Mathematics 6

Place value works the same in both directions from the decimal point: ones, tens, hundreds, thousands… and tenths, hundredths, thousandths — each place is 10 times its neighbour.

A factor of a number divides into it evenly with no remainder (factors of 12: 1, 2, 3, 4, 6, 12). A multiple is what you get by multiplying a number by whole numbers (multiples of 4: 4, 8, 12, 16…).

An improper fraction (like 7/2) has a numerator equal to or bigger than its denominator, meaning the amount is a whole number or more.

A ratio compares two quantities and can be written as 'a to b', 'a : b', or as a fraction a/b — like 2 cups of flour to 1 cup of sugar, written 2:1.

Percent means 'out of 100' — 25% is the same as 25/100 or 0.25.

Multiplication and division are opposite (inverse) operations — if you know 7 × 8 = 56, you also know 56 ÷ 8 = 7 and 56 ÷ 7 = 8.

Work out anything in brackets first, then do all multiplication and division (left to right), then all addition and subtraction (left to right).

Multiply decimals like whole numbers first, then count the total decimal places in the numbers being multiplied to place the decimal point in the answer.

Use patterns and known facts to find unknown ones fast — like doubling (6×4 = double of 6×2), or using a nearby known fact (9×7 = 10×7 minus 7).

Order of operations exists so that any two people evaluating the same expression always get the same answer.

An increasing pattern grows by the same amount (or rule) each step; a decreasing pattern shrinks by the same amount (or rule) each step.

An equation like 4n = 24 or n + 9 = 15 says two things are equal; solving means finding the whole number that makes it true.

The same functional relationship can be shown as an expression (like 2n + 3), a table of input/output values, or points on a graph — all three describe the same rule.

Use the opposite (inverse) operation to undo what is being done to the unknown — undo addition with subtraction, undo multiplication with division.

A table or expression can be used to predict terms further along the pattern without building every step in between.

Perimeter is the total distance all the way around the outside edge of a shape — add up every side length.

A parallelogram's area is base × height — it can be reshaped into a rectangle with the same base and height.

Volume is the amount of space a 3D object takes up, often measured by counting unit cubes that fill it.

In an L-shape or other complex shape, some side lengths may be missing but can be figured out because opposite or aligned sides must add up correctly.

A triangle's area is (base × height) ÷ 2, because two identical triangles fit together to make a parallelogram.

An angle is measured in degrees using a protractor, lining up its base line with one arm of the angle and reading where the other arm crosses the scale.

By sides: scalene (no equal sides), isosceles (two equal sides), equilateral (all three sides equal).

A combination of transformations means doing two or more moves — translation (slide), rotation (turn), reflection (flip) — one after another on the same shape.

Angles are classified by size: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°), and reflex (more than 180°).

By angles: acute (all angles under 90°), right (one 90° angle), obtuse (one angle over 90°).

A line graph plots points over time (or another continuous variable) and connects them with a line, showing how a quantity rises, falls, or stays steady.

Theoretical probability is calculated using math (favourable outcomes ÷ total possible outcomes) before ever running an experiment.

A budget lists income (money coming in) and expenses (money going out) for a period of time, and checks that expenses don't add up to more than income.

Always check both axes' labels and scale before reading a line graph — the same-looking line can mean very different things at different scales.

Experimental probability comes from actually doing the trials and tallying results (times it happened ÷ total trials run).