Foundation - Numerical operations - GCSE Mathematics

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Foundation - Numerical operations

infoWhy this? Accurate calculation with integers, negative numbers, powers, and roots enables us to solve multi-step problems using written methods and calculators appropriately. Index laws and standard form provide efficient ways to represent and calculate with very large or very small quantities.

scheduleWhy now? This Spring Term unit consolidates the arithmetic and index laws used in autumn algebra and proportion, then extends their application to standard form. Secure work with negative numbers, powers, and roots supports forthcoming sequences and graphs, as well as Pythagoras' theorem in Year 11.

The formal written method for multiplication (long multiplication) can be used to multiply numbers up to 4 digits by a two-digit number.
The formal written method for division (long division) can be used to divide numbers up to 4 digits by a two-digit number.
Negative numbers follow specific rules for addition, subtraction, multiplication, and division (e.g., a negative times a negative is a positive).
The square of a number is the result of multiplying the number by itself.
The square root of a number is a value that, when multiplied by itself, gives the original number.
The cube of a number is the result of multiplying the number by itself twice (number × number × number).
The cube root of a number is a value that, when used three times in a multiplication, gives the original number.
Calculators follow the order of operations (BIDMAS) when performing calculations.
The laws of indices include:
( am x an = am+n )
( am ÷ an = am-n )
( (a(m)^n) = am x n )
(a^0 = 1 ) (for ( a ≠ 0 ))
(a^1 = a )
The laws of indices apply to algebraic bases as well as numerical bases.
Standard form is a way of writing very large or very small numbers as ( a x 10n ), where ( 1 ≤ a < 10) and (n) is an integer.
Large numbers in standard form have positive powers of 10; small numbers (less than 1) have negative powers of 10.
To convert a number from standard form to an ordinary number, multiply the coefficient by the appropriate power of 10.
To order numbers in standard form, compare the powers of 10 first, then the coefficients if the powers are equal.
When multiplying numbers in standard form, multiply the coefficients and add the powers of 10.
When dividing numbers in standard form, divide the coefficients and subtract the powers of 10.
When adding or subtracting numbers in standard form, the powers of 10 must be the same.
Estimating powers and roots involves finding two consecutive integers between which the answer lies

rocket_launchYou must be able to

Multiply numbers up to 4 digits by a two-digit number using the formal written (long multiplication) method.
Divide numbers up to 4 digits by a two-digit number using the formal written (long division) method.
Add, subtract, multiply, and divide negative numbers accurately.
Calculate squares, square roots, cubes, and cube roots of integers (with and without a calculator).
Use a calculator accurately to perform multi-step calculations, ensuring correct use of brackets and order of operations.
Apply the laws of indices to simplify expressions with numerical and algebraic bases.
Write large or small numbers in standard form and convert numbers in standard form to ordinary numbers.
Order a list of numbers given in standard form.
Multiply and divide numbers in standard form, expressing the answer in standard form.
Add and subtract numbers in standard form, expressing the answer in standard form.

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