Introduction to standard index form/Teacher Notes - Revision history

Caroline.jestaz at 16:41, 29 October 2012

2012-10-29T16:41:57Z

← Older revision		Revision as of 16:41, 29 October 2012
Line 34:		Line 34:

	'''Solar System - Excel worksheet:'''		'''Solar System - Excel worksheet:'''
	* The Excel worksheet containing solar system data ([[file:solar system data.xls]] allows pupils to see the point of using standard index form. They will write some numbers in standard index form and do some conversions.		* 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.		* Ask the class to fill in empty columns on the sheet and put the masses in ascending order. <br />
	The worksheet has interesting features for the pupils to wonder about.
			The worksheet has interesting features for the pupils to wonder about. <br />

	* Why is Pluto included even though it is no longer regarded as a planet? By definition it is now a ‘Plutoid’.		* 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 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)~~.		* 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:'''		'''Follow up ideas:'''

Caroline.jestaz at 15:57, 29 October 2012

2012-10-29T15:57:53Z

Caroline.jestaz at 15:49, 29 October 2012

2012-10-29T15:49:14Z

← Older revision		Revision as of 15:49, 29 October 2012
Line 4:		Line 4:

	'''What you need:'''		'''What you need:'''
	* ~~Teachers~~ notes - read below or download [[file:introduction to standard index form - teacher notes.doc]]		* Teacher's notes - read below or download [[file:introduction to standard index form - teacher notes.doc]]
	* ~~Lesson~~ guide including opportunities for {{teachtag\|questioning}} - PowerPoint [[file:standard index form.ppt]]		* A lesson guide including opportunities for {{teachtag\|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.		* Calculators - the lesson was written for use with TI-82 Graphical Calculators but other calculators can also be used.

Bjoern: Fixing tagging, as well as cross-curric, vocabulary, distance learning, share practice, DfE, DfEScience templates

2012-09-28T08:42:40Z

Fixing tagging, as well as cross-curric, vocabulary, distance learning, share practice, DfE, DfEScience templates

← Older revision		Revision as of 08:42, 28 September 2012
Line 5:		Line 5:
	'''What you need:'''		'''What you need:'''
	* Teachers notes - read below or 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 {{teachtag\|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.		* Calculators - the lesson was written for use with TI-82 Graphical Calculators but other calculators can also be used.

Rf366 at 21:51, 19 September 2012

2012-09-19T21:51:07Z

Rf366 at 21:02, 19 September 2012

2012-09-19T21:02:00Z

← Older revision		Revision as of 21:02, 19 September 2012
Line 1:		Line 1:
	What you need		'''Teacher notes on Introduction to Standard Index Form'''

			[[File:introducingstandardform.jpg\|link=]]

			'''What you need:'''
	* Teachers notes - read below or 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.		* 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'''~~

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

	'''Learning objectives:'''		'''Learning objectives:'''
	* able to convert numbers between standard index form and ordinary form		* able to convert numbers between standard index form and ordinary form
	* whether a number is in standard index form or not		* know 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 ×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'''~~
	* 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 ‘<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.

	'''~~Common misconceptions~~'''		'''About:'''<br />
	* 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~~.		This activity is for pupils who are unfamiliar with standard index form: primary, secondary or sixth form as recap. 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 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.
			[[Image:StdIndexFormE.png]]

	'''~~Maths issues~~'''		'''Lesson Plan:'''
	~~There is only~~ one ~~rational number that cannot be written in~~ standard index form. ~~It's zero, but why?~~		* Ask the pupils what each of the sets of numbers have in common on slide one 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).
	~~There is a definition~~ to ~~show~~ the ~~pupils at the end of~~ the ~~lesson~~.

	~~'''Resource~~ set up'''		* 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 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.

	* ~~Graphical Calculator Investigative Introduction (OHT)~~		* 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 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.
	~~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 how certain numbers put up on the whiteboard will~~ be ~~displayed~~?		* There is only one rational number that cannot be written in standard index form. It's zero, but why? (The PowerPoint has a definition to show the pupils at the end of the lesson).

	* The calculator ~~uses 4E7 – because it can’t write them as 4 x 10<sup>7</sup>. We have to write them this way.~~		'''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 10<sup>7</sup> ).
			* 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 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 whiteboard using correct notation.

	Solar System ~~Worksheet~~: ~~Fill in empty columns and put the masses in ascending order.~~		'''Solar System - Excel worksheet:'''
	~~''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 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.		* 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.		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 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 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).		* 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'''		'''Follow up ideas:'''

	* 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.		* 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.
	* To use standard index form with small and large numbers in different contexts.		* 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.		* I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.

Rf366 at 19:24, 19 September 2012

2012-09-19T19:24:01Z

Show changes

Rf366 at 16:57, 19 September 2012

2012-09-19T16:57:56Z

← Older revision		Revision as of 16:57, 19 September 2012
Line 1:		Line 1:
	~~This page is also~~ available ~~as a .doc~~ download [[file:introduction to standard index form - teacher notes.doc]]		Summary
	~~It refers to a number of resources, which are available (and linked below)~~		* Teachers guide (below) and available to download [[file:introduction to standard index form - teacher notes.doc]]
	* [[file:standard index form.ppt]] ~~- which includes opportunities for {{tag\|questioning}} and guides the lesson~~		* Lesson guide including opportunities for {{tag\|questioning}} - PowerPoint [[file:standard index form.ppt]]
	* [[file:solar system data.xls]] ~~- which provides an opportunity for some more in depth thinking~~		* Solar system data in an opportunity for in depth thinking - Excel [[file:solar system data.xls]]

	~~<center>'''Teacher Notes'''</center>~~

	~~<center>Introduction to Standard Index Form</center>~~


	~~'''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<sup>th</sup> form (as a recap)~~


	~~'''Learning objectives'''~~

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

			'''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, 6<sup>th</sup> form (as a recap)
			Learning objectives:
	* Convert numbers between standard index form and ordinary form		* Convert numbers between standard index form and ordinary form
	* Understand whether a number is in standard index form or not		* Understand whether a number is in standard index form or not
			'''Resources'''
	'''Resources ~~required~~'''		This was originally written for use with TI-82 Graphical Calculators but other calculators can also be used.

	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'''		'''Background'''
			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.
	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'''		'''Important facts'''
			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.
	~~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.

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

	[[Image:StdIndexFormE.png]]		[[Image:StdIndexFormE.png]]

	'''~~About the~~ 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]].
	~~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 pupils are likely to find this difficult: the first set all have 1 significant figure, the second have 2 significant figures.

	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 ‘<nowiki>=</nowiki>’. 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~~.

			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.

	'''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.
	~~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.		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'''		'''Extension/follow up lesson'''

SimonKnight at 13:30, 17 September 2012

2012-09-17T13:30:51Z

← Older revision		Revision as of 13:30, 17 September 2012
Line 44:		Line 44:
	If a calculator is in ‘scientific mode’ it will display all numbers in standard index form.		If a calculator is in ‘scientific mode’ it will display all numbers in standard index form.

			[[Image:StdIndexFormE.png]]

	'''About the Lesson Plan'''		'''About the Lesson Plan'''

SimonKnight: SimonKnight moved page Introduction to Standard Index Form to Introduction to standard index form/Teacher Notes

2012-09-17T12:41:52Z

SimonKnight moved page Introduction to Standard Index Form to Introduction to standard index form/Teacher Notes

← Older revision

Revision as of 12:41, 17 September 2012

← Older revision		Revision as of 15:57, 29 October 2012
Line 6:		Line 6:
	* Teacher's notes - read below or download [[file:introduction to standard index form - teacher notes.doc]]		* 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]]		* A lesson guide including opportunities for {{teachtag\|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 is 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.		* Calculators - this lesson was written for use with TI-82 Graphical Calculators but other calculators can also be used.

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

	'''About:'''<br />		'''About:'''<br />
Line 19:		Line 19:

	'''Lesson Plan:'''		'''Lesson Plan:'''
	* Ask the pupils what each of the sets of numbers have in common on slide ~~one~~ 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 set have 2 significant figures).		* 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 ‘<nowiki>=</nowiki>’. They should then enter other '1 significant figure' numbers but as they do, predict what the calculator will show. It probably best to ~~stick to~~ big numbers at this stage. In the discussion that will follow, you may hear ~~lots of~~ explanations of what is ~~going on~~.		* 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.

	* 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. ~~Get the pupils~~ to enter increasing numbers of significant figures, until they can predict how the calculator will display '''any''' big number.		* 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 has a definition to show the pupils at the end of the lesson).		* 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: '''		'''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 10<sup>7</sup> ).		* 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 ~~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 10<sup>7</sup>. We have to write them this way).		* 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.		* Write some of the numbers on the whiteboard using correct notation.

	'''Solar System - Excel worksheet:'''		'''Solar System - Excel worksheet:'''
	* 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 Excel worksheet containing solar system data ([[file:solar system data.xls]] allows pupils to see the point of using 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.		* 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.		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 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 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).		* 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).

← Older revision		Revision as of 21:51, 19 September 2012
Line 14:		Line 14:

	'''About:'''<br />		'''About:'''<br />
	This activity is for pupils who are unfamiliar with standard index form: primary, secondary or sixth form as recap. 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 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.
	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.
	[[Image:StdIndexFormE.png]]		[[Image:StdIndexFormE.png]]

	'''Lesson Plan:'''		'''Lesson Plan:'''
	* Ask the pupils what each of the sets of numbers have in common on slide one 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 what each of the sets of numbers have in common on slide one 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 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 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.		* 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 probably best to stick to big numbers at this stage. In the discussion that will follow, you may hear lots of explanations of what is going on.

	* 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 ~~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.		* 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. Get the pupils 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 has a definition to show the pupils at the end of the lesson).		* There is only one rational number that cannot be written in standard index form. (It's zero, but why? The PowerPoint has a definition to show the pupils at the end of the lesson).

	'''Using standard form on the calculator: '''		'''Using standard form on the calculator: '''
Line 39:		Line 39:
	* Why is Pluto included even though it is no longer regarded as a planet? (By definition it is now a ‘Plutoid’).		* 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 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).		* 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:'''		'''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.		* 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.
	* ~~To use~~ standard index form with small and large numbers in different contexts.		* 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.		* I usually return to the calculators in a subsequent lesson to deal with numbers that are less than 1.