Mathematics 6

Negative numbers sit LEFT of zero on a horizontal number line (and BELOW zero on a vertical one, like a thermometer). Zero itself is neither positive nor negative.

The standard algorithms are reliable procedures: line up place values, work right to left, regroup (carry/borrow) when needed.

A composite number can always be written as a product of smaller numbers (factoring); a prime number can't be broken down further (only 1 and itself).

Multiply as if there were no decimal point, then place the point so the answer has as many decimal places as the factors combined.

In an equal-share situation, the numerator is the quantity being shared and the denominator is the number of shares: 3 pizzas for 4 people is ¾ each.

The conventional order: parentheses first, then powers, then multiplication/division, then addition/subtraction.

Powers come BEFORE multiplying: in 3 × 2², square first (4), then multiply (12).

Like terms have exactly the same variable (3x and 5x; constants are like terms with each other) — combine them by adding or subtracting: 3x + 5x = 8x.

The commutative, associative and distributive properties let you rearrange safely: a + b = b + a; a(b + c) = ab + ac.

Solving means finding the value that makes the equation true — simplify first (combine like terms), then reason out the unknown.

Symmetrical shapes can be mapped onto themselves by combinations of reflections (flips) and rotations (turns).

A tessellation tiles a plane with symmetrical shapes, no gaps or overlaps — First Nations and Métis star blanket designs are tessellations that convey specific purpose and meaning.

Congruent shapes are identical in size and shape — one maps exactly onto the other.

Shapes related by symmetry are always congruent, but two congruent shapes are NOT necessarily related by symmetry (they can just be copies placed anywhere).

An ordered pair (x, y) gives the horizontal distance from the y-axis first, then the vertical distance from the x-axis. The axes cross at the origin, (0, 0).

Order matters: (3, 5) and (5, 3) are different points.

A translation combines horizontal and vertical movement into one slide; a reflection flips across the x-axis or y-axis; a rotation turns 90°, 180° or 270° about one of the shape's vertices, clockwise or counter-clockwise.

Each movement can be described precisely: 'translate 4 right and 2 down', 'reflect over the y-axis', 'rotate 90° clockwise about vertex A' — and the image's coordinates relate back to the original's.

A parallelogram has two pairs of parallel, equal sides; any side can be the base, and the height is the PERPENDICULAR distance to the opposite side. Area = base × height.

Volume measures 3-D space. The standard units come from length units: a cubic centimetre (cm³) is a 1 cm × 1 cm × 1 cm cube; a cubic metre (m³) is a 1 m cube.

A triangle is half of a parallelogram with the same base and height, so its area is half — and two triangles with the same base and height always have the same area.

Choose the unit that fits the object: cm³ for a juice box, m³ for a moving van.

A composite shape splits into simpler shapes; its area is the SUM of the pieces' areas.

A variable stands for the values of a changing quantity. In a function, one quantity depends on another — height depends on the day, distance depends on the time.

The independent variable is the one you pick (day, time); the dependent variable is the one that responds (height, distance).

A table of values lists the independent variable in the first column and the dependent in the second — each row is one snapshot of the function.

Each row becomes a point: independent value as the x-coordinate, dependent as the y-coordinate. Plotting them reveals the pattern of change.

Relative frequency is the count for a category compared to the total — expressed as a fraction, decimal or percent (12 of 24 students is ½, or 50%).

Raw counts mislead when totals differ; relative frequencies put data sets on the same footing.

Equally likely outcomes have the same chance (each face of a fair die). An event is one or more outcomes — like 'rolling an even number'.

The law of large numbers: the MORE trials you run, the closer your experimental results tend to get to the expected likelihood.