# Mathematical Language

Using the correct language and definitions is crucial when teaching mathematics to students. It helps to avoid confusion and ensures that students have a clear understanding of the concepts being taught. Inaccurate or ambiguous language can lead to misunderstandings that can make it difficult for students to grasp the concepts, solve problems, and apply their knowledge. It is important to be consistent and accurate in the language and definitions used in mathematics to promote understanding, build confidence, and enable students to communicate their ideas effectively.

## Mathematical Definitions

### Collection

A defined set of objects that can be looked at as a group.

### Difference

The process of subtraction is where we look at how much one set of numbers or objects differs from another set.

### Digits

Numerical symbols used to represent numbers in a positional numbering system (0 - 9).

### Divide

The process of splitting a number or amount into equal parts.

### Efficient

Performing a method with the least amount of time and effort expended.

### Estimate

A rough calculation or an approximation of an amount or quantity.

### Figurative strategies

Using strategies for counting where the collections are partially or totally concealed (imagined quantities, trusting the count)

### Group marker

An object or item that is used to identify a group and everything represented in that group.

### Natural numbers

Positive whole numbers beginning at 1 and ending in infinity. All of the countable numbers.

### Non-place value

The value of a digit is not determined by its position in a number, but by its actual value or place in a set. For example, 135 can be renamed as 9 tens and 45 ones.

### Non-standard place value

Partitioning a number in flexible ways where the values of digits are assigned in a non-standard way based on their position. For example, 135 can be written 1 ten and 35 ones

### Number line

A line on which numbers are marked at regular intervals and that can be used to illustrate simple operations.

### Number sense

A person’s ability to think flexibly and fluently about numbers.

### Number triad

A way of representing a number that includes writing it using numerals and words and representing it using materials.

### Perceptual strategies

Relying on concrete representations of numbers to count collections (showing all).

### Place value

The “value” of a digit is dependent on its specific “place” or position in the number.

### Quantity

A number of objects that are given a numerical value.

### Share equally

Sharing a collection into equal parts among two or more groups.

### Standard place value

A numbering system in which the value of a digit is determined by its position in the number relative to a base value, usually 10.

### Subitise

To instantly recognise a collection or quantity without counting.

### Take-away

The process of subtracting something by removing objects or numbers from one group or quantity.