Scalar quantities have size only

1. A scalar quantity is fully described by a magnitude, which means a number together with a unit.
2. Nothing else is needed, so once you know a temperature is $18{}^{\circ }C$ you know everything that quantity carries.
3. Scalars used across the course include distance in $m$, speed in $m/s$, mass in $kg$, energy in $J$, time in $s$, temperature in ${}^{\circ }C$, density in ${kg/m}^3$ and power in $W$.
4. Scalars are combined by ordinary arithmetic, so walking $300m$ to the shop and $300m$ back gives a total distance of $600m$.

Vector quantities have size and direction

1. A vector quantity has a magnitude and a direction, and it is not fully described until both have been given.
2. A force of $20N$ is an incomplete description, while a force of $20N$ to the right is the complete vector.
3. Vectors used across the course include displacement in $m$, velocity in $m/s$, acceleration in ${m/s}^2$, force in $N$, weight in $N$ and momentum in $kg\; m/s$.
4. A vector is represented by an arrow, where the length is drawn to a scale to show the magnitude and the way the arrow points shows the direction.
5. Changing only the direction changes the vector, so a car driving north at $15m/s$ and a car driving south at $15m/s$ have the same speed but different velocities.
6. A direction can be given as a compass bearing, as left or right, as up or down, or as a positive or negative sign along a chosen line.
7. A negative sign in front of a vector therefore carries physical meaning, because a velocity of $-6m/s$ is a velocity of $6m/s$ in the opposite direction to the one chosen as positive.

Matched pairs of scalars and vectors

1. Several quantities come in pairs, one scalar and one vector, sharing a unit but not a meaning.
2. Distance is the total length of the path travelled, while displacement is the straight-line change in position together with its direction.
3. A runner who completes one lap of a $400m$ track has travelled a distance of $400m$ but has a displacement of $0m$, because the finish point is the start point.
4. Speed is how fast an object is moving, while velocity is speed in a stated direction.
5. A car driving round a roundabout at a steady $8m/s$ has a constant speed but a changing velocity, because its direction keeps changing.
6. Mass is the quantity of matter in an object, measured in $kg$, and it does not change when the object is moved somewhere else.
7. Weight is the gravitational force acting on that mass, measured in $N$, and it acts towards the centre of the planet or moon the object is near.
8. A $60kg$ astronaut still has a mass of $60kg$ on the Moon, but weighs about one sixth as much there, because the Moon's gravitational field strength is smaller.