KS3 Grade 6 - INTEGERS, POWERS & ROOTS
Lesson 6...MULTIPLYING AND DIVIDING INTEGERS
MULTIPLYING AND DIVIDING INTEGERS -->
There are 4 rules to be followed when either multiplying or dividing positive and negative integers:
+ x + = +
+ x - = -
- x + = -
- x - = +
Eg. - 6 ÷ - 3 = + 2
STARTER - Textbook Pg39 Integers game
TASK 1 - Textbook Pg41 Ex2
EXT - Textbook (Divisibility) Pg43-44 Ex3
HOMEWORK - Finish TASK 1
There are 4 rules to be followed when either multiplying or dividing positive and negative integers:
+ x + = +
+ x - = -
- x + = -
- x - = +
Eg. - 6 ÷ - 3 = + 2
STARTER - Textbook Pg39 Integers game
TASK 1 - Textbook Pg41 Ex2
EXT - Textbook (Divisibility) Pg43-44 Ex3
HOMEWORK - Finish TASK 1
Lesson 5...ADDING AND SUBTRACTING INTEGERS
An INTEGER is a positive or negative whole number
ADDING INTEGERS -->
(1) If the signs are the same: add the numbers and keep the sign
Eg. (+2) + (+3) = +5
(-2) + (-3) = -5
(2) If the signs are different: subtract the numbers and keep the sign of the number with the greatest absolute value
Eg. (+2) + (-3) = -1
(-2) + (+3) = +1
SUBTRACTING INTEGERS -->
(1) If subtracting a positive integer then move that number of places in the negative direction on a number line
Eg. (-2) - (+4) = -6
(2) If subtracting a negative integer then move that number of places in the positive direction on a number line
Eg. (-6) - (-11) = -6 + 11 = +5
TASK 1 - Textbook Pg35 Ex1
HOMEWORK - None set
ADDING INTEGERS -->
(1) If the signs are the same: add the numbers and keep the sign
Eg. (+2) + (+3) = +5
(-2) + (-3) = -5
(2) If the signs are different: subtract the numbers and keep the sign of the number with the greatest absolute value
Eg. (+2) + (-3) = -1
(-2) + (+3) = +1
SUBTRACTING INTEGERS -->
(1) If subtracting a positive integer then move that number of places in the negative direction on a number line
Eg. (-2) - (+4) = -6
(2) If subtracting a negative integer then move that number of places in the positive direction on a number line
Eg. (-6) - (-11) = -6 + 11 = +5
TASK 1 - Textbook Pg35 Ex1
HOMEWORK - None set
Lesson 4...SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
A SQUARE NUMBER is the result we get when we multiply a number by itself
Eg. 3 'squared' = 3 x 3 = 9
Finding the SQUARE ROOT of a number is the inverse operation of squaring that number
Eg. 5 x 5 = 25 --> √25 = 5
A CUBE NUMBER is the result we get when multiplying a number by itself three times
Eg. 4 'cubed' = 4 x 4 x 4 = 64
Finding the CUBE ROOT of a number is the inverse operation of cubing that number
Eg. 2 x 2 x 2 = 8 --> 3√8 = 2
TASK 1 - Textbook Pg52 Ex7
EXTENSION - Pg54 Puzzle, Pg59 Ex8
HOMEWORK - None set
Eg. 3 'squared' = 3 x 3 = 9
Finding the SQUARE ROOT of a number is the inverse operation of squaring that number
Eg. 5 x 5 = 25 --> √25 = 5
A CUBE NUMBER is the result we get when multiplying a number by itself three times
Eg. 4 'cubed' = 4 x 4 x 4 = 64
Finding the CUBE ROOT of a number is the inverse operation of cubing that number
Eg. 2 x 2 x 2 = 8 --> 3√8 = 2
TASK 1 - Textbook Pg52 Ex7
EXTENSION - Pg54 Puzzle, Pg59 Ex8
HOMEWORK - None set
Lesson 3...HIGHEST COMMON FACTOR & LOWEST COMMON MULTIPLE
The HIGHEST COMMON FACTOR (HCF) is the highest number that can be divided exactly into each of two or more numbers
Eg. The HCF of 24 and 56 is 8
The LOWEST COMMON MULTIPLE (LCM) is the lowest value that is a multiple of two or more given quantities
Eg. The LCM of 24 and 56 is 168
To find the HCF and LCM of two values first write each value as a product of its prime factors. Using the example above (18 and 24) gives:
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
The HCF is found by recognising the common prime factors in each decomposition above.
There is a 2 and a 3 in each decomposition, we then multiply these together to give:
HCF = 2 x 3 = 6
The LCM is then found by taking the HCF and multiplying by any remaining prime factors in the decomposition to give:
LCM = HCF x 2 x 2 x 3 = 6 x 2 x 2 x 3 = 72
TASK 1 - Textbook Pg50 Ex6 Q1-5
EXTENSION - MathsLoops C1
HOMEWORK - HCF, LCM and Prime Factors worksheet to be submitted 10/9
Eg. The HCF of 24 and 56 is 8
The LOWEST COMMON MULTIPLE (LCM) is the lowest value that is a multiple of two or more given quantities
Eg. The LCM of 24 and 56 is 168
To find the HCF and LCM of two values first write each value as a product of its prime factors. Using the example above (18 and 24) gives:
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
The HCF is found by recognising the common prime factors in each decomposition above.
There is a 2 and a 3 in each decomposition, we then multiply these together to give:
HCF = 2 x 3 = 6
The LCM is then found by taking the HCF and multiplying by any remaining prime factors in the decomposition to give:
LCM = HCF x 2 x 2 x 3 = 6 x 2 x 2 x 3 = 72
TASK 1 - Textbook Pg50 Ex6 Q1-5
EXTENSION - MathsLoops C1
HOMEWORK - HCF, LCM and Prime Factors worksheet to be submitted 10/9
Lesson 2...PRIME FACTOR DECOMPOSITION
PRIME FACTOR DECOMPOSITION of a number means writing it as a product of prime factors
Eg. The Prime Factor Decomposition of 180 = 2 x 2 x 3 x 3 x 5
TASK 1 - Find all of the factors of the following numbers: 10, 130, 56, 72, 224, 20, 40, 150, 142, 69
TASK 2 - Textbook Pg46 - Read and then attempt Ex4
TASK 3 - Textbook Pg48 Ex5
HOMEWORK - None set
Eg. The Prime Factor Decomposition of 180 = 2 x 2 x 3 x 3 x 5
TASK 1 - Find all of the factors of the following numbers: 10, 130, 56, 72, 224, 20, 40, 150, 142, 69
TASK 2 - Textbook Pg46 - Read and then attempt Ex4
TASK 3 - Textbook Pg48 Ex5
HOMEWORK - None set
Lesson 1...MULTIPLES, FACTORS AND PRIME NUMBERS
A MULTIPLE of a number is found by multiplying that number by 1, 2, 3, 4, ...
Eg. Multiples of 3 are 3, 6, 9, 12, 15, ...
The FACTORS of a number are all of the numbers that will divide into that number exactly
Eg. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
A PRIME NUMBER has exactly two factors, itself and 1
Eg. The first 10 Prime Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
TASK 1 - Write out a multiplication table for all multiples up to 12 x 12
TASK 2 - Find all of the factors of the following numbers: 10, 130, 56, 72, 224, 20, 40, 150, 142, 69
TASK 3 - Textbook Pg46 - Read and then attempt Ex4
EXTENSION - Find 4 numbers less that 100 with exactly 12 factors. Find a number with exactly 15 factors. Textbook Pg48 Puzzle.
HOMEWORK - None set
Eg. Multiples of 3 are 3, 6, 9, 12, 15, ...
The FACTORS of a number are all of the numbers that will divide into that number exactly
Eg. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
A PRIME NUMBER has exactly two factors, itself and 1
Eg. The first 10 Prime Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
TASK 1 - Write out a multiplication table for all multiples up to 12 x 12
TASK 2 - Find all of the factors of the following numbers: 10, 130, 56, 72, 224, 20, 40, 150, 142, 69
TASK 3 - Textbook Pg46 - Read and then attempt Ex4
EXTENSION - Find 4 numbers less that 100 with exactly 12 factors. Find a number with exactly 15 factors. Textbook Pg48 Puzzle.
HOMEWORK - None set