Number and Algebra: Number knowledge, Level 2
AO1: Know forward and backward counting sequences with whole numbers to at least 1000. 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, e.g. 358, 348, 338,..., and one hundred, e.g. 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, e.g. If a set contains 800 items, 799 items are left if one is removed. This also applies to the sequence in tens and hundreds, e.g. ten removed from a set of 503 results in 493 objects left..
AO2: Know the basic addition and subtraction facts.
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, e.g. 4 + 7 = 7 + 4, and the inverse nature of addition and subtraction, e.g. 6 + 7 = 13 so
13 – 7 = 6, as a foundation for more difficult problems, as well as a way to connect basic facts.
Students also need to encounter the unknown in different positions within their basic facts, e.g. 4 + 
= 12
and – 5 = 8.
AO3: Know how many ones, tens, and hundreds are in whole numbers to at least
1000.
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, e.g. 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, e.g. 456 has 45 tens and 456 ones. An understanding of nested place value is best
demonstrated by calculations where tens must be constructed from ones, hundreds constructed from tens, tens created from breaking hundreds and
ones created from breaking tens. For example, calculations like 456 + 70 = or
456 - = 396, show whether students can apply place value in this way.
AO4 Know simple fractions in everyday use. 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, e.g. 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, e.g. In 4/3 there are four parts. The parts are thirds created by splitting one into three equal parts. This means that fractions can be greater than one, e.g. 4/3 = 1 1/3, and that fractions have a counting order if the denominators are the same, e.g. 1/3, 2/3, 3/3, 4/3,... Note that whole numbers can be written as fractions, e.g. = 1. Fractions in everyday usage include halves, thirds, quarters (fourths), fifths, eighths, and tenths..
