The Ordinary Processes of Number Manipulation
Basics of Numbers
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Place Value: Understand the place value of digits in a number. For example, in the number 456, 4 is in the hundreds place, 5 in the tens place, and 6 in the units place.
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Number Types: Identify the different types of numbers such as whole numbers, natural numbers, integers, fractions, and decimals.
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Rounding Numbers: Know how to round numbers to the nearest ten, hundred or thousand, and understand the difference between rounding up and rounding down.
Operations with Numbers
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Basic Operations: Perform the four basic operations – addition, subtraction, multiplication, and division – with any type of number.
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BODMAS/BIDMAS Rule: Understand the importance of following correct order of operations: Brackets, Orders (or Indices), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
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Negative Numbers: Understand how to add, subtract, multiply, and divide with negative numbers. For example, multiplying two negative numbers results in a positive number.
Fractions, Decimals and Percentages
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Equivalent Fractions: Identify and create equivalent fractions. For example, 1/2 is equivalent to 2/4, 3/6, etc.
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Decimal and Fraction Conversion: Convert between fractions and decimals. For example, 0.75 is equivalent to 3/4.
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Percentage Calculations: Convert between fractions, decimals, and percentages. For example, 0.20 is equivalent to 20% or 1/5.
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Operations with Fractions, Decimals, and Percentages: Understand how to add, subtract, multiply, and divide fractions, decimals, and percentages.
Prime factors, Highest Common Factor and Lowest Common Multiple
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Prime factors: Understand the concept of prime factors and how to find the prime factorisation of a number.
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Highest Common Factor (HCF): Identify the HCF of two or more numbers, which is the greatest number that divides exactly into those numbers.
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Lowest Common Multiple (LCM): Identify the LCM of two or more numbers, which is the smallest number that is a multiple of those numbers.
Handling Data
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Mean, Median and Mode: Understand how to calculate the mean (average), median (middle value), and mode (most frequently occurring value) of a set of numbers.
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Range: Calculate the range of a set of data by subtracting the smallest number from the largest number. This provides a measure of dispersion or spread in the data.
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Handling Large Numbers and Standard Form: Be able to manipulate very large and very small numbers and convert numbers into standard form (also known as scientific notation).