Numerical Operations

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infoWhy this? Fluent numerical operations allow us to calculate accurately, select efficient methods, and judge whether answers are reasonable. Work with negative integers, formal methods, BIDMAS, and calculators supports problem-solving throughout mathematics.

scheduleWhy now? Year 7 is an important point at which to align prior calculation methods and extend them consistently to negative numbers and multi-step expressions. This fluency supports subsequent work with fractions, formulae, percentages, and measures.

When two integers with the same sign are added, their absolute values are added and the common sign is retained; when two integers with different signs are added, the smaller absolute value is subtracted from the larger and the sign of the integer with the larger absolute value is retained, or the sum is zero if their absolute values are equal.
Subtracting an integer is equivalent to adding its additive inverse.
The product of two integers is positive if both integers have the same sign, and negative if they have different signs.
The quotient of two integers is positive if both integers have the same sign, and negative if they have different signs.
Multiplying by zero always results in zero.
Dividing by zero is undefined.
The order of operations (BIDMAS/BODMAS: Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction) determines the sequence in which calculations are performed: brackets and indices or orders are completed first, multiplication and division have equal priority and are completed from left to right, and addition and subtraction have equal priority and are completed from left to right.
Calculators follow the order of operations when evaluating expressions.
When dividing integers, the absolute value of any remainder is less than the absolute value of the divisor, and a non-zero remainder has the same sign as the dividend.
In formal written calculations with large integers, digits must be aligned in columns according to their place value.
A calculator displays an error for an undefined operation such as division by zero.

rocket_launchYou must be able to

Add and subtract integers with more than four digits accurately, including both positive and negative numbers.
Multiply integers up to four digits by a one-digit integer, including negative numbers.
Divide integers up to four digits by a one-digit integer, including negative numbers.
Multiply integers up to four digits by a two-digit integer, including negative numbers, using formal written methods such as long multiplication.
Divide integers up to four digits by a two-digit integer, including negative numbers, using formal written methods such as long division.
Apply the rules for multiplying and dividing negative numbers in calculations.
Apply the rules for adding and subtracting negative numbers in calculations.
Use the order of operations (BIDMAS) to carry out multi-step calculations accurately by evaluating brackets and indices first, then multiplication and division with equal priority from left to right, and finally addition and subtraction with equal priority from left to right.
Perform calculations using a calculator accurately and effectively, including entering negative numbers, using brackets, and interpreting calculator displays.

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