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Introduction to standard index form/Teacher Notes: Difference between revisions
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Introduction to standard index form/Teacher Notes (view source)
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'''About:'''<br /> | '''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. | |||
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 | * 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 | * 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? | * 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: ''' | ||
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* 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. | ||
* | * 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. | ||
