Number and Algebra: Patterns and relationships, Level 2
AO1: Generalise that whole numbers can be partitioned in many ways.
Students at level two should understand that numbers are counts that can be split in ways that make the operations of addition, subtraction, multiplication and division easier. From Level One students understand that counting a set tells how many objects are in the set. An advance on this thinking is to realise that the count of a set can be partitioned and that the count of each subset tells how many objects are in that subset. Also required is understanding that partitions of a count can be recombined. For example, a count of ten can be partitioned into 1 and 9, 2 and 8, 3 and 7, etc. This objective also involves critical choice of partitioning. For example, 8 + 6 =
can be solved by partitioning 6
into 1 and 5, 2 and 4, 3 and 3. Of these partitions 2 and 4 is the best strategic choice since it recombines into a “ten and...” fact, i.e. 8 + 6 = 8 + 2 + 4 = 10 + 4. At Level Two students are expected to understand the strategic importance of using place value as a way to partition numbers. Students should apply their partitioning generalisation to many problem types including combining (e.g. 27 + 9 = ) ,
separating (e.g. 105 - 19 = ), comparing (e.g. 45 +
= 106), duplicating (e.g. 8 x 5 = ) and sharing (e.g. 20 ÷ 4 = ).
AO2: Find rules for the next member in a sequential pattern.
This means students will explore sequential patterns, both can be either spatial,
e.g. 
,.. or numeric, e.g. 1, 3, 5, 7, ... A pattern has consistency so further ter
ms of it can be anticipated from those already known. In spatial patterns students should be able to
identify the repeating element, e.g. 
in that above,
and use this to predict the shape in a given
ordinal position, e.g. the next shape is 
,
the eleventh shape will be 
. For simple number patterns
students should identify the consistent “gap” between the terms, e.g. 1, 3, 5, 7,... two is added each
time, and use this additive difference to find further terms. Students should also develop their concept
of relations between variables using
spatial patterns that can be represented using numeric tables of values, e.g. For this pattern, how many squares make 7 crosses?
 |
|
|
| 1 cross 5 squares |
2 crosses 10 squares |
3 crosses 15 squares |
Click to download a PDF of second-tier material relating to Level 2 Patterns and Relationships (203KB)
