Mathematics 5

Each place value is 10 times bigger than the place to its right — ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, then a million.

After the decimal point, the places are tenths, hundredths, and thousandths — each one is 10 times smaller than the one before it.

Multiplying (or dividing) the numerator and denominator by the same number gives an equivalent fraction — the amount doesn't change, just how it's cut up.

Benchmarks are easy-to-picture numbers — like 0, 1/2, 1, 10, or 100 — that we compare other numbers to.

Line up the digits by place value (ones under ones, tens under tens, and so on) before adding or subtracting.

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

A variable (like x or n) stands for an unknown number, and the equation tells you a fact about it.

The same rule can be written in words ('start at 3, add 3 each time'), as a number sentence, or using a variable like n (for example, 3 × n).

To find the variable's value, use the opposite (inverse) operation — if the equation adds, subtract to solve; if it multiplies, divide to solve.

Area is the amount of flat space inside a shape, measured in square units (like square centimetres).

Area (space inside) and perimeter (distance around the outside) measure different things, and one doesn't determine the other.

Duration is the amount of time between a start time and an end time.

For a rectangle or square, area = length × width — this counts how many unit squares fit inside without measuring each one.

Shapes can have the same area but different perimeters — a long skinny rectangle and a more square-ish one can cover the same space but need different amounts of fencing.

A prism has two matching parallel bases connected by rectangle (or parallelogram) faces; a pyramid has one base and triangular faces that meet at a single point (the apex).

A translation slides a shape without turning or flipping it; a rotation turns a shape around a point; a reflection flips a shape over a line like a mirror.

Prisms and pyramids are named after the shape of their base — a rectangular prism has rectangle bases, a triangular pyramid has a triangle base.

In all three transformations, the shape's size and form stay exactly the same — only its position or orientation changes.

In a one-to-one graph, each symbol or square represents exactly one item.

A single event or outcome (like rolling exactly a 4, or landing on 'blue') has a probability that can be written as a fraction: favourable outcomes out of total possible outcomes.

In a many-to-one graph, each symbol represents more than one item (like 1 star = 5 medals) — always check the legend or key first before reading the graph.

Running the experiment many times and tallying results lets you compare what ACTUALLY happened to what was theoretically expected.

Probability tells you what is likely over many trials — it does not guarantee an exact result in any small number of trials.

Making change with larger amounts (up to $1000) works the same way as with smaller amounts — count up from the price to the amount given, or subtract.

A simple financial plan starts with a goal amount, subtracts what's already saved, and divides what's left by a savings rate to estimate how long it will take.

Keeping a running total (of change owed, or of savings progress) helps track money accurately over several steps.