My Maths Toolkit: Primary & Middle Years Mathematics Reference

Comprehensive vocabulary flashcards covering the key mathematical rules, operations, terms, and measurement conversions from the 15-part Maths Toolkit reference series.

Place Value

The numerical value that a digit has by virtue of its position in a number, where every column to the left is $10\times$ larger and every column to the right is $10\times$ smaller.

Expanded Form

A way of writing a number that shows the sum of the values of each of its individual digits (e.g., $4\,000\,000 + 300\,000 + 5\,000 + 800 + 60 + 2 + 0.7 + 0.05$).

Placeholder Zero

A zero used to keep an empty place value column tidy so that other digits retain their correct value (e.g., $405$ is not $45$).

Decider Digit

The digit immediately to the right of the place value being rounded; if it is $0\text{--}4$, the rounded digit stays, and if it is $5\text{--}9$, the rounded digit goes up by $1$.

The 9 Roll-Over

A rounding scenario where an underlined $9$ must increase by $1$, making it $10$ and carrying $1$ over into the next higher place value column (e.g., $2\,960$ to the nearest hundred rounds to $3\,000$).

Prime Number

A whole number with exactly two factors: $1$ and itself (e.g., $2, 3, 5, 7, 11$). Note that $2$ is the only even prime, and $1$ is neither prime nor composite.

Composite Number

A whole number that has more than two factors (e.g., $4, 6, 8, 9, 12$).

Square Numbers

Numbers produced by multiplying an integer by itself ($n \times n$), forming a square array of dots ($1, 4, 9, 16, 25, 36, 49, 64, 81, 100$).

Triangular Numbers

Numbers that can form an equilateral triangular dot pattern by adding consecutive rows ($1, 3, 6, 10, 15, 21, 28, 36, 45, 55$).

Factor

A number that divides exactly into another number with no remainder; factors fit inside and are always the same size or smaller than the given number.

Multiple

The product of multiplying a number by an integer; multiples grow outward in times tables and are the same size or larger than the given number.

Highest Common Factor (HCF)

The largest factor that two or more numbers share, commonly used to simplify fractions.

Lowest Common Multiple (LCM)

The smallest non-zero multiple shared between two or more numbers, commonly used as a common denominator for adding and subtracting fractions.

Order of Operations

The standard sequence of mathematical calculation: brackets first, followed by multiplication and division from left to right, then addition and subtraction from left to right.

Inverse Operations

Opposite operations that undo each other when solving for a missing number ($+ \leftrightarrow -$ and $\times \leftrightarrow \div$).

Numerator

The top number in a fraction that indicates how many parts are being considered.

Denominator

The bottom number in a fraction that indicates the total number of equal parts the whole is divided into.

Equivalent Fractions

Different fractions that represent the same value, created by multiplying or dividing both the numerator and denominator by the same number.

Mixed Number

A number represented as a whole number combined with a proper fraction (e.g., $2\frac{3}{4}$).

Improper Fraction

A fraction where the numerator is greater than or equal to the denominator (e.g., $\frac{11}{4}$).

Multiplying Decimals by 10, 100, or 1000

Sliding the digits to the left past the stationary decimal point ($1$ jump left for $10$, $2$ jumps for $100$, $3$ jumps for $1\,000$) to make the number larger.

Dividing Decimals by 10, 100, or 1000

Sliding the digits to the right past the stationary decimal point ($1$ jump right for $10$, $2$ jumps for $100$, $3$ jumps for $1\,000$) to make the number smaller.

Percentage

A fraction or ratio expressed with a denominator of $100$, meaning 'out of $100$' and written with the $({\%})$ symbol (e.g., $7\% = 0.07$).

Counting Up Method

A method of calculating cash change like a shopkeeper by jumping forward from the item cost to the next $10\text{c}$, then to the next whole dollar, and finally to the paid amount.

Best Buy

A comparison strategy where total price is divided by quantity to determine the unit cost of one item; the lowest unit cost represents the best value.

Integer Number Line

A line showing integers where values increase to the right (warmer, saving) and decrease to the left of zero (colder, owing).

Cartesian Quadrants

The four regions of a coordinate plane formed by the axes: 1st quadrant $(+,+)$, 2nd quadrant $(-,+)$, 3rd quadrant $(-,-)$, and 4th quadrant $(+,-)$.

Coordinates (x, y)

An ordered pair defining a location on a grid, plotted by moving horizontally along the $x$-axis first ('along the corridor') and then vertically along the $y$-axis ('up or down the stairs').

Metric Length Staircase

Conversion system for length where moving down multiplies and moving up divides: $1\,km = 1\,000\,m$, $1\,m = 100\,cm$, and $1\,cm = 10\,mm$.

Metric Mass Conversions

Weight units converted in steps of $1\,000$: $1\,\text{tonne}\,(t) = 1\,000\,kg$ and $1\,\text{kilogram}\,(kg) = 1\,000\,g$.

Metric Capacity Conversions

Fluid volume units converted in steps of $1\,000$: $1\,\text{kilolitre}\,(kL) = 1\,000\,L$ and $1\,\text{litre}\,(L) = 1\,000\,mL$.

Area

The amount of flat surface covered inside a 2D shape (nap inside like Rug), calculated for rectangles as $\text{length} \times \text{width}$ and expressed in square units ($cm^2$, $m^2$).

Perimeter

The continuous boundary or total distance around the outside edge of a 2D shape (walk around like Fence), calculated by adding the lengths of all sides.

24-Hour Time

A time system where days run from midnight ($00:00$) to $23:59$; converting from 12-hour pm time requires adding $12$ hours (e.g., $3:15\,\text{pm} = 15:15$).

Acute Angle

An angle that measures strictly less than $90^\circ$.

Right Angle

An angle that measures exactly $90^\circ$.

Obtuse Angle

An angle that measures strictly between $90^\circ$ and $180^\circ$.

Reflex Angle

An angle that measures strictly between $180^\circ$ and $360^\circ$.

Angles on a Straight Line

Adjacent angles that form a straight line and always sum to $180^\circ$.

Angles Around a Point

Angles that meet at a single central point to complete a full revolution, summing to $360^\circ$.

Vertically Opposite Angles

The pairs of opposing angles formed by two straight lines intersecting in an 'X' shape, which are always equal to each other.

Probability

The numerical likelihood of an event occurring, calculated as $\frac{\text{favourable outcomes}}{\text{total outcomes}}$ and ranging strictly from $0$ (impossible) to $1$ (certain).

Mode

The number or value that appears most frequently in a dataset.

Range

The spread of a dataset, calculated as the difference between the largest value and the smallest value ($\text{Range} = \text{biggest} - \text{smallest}$).