Page 27 - 新思维数学教师用书9 试读样张

1 number And CALCuLAtion

LANGUAGE SUPPORT

Scientific notation: the same as standard form Mathematicians use the term standard form.
Standard form: a way of writing very large or very Scientists use the term scientific notation.
small numbers in the form a × 10 , where 1 ≤ a < 10 The meaning is identical.
n
and n is an integer

Common misconceptions

Misconception How to identify How to overcome
Not understanding that for a Check that answers in Exercise 1.2 Always emphasise this point in
number written in standard form, are written correctly. discussion, giving examples of
n
the value of a in a × 10 is always 1 correct and incorrect forms.
or more but less than 10.

Starter idea Explain that numbers written in this way are said to be in
standard form.
Powers of 10 (5 minutes) Now, on the board, write ‘3.8 × 10 ’. Point out that this
5
Resources: None is written in standard form. Ask learners to write this
Description: On the board, write ‘2 ’. Ask learners for number out in full. It is 380 000.
2
the value. Repeat with 2 , 2 , etc. Ask ‘How do you work Repeat with an arbitrary choice of other numbers written
4
3
out each successive number?’. Learners should see you in standard form, asking learners to write down the
multiply the previous number by 2. answer and then checking they are correct. Learners
Repeat with powers of 10. In this case multiplying by 10 could do this in pairs first, using peer assessment.
is easy. This is often described as ‘add a 0’, but emphasise A common error is to assume that the index is the number
what you are actually doing is multiplying by 10. This is of 0s to be written on the end. Look for this error and
not an addition! make sure it is corrected.
Ask some reverse questions such as ‘What power of 10 is Finally, say that standard form is sometimes called
100 000?’ scientific notation when it is used in a scientific context.
Standard form and scientific notation are identical.
Main teaching idea Differentiation ideas: For learners that are struggling
with this concept, use examples of a similar type.
Standard form (10 minutes) For example, you might use 6.2 × 10 and then 6.28 × 10
6
6
Learning intention: To learn how to write large numbers and then 6.289 × 10 to clarify how many 0s are needed.
6
in standard form. For learners who have understood this concept, you could
Resources: None give a number between 0 and 100 times a power of 10
Description: On the board, write ‘6.38 × 10’. Ask for the and ask for it to be written in standard form. For example,
3
4
answer. It is 63.8 of course. 45 × 10 = 4.5 × 10 .
Next, on the board, write ‘6.38 × 10 ’. Ask for the answer.
2
Make sure that learners realise that this could also be Plenary idea
written as ‘6.38 × 100’ or ‘6.38 × 10 × 10’, three different Recap (5 minutes)
ways of writing the same thing.
Resources: None
Continue in the same way with ‘6.38 × 10 ’ and then Description: Ask learners to give examples of large
3
‘6.38 × 10 ’. numbers where it is useful to write the numbers in
4
Point out that in each case you started with a number with standard form. There were examples in Exercise 1.2.
a single digit in front of the decimal point and that digit
was not zero.

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