Foundation plus - Numerical properties and rounding - GCSE Mathematics

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Foundation plus - Numerical properties and rounding

infoWhy this? Understanding factors, multiples, and prime decomposition reveals number structure and helps us solve problems involving grouping and repeating events. Rounding, estimation, bounds, and error intervals enable us to check calculations and communicate the precision and limitations of numerical information.

scheduleWhy now? Early in Year 10, this unit establishes number skills that can be applied throughout the course. Factors and powers support the following algebraic manipulation unit, while estimation and bounds provide ways to check later calculations involving rates, measurements, and financial quantities.

A square number is the product of an integer multiplied by itself (e.g., 1, 4, 9, 16, 25, ...).
A cube number is the product of an integer multiplied by itself twice (e.g., 1, 8, 27, 64, 125, ...).
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself (e.g., 2, 3, 5, 7, 11, ...).
A factor of a number is a whole number that divides exactly into that number.
A multiple of a number is the product of that number and an integer.
The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of them.
The highest common factor (HCF) of two or more numbers is the largest number that divides exactly into each of them.
Rounding a number means adjusting it to a specified degree of accuracy (nearest integer, 10, 100, 1000, decimal place, or significant figure).
Estimation involves rounding numbers (often to one significant figure) to make calculations simpler and quicker.
Truncating a number means shortening it to a specified number of decimal places or significant figures without rounding.
A number can be expressed as a product of its prime factors (prime factorisation).
Prime decomposition is the process of breaking down a number into its prime factors.
The LCM and HCF can be found using the prime factorisations of numbers.
Upper and lower bounds represent the maximum and minimum possible values of a rounded or measured quantity.
Error interval notation is used to describe the range of possible values a number could take, given a degree of accuracy (e.g., ( 3.5 \leq x < 3.6 )).

rocket_launchYou must be able to

List all square, cube, and prime numbers up to a given value.
List all factors and multiples of a given number.
Identify the LCM and HCF of any two or more numbers, including using prime factorisation.
Round numbers to the nearest integer, 10, 100, 1000, decimal place, or significant figure as specified.
Estimate answers to calculations by rounding each number to one significant figure and performing the calculation.
Truncate numbers to a specified number of decimal places or significant figures.
Express any number as a product of its prime factors, using index notation where appropriate.
Use prime decomposition to find the LCM and HCF of two or more numbers.
Solve worded problems involving LCM and HCF in real-life contexts (e.g., finding when events coincide, grouping items).
Find upper and lower bounds for a value given a degree of accuracy (e.g., rounding or measurement).
Write error intervals for numbers rounded to a given degree of accuracy, using correct mathematical notation.

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