# Glossary

Parallel lines are lines in a plane which do not intersect or touch each other at any point. Parallel lines can never intersect, even if they were to continuously extend toward infinity.

Two lines are parallel, if they have the same gradient (or slope).

The lines below are parallel to one another, as indicated by the use of the arrow signs. In text, the symbol ∥ is used to denote parallel lines; for example, a∥b is read as “line a is parallel to line b”.

Partial products are used in multiplying multi-digit numbers. For example, 53 x 24 = (50 + 3) x (20 + 4). This product can be represented as finding the area of a rectangle with side lengths 50 + 3 and 20 + 4. The partial products are then the areas of each part of the rectangle: 50 x 20 = 1000, 50 x 4 = 200, 3 x 20 = 60, 3 x 4 = 12. Treating the total area as the sum of its parts means 53 x 24 = 1000 + 200 + 60 + 12 = 1272.

Partitioning means dividing a quantity into parts. In the early years, it commonly refers to the ability to think about numbers as made up of two or more parts, such as, 10 is 8 and 2 or 126 is 100 and 20 and 6. In later years it refers to dividing both continuous and discrete quantities into equal parts.

Part-whole knowledge of numbers refers to recognising that 7 = 5 + 2 additively or 7 = 4 + 3. The whole is the sum of its parts, also sometimes called part-part-whole.

Counting items that can be perceived (seen, heard or touched) by matching the number word sequence to the items and recognising that the last number word corresponds to the total.

Markers for equal groups that can be perceived. For example, opaque containers standing for equal groups of items or fingers used to represent each group.

In geometry, two lines are said to be perpendicular to each other, if they meet at a right angle (90 degrees).

The place value periods are formed in groups of three within a numeral. For example, ‘hundreds, tens and ones’ forms one period.

The place value system of our numbers is based on 10. The value of a digit in a numeral is determined by multiplying its face value by the power of ten assigned to its position (283 = 2 x 100 + 8 x 10 + 3 x 1). The quantity represented by a numeral is then the sum of the values represented by its individual digits (283 = 200 + 80 + 3). The base-ten place value system used to write numerals has both multiplicative and additive properties.

A population is the complete set of individuals, objects, places, etc, that we want information about. A census is an attempt to collect information about the whole population.

The value determined by the position a digit occupies in a numeral (for example, the "ones place", "tens place", "hundreds place").

A product is the result of multiplying together two or more numbers. For example, 36 is the product of 9 and 4, and x2 – y2 is the product of x – y and x + y.