Page 30 - 新思维数学教师用书8 试读样张

mathematics 8 teacher’s resource

CONTINUED

Framework codes Learning objectives success criteria
8ni.07 • Recognise positive and • Find the cube roots of 64 and of −64.
negative cube numbers, and
the corresponding cube roots.
1
8ni.04 • Understand the hierarchy of • Place 3, −4 and 3 in the correct places
4
natural numbers, integers and in a Venn diagram showing the types of
rational numbers.
number.

LANGUAGE SUPPORT
Cube root: the number that produces the given cube root. Natural numbers are what learners
number when the number is cubed; the cube root have probably called counting numbers in the
3
of 125 is 5 because 5 is 125 past, with the addition of 0. Learners need to
square root: the square root of a number understand that rational numbers are any numbers
multiplied by itself gives that number; the square that can be written as a fraction, positive or
root of 36 is 6 or −6 negative, and they include all the integers. It
4
Learners should already be familiar with the terms might help to think, for example, of 4 as .
square number, square root, cube number and 1

Common misconceptions

Misconception How to identify How to overcome
Learners may not be aware that Ask for the solution of the Emphasise that 9 = 3 is the positive
every positive square number has equation x² = 9 square root of 9 and that
two integer square roots. Learners need to identify 3 − 9 = −3 is another square root.
and −3 as solutions.

Because a negative number can Ask for the square roots of Emphasise the difference between
have a cube root, learners can think negative numbers such as −9 square roots and cube roots in this
it also has a square root. or −25. respect.

the numbers marked. These are integers. Say that the
Starter idea integers include the natural numbers. All natural numbers
Types of number (10 minutes) are integers.
Resources: None Ask learners to draw a Venn diagram to show natural
Description: Draw a number line. Mark on it the numbers and integers. They may need reminding what
a Venn diagram is. If some learners cannot remember
numbers 0, 1, 2, 3, 4, 5, . . . Say that these are ask a learner who does know to explain. It is a diagram
called natural numbers. They are the counting numbers, where sets are represented by overlapping loops. Learners
the first numbers children learn. may draw something like this (N = natural numbers,
Then mark in −1, −2, −3, −4, . . . Ask for the name of all I = integers):

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