator set-up: working in pairs, with one or two calculators: turn on, press mode (top left), press the right arrow so that sci is flashing, and then enter. Press quit (press 2nd and then mode). The calculator is now set to change all numbers into standard form (using 4E7 notation to stand for 4 x 10<sup>7</sup> ).
* Can pupils predict how certain numbers put up on the whiteboard will be displayed? (The calculator uses 4E7 – because it cannot write them as 4 x 10<sup>7</sup>. We have to write them this way).
* Write some of the numbers on the whiteboard using correct notation.


In the discussion that follows there are likely to be lots of ways to explain what is going on.
'''Solar System - Excel worksheet:'''
* The Excel worksheet containing solar system data ([[file:solar system data.xls]]) allows pupils to see the point of using the standard index form. They will write some numbers in standard index form and do some conversions.
* Ask the class to fill in empty columns on the sheet and put the masses in ascending order. <br />


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 worksheet has interesting features for the pupils to wonder about. <br />


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.
* Why is Pluto included even though it is no longer regarded as a planet? By definition it is now a ‘Plutoid’.
* Why are the distances of the objects from the sun averages? The planets do not have circular orbits – which is a common misconception.
* Why does the Moon not have a distance from the Sun? Its average distance from the Sun is the same as that of the Earth.  


I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.
'''Follow up ideas:'''


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.  
* A homework idea is for pupils to write up what they discovered during the lesson. Since they must revisit the topic after they first explored it, this will provide evidence of what they have taken from the lesson. You can use this to assess their understanding.
 
* Use standard index form with small and large numbers in different contexts.
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? <nowiki>[They do not have circular orbits – which is a common misconception.] </nowiki>The moon does not have a distance given – because its average distance from the sun is the same as that of the earth (why?). There is only one rational number that cannot be written in standard index form – that is zero (why?).
* I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.
 
There is then a definition to show the pupils at the end of the lesson.
 
* <nowiki>Graphical Calculator Investigative Introduction [OHT] </nowiki>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 10<sup>7</sup> ).
 
* 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 10<sup>7</sup> - 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.

Latest revision as of 16:41, 29 October 2012

Teacher notes on Introduction to Standard Index Form

Introducingstandardform.jpg

What you need:

Learning objectives:

  • Being able to convert numbers between standard index form and ordinary form.
  • Knowing whether a number is in standard index form or not.

About:
Numbers that are too big or too small for the calculator 10-digit display are shown in standard index form. Many calculators now use ×10n but older calculators may use ‘E’ in the display instead. If a calculator is in ‘scientific mode’ it will display all numbers in standard index form. This activity is for secondary school pupils who are unfamiliar with standard index form. It is an intriguing investigation (one hour) when pairs of students explore the way a that calculator converts numbers. They find out how it works for themselves - the pairing-up helping to make the task accessible to more pupils.

StdIndexFormE.png

Lesson Plan:

  • Ask the pupils what each of the sets of numbers have in common on the first slide of the PowerPoint File:Standard index form.ppt. They are likely to find this difficult (the first set all have 1 significant figure, the second set have 2 significant figures).
  • Ask the pupils to put their calculator into Scientific Mode. If you own the calculators then they can be set up in advance. Starting with '1 significant figure' numbers, pupils should enter them in turn and press ‘=’. They should then enter other '1 significant figure' numbers but as they do, predict what the calculator will show. It is probably best to use only big numbers at this stage. In the discussion that will follow, you may hear many explanations of what is happening.
  • Ask pupils what they think would happen if they enter a number with 2 significant figures. A common misconception is that they assume the result will also have two digits and that the index will denote the number of zeroes. They should now try some examples on their calculators and improve the theory. Ask them to enter increasing numbers of significant figures, until they can predict how the calculator will display any big number.
  • There is only one rational number that cannot be written in standard index form. It's zero, but why? The PowerPoint presentation has a definition to show to the pupils at the end of the lesson.

Using standard form on the calculator:

  • Graphical calculator set-up: working in pairs, with one or two calculators: turn on, press mode (top left), press the right arrow so that sci is flashing, and then enter. Press quit (press 2nd and then mode). The calculator is now set to change all numbers into standard form (using 4E7 notation to stand for 4 x 107 ).
  • Can pupils predict how certain numbers put up on the whiteboard will be displayed? (The calculator uses 4E7 – because it cannot write them as 4 x 107. We have to write them this way).
  • Write some of the numbers on the whiteboard using correct notation.

Solar System - Excel worksheet:

  • The Excel worksheet containing solar system data (File:Solar system data.xls) allows pupils to see the point of using the standard index form. They will write some numbers in standard index form and do some conversions.
  • Ask the class to fill in empty columns on the sheet and put the masses in ascending order.

The worksheet has interesting features for the pupils to wonder about.

  • Why is Pluto included even though it is no longer regarded as a planet? By definition it is now a ‘Plutoid’.
  • Why are the distances of the objects from the sun averages? The planets do not have circular orbits – which is a common misconception.
  • Why does the Moon not have a distance from the Sun? Its average distance from the Sun is the same as that of the Earth.

Follow up ideas:

  • A homework idea is for pupils to write up what they discovered during the lesson. Since they must revisit the topic after they first explored it, this will provide evidence of what they have taken from the lesson. You can use this to assess their understanding.
  • Use standard index form with small and large numbers in different contexts.
  • I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.
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