MATHEMATICS GRADE 8-9
NEW NAMIBIAN CARRICULLUM
REVISED BY MR. RIAMEKEE N. NGEZEMBA
TOPIC 1; NUMBERS
GRADE 8 &9 LEANERS SHOULD BE ABLE TO;
1.1 WHOLE NUMBERS
• list multiples of numbers smaller than 10
• find the factors of a number
• determine if any number in the range of 1 – 100 is prime or composite
• find prime factors of numbers and express numbers as products of their prime factors in index
notation
• determine the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of up to three
given whole numbers
• determine an answer to another calculation e.g. if 30 × 25 = 750, work out 31 × 25 or work out 32 × 25
• apply multiplication and division facts to multiply and divide decimals e.g. 0.05 × 7 gives 0.35 since 5
× 7 = 35 and 4.2 ÷ 6 gives 0.7 since 42 ÷ 6 = 7
• recognize where to place decimal point for equivalent calculations e.g. 4.37 × 0.3 = (4.37 ×3) ÷ 10 =
1.311
• apply the four basic operations to whole numbers including the application of BODMAS {brackets, of,
division and multiplication (from left to right) is done first, and then addition and subtraction (from left to
right)}
PRIME NUMBERS
Are numbers that has only
two factors; 1 and itself {2,
3, 5, 7, 11, 15, ….}
• The table shows the Prime
Numbers from 0 – 100 ;
Prime factors or Prime Factorization
• Product of prime factors → Are factors of a number which
are also prime numbers
Example; Find the prime factors of 20;
20 = 2 x 2 x 5 (therefore the prime factors of 20 is 2 and 5)
• Composite Numbers → Are numbers with more than two
factors; {4; 6; 8; 9; 10; ……} the numbers that are not
shaded in the prime number table on the previous page
are composite numbers EXCLUDING 1.
Is 1 a Prime number?
NO because 1 has only one factor, meaning that 1 can only go
into itself and nothing else.
Consider the problem;
𝟐 𝒐𝒇 𝟒 × 𝟒 − 𝟔 × 𝟑 + 𝟒 + 𝟑 − 𝟏𝟔 ÷ 𝟒
• B – Complete all operations in Brackets (from left to right)
𝟐 𝒐𝒇 𝟒 × 𝟒 − 𝟔 × 𝟑 + 𝟕 − 𝟏𝟔 ÷ 𝟒
• O – Complete all operations in Of (x) (from left to right)
8 × 𝟒 − 𝟔 × 𝟑 + 𝟕 − 𝟏𝟔 ÷ 𝟒
• D (÷) M (×) – Complete all operations in Division and/or Multiplication
(from left to right)
𝟖 × 𝟒 − 𝟔 × 𝟑 + 𝟕 − 𝟏𝟔 ÷ 𝟒
𝟑𝟐 − 𝟔 × 𝟑 + 𝟕 − 𝟏𝟔 ÷ 𝟒
𝟑𝟐 − 𝟏𝟖 + 𝟕 − 𝟏𝟔 ÷ 𝟒
𝟑𝟐 − 𝟏𝟖 + 𝟕 − 𝟒
• A (+) S (˗) – Complete all operations in Addition and/or Subtraction
(from left to right)
𝟑𝟐 − 𝟏𝟖 + 𝟕 − 𝟒
𝟏𝟒 + 𝟕 − 𝟒
𝟐𝟏 − 𝟒
17
Lowest Common Multiple (LCM)
• the lowest number where the multiples of two or more numbers are the
same /common
HINT: List the multiples of each number until you meet the first
common one. That is the LCM.
Example 1
Find the LCM of 6 and 8;
Multiples of 6; 6, 12, 18, 24, 36,……..
Multiples of 8; 8, 16, 24, 32, ………
The first multiples that appear in both is the lowest common multiple.
24 is the LCM of 6 and 8
Highest Common Factor (HCF)
• The highest number that can divide into the given numbers.
• HINT: Make sure you have listed all the factors of each number
Example
Find the HCF of 16 and 24
Factors of 16; 1, 2, 4, 8 and 16.
Factors of 24; 1, 2, 3, 4, 6, 8, 12 and 24
As you can see 2 and 8 are both common but 8 is the highest common
factor.
Directed Numbers
• 1.Using the line below, simplify the given problems.
–8 –7 –6
–5
–4 –3 –2
–1 0 1 2 3 4
• a)10 – 7b) –5 + 2 c) 7 – 12 + 5
5
6 7
8
9
10 11