KS4 Grade 9 - NUMBER
Lesson 7...APPROXIMATION AND MEASUREMENTS/BOUNDS
![Picture](/uploads/1/3/3/4/13343229/3258189.jpg?235)
Rounding to:
- the nearest whole number
- a certain number of significant figures (S.F.)
- a number of decimal places (D.P.)
Eg. 7.8126
to nearest whole number = 8
to 3 S.F. = 7.81
to 3 D.P. = 7.813
If a measurement is given to a certain accuracy then this is an approximation and the measurement can take a range of values
Eg. A length is measured as 145cm to the nearest cm, therefore the length could be as low as 144.5cm (lower bound) or as high as 145.4999cm (upper bound)
This can be expressed as:
144.5 ≤ length (cm) < 145.5
TASK 1 - Textbook Pg10 Ex10
TASK 2 - Textbook Pg11 Ex11, Ex12
HOMEWORK - None set
- the nearest whole number
- a certain number of significant figures (S.F.)
- a number of decimal places (D.P.)
Eg. 7.8126
to nearest whole number = 8
to 3 S.F. = 7.81
to 3 D.P. = 7.813
If a measurement is given to a certain accuracy then this is an approximation and the measurement can take a range of values
Eg. A length is measured as 145cm to the nearest cm, therefore the length could be as low as 144.5cm (lower bound) or as high as 145.4999cm (upper bound)
This can be expressed as:
144.5 ≤ length (cm) < 145.5
TASK 1 - Textbook Pg10 Ex10
TASK 2 - Textbook Pg11 Ex11, Ex12
HOMEWORK - None set
Lesson 6...STANDARD FORM (SCIENTIFIC NOTATION)
![Picture](/uploads/1/3/3/4/13343229/329962.jpg?244)
Scientific Notation (or Standard Form):
A x 10^n where 1 ≤ A < 10 and n is an integer
Eg. Convert 345 into Standard Form
345 = 3.45 x 10^2
Eg. Express 0.0678 using Scientific Notation
0.0678 = 6.78 x 10^-2
TASK 1 - Scientific Notation worksheet
TASK 2 - Textbook Pg16 Ex15
HOMEWORK - None set
A x 10^n where 1 ≤ A < 10 and n is an integer
Eg. Convert 345 into Standard Form
345 = 3.45 x 10^2
Eg. Express 0.0678 using Scientific Notation
0.0678 = 6.78 x 10^-2
TASK 1 - Scientific Notation worksheet
TASK 2 - Textbook Pg16 Ex15
HOMEWORK - None set
Lesson 5...LAWS OF INDICES
![Picture](/uploads/1/3/3/4/13343229/8318746.jpg)
See image on left for summary of the Laws of Indices
TASK 1 - Indices worksheet
TASK 1 - Indices worksheet
Lesson 4...FRACTIONS & DECIMALS
![Picture](/uploads/1/3/3/4/13343229/7259903.jpg?119)
Converting fractions to decimals
Eg. To express 7/8 as a decimal, divide 8 into 7 using long division
7/8 = 0.875
Converting decimals to fractions
Eg. To express 0.35 as a fraction, write as a value over 100 and then simplify
0.35 = 35/100 = 7/20
TASK 1 - Textbook Pg5 Ex4
EXTENSION - MyIMaths.com exercises
HOMEWORK - None set
Eg. To express 7/8 as a decimal, divide 8 into 7 using long division
7/8 = 0.875
Converting decimals to fractions
Eg. To express 0.35 as a fraction, write as a value over 100 and then simplify
0.35 = 35/100 = 7/20
TASK 1 - Textbook Pg5 Ex4
EXTENSION - MyIMaths.com exercises
HOMEWORK - None set
Lesson 3...FRACTIONS
![Picture](/uploads/1/3/3/4/13343229/1527659.jpg?261)
A NUMERATOR is the value on the top of a fraction.
A DENOMINATOR is the value on the bottom of a fraction.
ADDITION - Change any mixed numbers to top-heavy fractions, find the lowest common denominator and make equivalent fractions, add the numerators, simplify the answer if possible.
SUBTRACTION - Change any mixed numbers to top-heavy fractions, find the lowest common denominator and make equivalent fractions, subtract the numerators, simplify the answer if possible.
MULTIPLICATION - Change any mixed numbers to top-heavy fractions, multiple the numerators together, multiply the denominators together, simplify the answer if possible.
DIVISION - Change any mixed numbers to top-heavy fractions, replace the division sign with a multiplication sign and reverse the second fraction (i.e. denominator becomes numerator), multiply the numerators together, multiply the denominators together, simplify the answer if possible.
TASK 1 - Complete MathsLoops C1 in pairs
TASK 2 - Textbook Pg4 Ex3 All Qs
HOMEWORK - None set
A DENOMINATOR is the value on the bottom of a fraction.
ADDITION - Change any mixed numbers to top-heavy fractions, find the lowest common denominator and make equivalent fractions, add the numerators, simplify the answer if possible.
SUBTRACTION - Change any mixed numbers to top-heavy fractions, find the lowest common denominator and make equivalent fractions, subtract the numerators, simplify the answer if possible.
MULTIPLICATION - Change any mixed numbers to top-heavy fractions, multiple the numerators together, multiply the denominators together, simplify the answer if possible.
DIVISION - Change any mixed numbers to top-heavy fractions, replace the division sign with a multiplication sign and reverse the second fraction (i.e. denominator becomes numerator), multiply the numerators together, multiply the denominators together, simplify the answer if possible.
TASK 1 - Complete MathsLoops C1 in pairs
TASK 2 - Textbook Pg4 Ex3 All Qs
HOMEWORK - None set
Lesson 2...NUMBER PRACTICE
![Picture](/uploads/1/3/3/4/13343229/5929225.jpg)
TASK 1 - Revision sheet - Factors and Primes
TASK 2 - Textbook Pg6 Ex5 - All Qs
TASK 3 - Textbook Pg6-7 Ex6 Q1-3. EXTENSION Pg6-7 Ex6 Q4-7
HOMEWORK - Multiples, Factors, Primes worksheet
TASK 2 - Textbook Pg6 Ex5 - All Qs
TASK 3 - Textbook Pg6-7 Ex6 Q1-3. EXTENSION Pg6-7 Ex6 Q4-7
HOMEWORK - Multiples, Factors, Primes worksheet
Lesson 1...NUMBER KNOWLEDGE
![Picture](/uploads/1/3/3/4/13343229/491991.jpg?361)
An INTEGER is a whole numberA 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
A SQUARE NUMBER is the result of multiplying a number by itself
Eg. The first 5 Square Numbers are 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5)
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 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, ...
A RATIONAL NUMBER can always be written exactly in the form a/b where a and b are integers
Eg. 3/7, 5.14, 0.6 reoccurring
An IRRATIONAL NUMBER cannot be written in the form a/b
Eg. √2, π, √n where n not a square number
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
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
TASK 1 - Revision sheet - Factors and Primes
HOMEWORK - None set
Eg. The first 10 Prime Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
A SQUARE NUMBER is the result of multiplying a number by itself
Eg. The first 5 Square Numbers are 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5)
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 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, ...
A RATIONAL NUMBER can always be written exactly in the form a/b where a and b are integers
Eg. 3/7, 5.14, 0.6 reoccurring
An IRRATIONAL NUMBER cannot be written in the form a/b
Eg. √2, π, √n where n not a square number
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
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
TASK 1 - Revision sheet - Factors and Primes
HOMEWORK - None set