Level Two

This means students will understand the meaning of the digits in a fraction, how the fraction can be written in numerals and words, or said, and the relative order and size of fractions with common denominators (bottom numbers). Fundamental concepts are that fractions are iterations (repeats) of a unit fraction, for example, 3/4 = 1/4 + 1/4 + 1/4 and 4/3 = 1/3 + 1/3 + 1/3 + 1/3 . This means the numerator (top number) is a count and the denominator tells the size of the parts, for example, in 4/3 there are four parts. The parts are thirds created by splitting one into three equal parts.

This means students will develop an additive view of whole number place value by knowing the significance of the position of digits in a whole number, for example, in 456 the 5 means five tens. However, many strategies for computation require a nested view of place value. This means that nested in the hundreds are tens in the same way that nested in the hundreds and tens are ones, for example, 456 has 45 tens and 456 ones.

This means students will know the basic addition facts from 0 + 0 = 0 to 9 + 9 = 18. So 4 + 1 = 5, 8 + 6 = 14, and 9 + 3 = 12 are all basic addition facts. The basic subtraction facts are the subtraction equivalent of the addition facts, so 5 – 1 = 4, 5 – 4 = 1, 12 -3 = 9 and 12 – 9 = 3 are all examples. It is important that students understand the commutative property of addition (for example, 4 + 7 = 7 + 4), and the inverse nature of addition and subtraction (for example, 6 + 7 = 13 so 13 – 7 = 6), as a foundation for more difficult problems, as well as a way to connect basic facts.

This means students will know the forward number word sequence to 1000 is the counting pattern of words and symbols, 0, 1, 2, 3, 4...1000 while the backward sequence is the pattern 1000, 999, 998, 997 ... At level Two students should know these sequences in multiples of one ten (for example, 358, 348, 338...) and one hundred (for example, 247, 347, 447...) An important part of knowing these sequences is being able to name the number before and after a given number since this relates to taking an item off or putting an item onto an existing set.

This means students will learn to treat whole numbers as units of ones that can be split and recombined to make calculations easier. Additive strategies are about a type of thinking not the operation of addition. So additive strategies can be applied to addition (for example, 47 + 38 is 50 + 40 – 5), subtraction (for example, 74 – 8 =  as 74 – 4 – 4 = ), multiplication (for example, 4 x 4 =