Volume, Length and Averages

Volume of a Cuboid #

How many unit cubes fit inside.

Volume is how many unit cubes fit inside

A box 4 along, 3 up, 3 deep — fill it right up with cubes and count.

One layer is 4 across and 3 up, so it holds 4 × 3 = 12 cubes.

3 layers stack: 12 × 3 = 36 cubes. Volume is length × width × height.

Backwards: 36 cubes on a 4 × 3 base. 36 ÷ 12 = 3 layers — the edge is volume ÷ base.

The Mean #

What each would get if shared out evenly.

The mean is what everyone would get if the total were shared out evenly

Three different heights, leveled off. The line is where they all settle.

Add and share: 2 + 6 + 4 = 12, and 12 ÷ 3 = 4. This average is called the mean.

Reading a Ruler #

Measure from zero, not from the end.

Measure from the zero mark, not from the end of the ruler

Line the object up with 0, then read the number at the far end.

Not starting at 0? Take the start off the end: 7 − 2 = 5 cm.

Drawing a Line Segment #

Start at zero, stop on the length’s mark.

A segment drawn from the 0 mark ends on the mark that names its length

Start the pencil on the 0 mark and stop on 7: the segment is exactly 7 cm.

Started at 1 by mistake? The end mark lies: 8 − 1 = 7 cm, not 8.