Page 32 - 新思维数学教师用书7 试读样张

MATHEMATICS 7 TEACHER’S RESOURCE

Common misconceptions

Misconception How to identify How to overcome
Learners do not think of 1 and the number Check when learners list Remind learners of these two
itself as factors of a given number. the factors. factors as much as possible.

Starter idea For example, or 18 or 30 .
16
24 45 40
Reminder of factors (10 minutes)
Description: On the board write ‘20 is a multiple of 5.’ Show learners that you could divide the numbers 16 and
16
Then, under the first sentence, write ‘5 is a ______ of 20.’ 24 in the fraction repeatedly by 2 or by 4. However, if
24
Ask ‘What is the missing word?’ Learners should know you use the HCF, then you need to do only one division.
the word factor. Question 7 is an example of this. Learners should
Ask learners in turn to give more pairs of similar consider this when they answer Question 8.
sentences. The first should be ‘20 is a multiple of __.’
Ask ‘Have we got all the factors?’ Learners should be Answers:
able to agree that there are six factors. 7 a 7
The factors of 20 are 1, 2, 4, 5, 10 and 20. Make sure b 5
learners do not forget 1 and 20. 8
Now, ask learners to work in pairs to find numbers with reflection For example: When you divide the
exactly: four factors, two factors, eight factors, three numerator and the denominator by the
factors and five factors. highest common factor, you have the
Then collect their answers. Ask ‘Can you see fraction in its simplest form.
any patterns?’ 8 a 1
Possible answers include: b You simplify by dividing 25 and 36 by a
25
36
• ‘It is not true that larger numbers always have common factor. Since 1 is the only common
more factors.’ factor, the fraction cannot be simplified.
• ‘Prime numbers have just two factors.’ (Learners
might not know about prime numbers.) Differentiation ideas: Using the HCF is not essential.
• ‘Square numbers have an odd number of factors.’ Learners who find it difficult can use repeated division,
If learners do not give the answers listed, then elicit them. using any common factor each time. The activity can be
The act of looking for factors and writing all the factors extended to include vulgar fractions.
of a number is the focus here. Look at learners’ work as
they are finding factors. Make sure they always include 1 Plenary idea
and the number itself. Make sure learners use the words
factor and multiple correctly. The relation between factors and
multiples (10 minutes)
Main teaching idea Resources: Squared paper

Simplifying fractions (5 minutes) Description: Ask learners to number a grid, as shown
Learning intention: To make connections between here. Instruct them to use a pencil so that they can correct
any mistakes.
different areas of mathematics.
Resources: Learner’s Book Exercise 1.4, Questions 7
and 8
Description: Write some fractions and ask learners to
simplify them.

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4+ ྍනົඔ࿐࢝ഽႨ඀ ᆞ໓č1 Ď ཮@නૼ JOEE