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

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Summary
What you need
* Teachers guide (below) and available to download [[file:introduction to standard index form - teacher notes.doc]]
* Teachers notes - read below or download [[file:introduction to standard index form - teacher notes.doc]]
* Lesson guide including opportunities for {{tag|questioning}} - PowerPoint [[file:standard index form.ppt]]  
* Lesson guide including opportunities for {{tag|questioning}} - PowerPoint [[file:standard index form.ppt]]  
* Solar system data in an opportunity for in depth thinking - Excel [[file:solar system data.xls]]
* Solar system data in an opportunity for in depth thinking - Excel [[file:solar system data.xls]]
* Calculators - the lesson was written for use with TI-82 Graphical Calculators but other calculators can also be used.


'''Teacher notes on Introduction to Standard Index Form'''
'''Teacher notes on Introduction to Standard Index Form'''


Type of lesson: = Investigation with discussion in pairs to explore the way the calculator converts numbers. This means it is accessible to large numbers of pupils.(one hour).
Level: years 7-12, KS3, KS4. It could be used to review the topic with Sixth form students.
Level: years 7-12, KS3, KS4, 6<sup>th</sup> form (as a recap)
Learning objectives:
* Convert numbers between standard index form and ordinary form
* Understand whether a number is in standard index form or not
'''Resources'''
This was originally written for use with TI-82 Graphical Calculators but other calculators can also be used.


'''Background'''
'''Learning objectives:'''
This lesson is for pupils who haven’t yet been introduced to standard index form. It aims to intrigue them have them explore how it works for themselves. It could be used to review the topic with Sixth form students.
* able to convert numbers between standard index form and ordinary form
* whether a number is in standard index form or not


'''Important facts'''
'''About'''
Numbers that are too big or too small for the 10-digit display on calculators 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 pupils who are unfamiliar with standard index form. It is an intriguing investigation (one hour) when pairs of students explore the way a calculator converts numbers. They find out how it works for themselves - the grouping helps make the task accessible to more pupils..
[[Image:StdIndexFormE.png]]
 
Numbers that are too big or too small for the 10-digit display on calculators 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. [[Image:StdIndexFormE.png]]


'''Lesson Plan'''
'''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]].
* 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]]. The pupils are likely to find this difficult: the first set all have 1 significant figure, the second have 2 significant figures.
The pupils are likely to find this difficult: the first set all have 1 significant figure, the second have 2 significant figures.


Ask the pupils to put their calculator into Scientific Mode. If you use the school's calculators then these can be set up in advance. Starting with the numbers with 1 significant figure pupils should type them in and press ‘<nowiki>=</nowiki>’. They should then enter other 1 significant figure numbers but predict what the calculator will show. It probably best to stick to big numbers at this stage.
* Ask the pupils to put their calculator into Scientific Mode. If you use the school's calculators then these can be set up in advance. Starting with the numbers with 1 significant figure pupils should type them in and press ‘<nowiki>=</nowiki>’. They should then enter other 1 significant figure numbers but predict what the calculator will show. It probably best to stick to big numbers at this stage. In the discussion that will follow there are likely to be lots of explanations of what is going on.
In the discussion that will follow there are likely to be lots of explanations of what is going on.


'''Common misconceptions'''
'''Common misconceptions'''
Ask pupils what they think would happen if they entered a number with 2 significant figures. 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.
* Ask pupils what they think would happen if they enter a number with 2 significant figures. (Usually they assume that 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 produce a new theory. Move the pupils on to enter increasing numbers of significant figures, until they can  predict what the calculator will do with '''any''' big number.
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? <nowiki>[They</nowiki> 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.


'''Maths issues'''
There is only one rational number that cannot be written in standard index form. It's zero, but why?
There is a definition to show the pupils at the end of the lesson.


'''Resource set up'''
'''Resource set up'''


* Graphical Calculator Investigative Introduction <nowiki>[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> ).
* Graphical Calculator Investigative Introduction (OHT)
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 they predict what certain numbers put up on the w/b will be displayed as?
* Can they predict how certain numbers put up on the whiteboard will be displayed?


* 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.
* The calculator uses 4E7 – because it can’t 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.
: 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.
Solar System Worksheet: Fill in empty columns and put the masses in ascending order.
''Solar system'''
The Excel worksheet containing solar system data ([[file:solar system data.xls]] allows the pupils to see the point of using standard index form. They will write some numbers in standard index form, and do some conversions.
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 a distance from the sun? (Its average distance from the sun is the same as that of the earth).


'''Assessment - Follow up'''


'''Assessment/ homework opportunities'''
* A homework idea is for pupils to write up what they have discovered during the lesson. Since they must revisit the topic a while 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.
 
* To use standard index form with small and large numbers in different contexts.
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.
* I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.
 
 
'''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'''

Revision as of 19:24, 19 September 2012

What you need

Teacher notes on Introduction to Standard Index Form

Level: years 7-12, KS3, KS4. It could be used to review the topic with Sixth form students.

Learning objectives:

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

About This activity is for pupils who are unfamiliar with standard index form. It is an intriguing investigation (one hour) when pairs of students explore the way a calculator converts numbers. They find out how it works for themselves - the grouping helps make the task accessible to more pupils..

Numbers that are too big or too small for the 10-digit display on calculators 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. 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. The pupils are likely to find this difficult: the first set all have 1 significant figure, the second have 2 significant figures.
  • Ask the pupils to put their calculator into Scientific Mode. If you use the school's calculators then these can be set up in advance. Starting with the numbers with 1 significant figure pupils should type them in and press ‘=’. They should then enter other 1 significant figure numbers but predict what the calculator will show. It probably best to stick to big numbers at this stage. In the discussion that will follow there are likely to be lots of explanations of what is going on.

Common misconceptions

  • Ask pupils what they think would happen if they enter a number with 2 significant figures. (Usually they assume that 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 produce a new theory. Move the pupils on to enter increasing numbers of significant figures, until they can predict what the calculator will do with any big number.

Maths issues There is only one rational number that cannot be written in standard index form. It's zero, but why? There is 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 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 they predict how certain numbers put up on the whiteboard will be displayed?
  • The calculator uses 4E7 – because it can’t 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 Worksheet: Fill in empty columns and put the masses in ascending order. Solar system' The Excel worksheet containing solar system data (File:Solar system data.xls allows the pupils to see the point of using standard index form. They will write some numbers in standard index form, and do some conversions. 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 a distance from the sun? (Its average distance from the sun is the same as that of the earth).

Assessment - Follow up

  • A homework idea is for pupils to write up what they have discovered during the lesson. Since they must revisit the topic a while 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.
  • To 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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