The key idea of number knowledge at Level 3 is that numbers can be represented in a variety of ways.
At level 3 students need to be able to use a variety of types of numbers rather than just the ‘counting numbers’. In particular, fractions, decimals and percentages are important for representing both small numbers, and numbers that lie between the whole numbers.
- Fractions are numbers which describe a relative amount, usually expressed as the quotient of two numbers written in the form a/b. For example, in the fraction 3/4 the denominator, 4, represents the number of equal parts the whole is divided into, and the numerator, 3, indicates how many of those parts are included in the number.
- Decimals are an extension of the place value structure described in the key idea of Number Knowledge at level 2. A decimal point is used to separate the integer part of the number from the decimal part. Each column to the right of the decimal point is worth one tenth as much as the one to its left. Decimal numbers are sometimes described as decimal fractions because they can be thought of as a fraction with a denominator which is a power of 10.
- Percentages can be thought of as fractions, where the amount is always described relative to 100. The term percent is another name for hundredths. For example 75% is the same as 0.75 or 75/100 (3/4) of the same thing.
This key idea develops from the key idea of number knowledge at level 2 where students understand the place value structure of whole numbers.
This key idea is extended in the key idea of number strategies and knowledge at level 4 where students understand how to use rational numbers to solve problems.