Level 2
Number and Algebra
Number strategies
AO1: Use simple additive strategies with whole numbers and fractions.
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,
e.g. 47 + 38 is 50 + 40 – 5, subtraction, e.g. 74 – 8 = 
as 74 – 4 – 4 = , multiplication,
e.g. 4 x 6 = as 4 + 4 + 4 + 4 = , which is 8
+ 8 = , division, e.g. 18 ÷ 3 = , as 5 + 5 + 5 = 15 so 6 + 6 + 6 = 18.
Additive strategies may also be applied to finding fractions of sets
particularly halves, thirds, quarters, fifths, eighths and tenths.
Level Two corresponds to students being proficient at the Early Additive stage of the number framework.
Number knowledge
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..
Equations and expressions
AO1: Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols. This means students will be able to use words, symbols and diagrams to explain their number strategies to others. Recording also allows students to think through solutions to problems and allows them to reduce their working memory load by storing information in written form. This is particularly important for the solving of complex, multi-step problems. Students should be able to write the numerals for whole numbers, to 1000, and simple fractions. They should also be able to write addition, subtraction, multiplication and division equations with understanding of the meaning of these operations and of the equals sign as meaning “equal to”. Similarly they should know which operation to perform on a calculator if the numbers are beyond their mental range. Students should also be familiar with using empty number lines to record addition and subtraction strategies and of drawing arrays to record simple multiplication and division strategies. Formal written algorithms for multi-digit addition and subtraction should not be taught at Level Two until students have the place value knowledge required to understand them.
Patterns and relationships
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)
Geometry and Measurement
Measurement
AO1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time. This means students will recognise that the attributes length, area, volume and capacity, and weight can be measured. At Level Two students are expected to recognise that measurement units are countable and therefore able to be partitioned and recombined in the same way as other units of one, e.g. If a 8 unit length is cut from a 14 unit long strip the remainder will measure 6 units. Units of measure have other characteristics including being a part of the attribute they measure and uniformity (same size). When measuring the units need to fill a length, space, time etc, with no gaps or overlaps (this is known as tiling). Students should create measurement devices, e.g. rulers, rod towers, scales, to quantify the attributes of objects in numbers of units. In doing so they should develop an understanding that the marks on a linear scale show the endpoint of units and that scales always have a baseline (zero). Less tangible attributes such as turn (angle), temperature and time should also be measured. While the focus at Level Two is on students’ understanding the role of units in measurement it is also expected that students will encounter simple standard measures such as metres, centimetres, kilometres, minutes, seconds, kilograms, litres, etc, through using everyday measurement instruments.
AO2: Partition and/or combine like measures and communicate them, using numbers and units. This means students will perform and communicate calculations involving like measures. Like measures involve the same units for the same attribute. This allows the result of joining or separating units to be anticipated using additive number strategies, e.g. A box has a volume of 36 cubes. If a 3 by 4 cube layer is put in the empty box then there will be space for 36 – 12 = 24 more cubes. At Level Two students should be able to use numbers and common symbols to communicate measurement results, e.g. my lunchbox holds 60 cubes. I took 13 minutes to walk home. My pencil is 14 cm long. I weigh 26 kg.
Click to download a PDF of second-tier material relating to Level 2 Measurement (119KB)
Shape
AO1: Sort objects by their spatial features, with justification. This means students will sort objects by selecting an attribute or attributes by which to classify items and allocating the items into groups by commonality of that attribute. At Level Two students should be able to find their own system to classify items, using attributes like shape, colour, size, texture, thickness, material, purpose, etc and justify their allocation of items into categories, e.g. "all of these shapes have three sides". In doing so students should develop geometric language for attributes such as "side", "corner", "centre", "face", "edge", "curved", "straight", "larger", "smaller", etc.
AO2: Identify and describe the plane shapes found in objects. This means students will be able to identify plane (flat) shapes in objects and structures around them and consider why the given shape is suitable for its purpose, e.g. wheels are circular so they roll freely, floors are usually rectangles because they are easier to build and things fit efficiently, etc. They should consider how three dimensional objects are built from flat shapes through pulling packets apart and constructing solids of their own, e.g. nets for cubes.
Click to download a PDF of second-tier material relating to Level 2 Shape (83KB)
Position and orientation
AO1: Create and use simple maps to show position and direction. At Level Two students should be able to use simple schematic maps, e.g. plans of their school, road maps of their local area. This involves finding their current position on a map by connecting landmarks they can see with locations on the map. Similarly it involves finding the place that matches a given point on the map and describing how they would move from one point to another. Descriptions of movement should include features such as main compass directions (N, S, E, W), half and quarter turns, and approximate distances in whole numbers of metres (e.g. about 12 metres) . Students should use simple co-ordinates (e.g. B5) to specify locations on schematic maps.
AO2: Describe different views and pathways from locations on a map. This objective requires students to see schematic maps as a two dimensional representation of the real world. By looking at a map students should be able to anticipate landmarks they will see from a given location and in which direction (N, S, E, W) those landmarks will be seen. From a map they should give a set of directions, using distances in whole numbers of metres and quarter/half turns, that will take a person from one position on the map to another, e.g. turn right and walk about 25 metres.
Click to download a PDF of second-tier material relating to Level 2 Position and orientation (126KB)
Transformation
AO1: Predict and communicate the results of translations, reflections, and
rotations on plane shapes.
This means students will experience physically moving shapes so that they can predict the
location and orientation of the shape after it has been translated, reflected or rotated, e.g.
draw/show what this shape will look like if I give it a half turn about its centre.
Students should be able to identify how many mirror lines a shape has that maps it onto itself,
e.g. a square has four mirror lines. Translations are images of a shape as it is shifted along a
line, e.g. 
... Reflections are
images of a shape as it is reflected in a mirror (sometimes called a flip), e.g. 
Note that the line may outside the object or within it. Rotations are images of a shape as it is turned about a point outside or within it,
e.g. 
.
Statistics
Statistical investigation
AO1: Conduct investigations using the statistical enquiry cycle:
This means students will use the statistical enquiry cycle in their investigations.
The cycle has five phases that relate to each other. Some enquiries follow these phases
in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:
At Level Two students should be able to pose questions that they want to investigate,
consider the appropriate data they need to collect, gather and sort the data in
order to develop an answer to their question. The data involved may be either
category data or whole number data. Category data arises from classifying and the
interest is in how many of the data items fall in each category (called frequency).
Colour and number of doors are two ways to classify cars that will produce category data.
Whole number data comes from situations where only whole number values are possible, e.g.
how many people live in your house? or from rounding of measures, e.g. how long is your pencil
to the nearest centimetre? The most common graphs for displaying category data are pictographs,
bar, strip and pie graphs. Whole number data can be displayed using dot plots or stem and leaf
graphs. Students should communicate their result through reference to their data displays with an
emphasis on similarity and difference, e.g. boys like outdoor games more than girls..
Click to download a PDF of second-tier material relating to Level 2 Statistical Investigations (584KB)
Statistical literacy
AO1: Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others. This means students will critically consider comments made by others, usually their classmates, by referring to the features of displays on which the person is making claims. These displays will be showing either category data (pictographs, bar, strip, and pie graphs) or whole number data (dot plots or stem and leaf graphs). Students should also consider whether the chosen display/s best shows patterns in the data, e.g. strip and pie graphs show proportions well, pictographs and bar graphs show differences well.
Probability
AO1: Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty. This means students will recognise that probability is about the chance of outcomes occurring. Through activities that involve them personally, students at Level Two are expected to consider the possible outcomes of events in predicting what might occur. Through carrying out experiments, e.g. playing a game of chance, and making simple models of all the outcomes, e.g. lists or tables, students should recognise when outcomes appear to be equally likely, e.g. getting an even number when tossing a dice. Students should also recognise that where an event has more than one possible outcome they cannot predict the outcome with certainty, e.g. "it probably won’t be a six but it might be" when rolling a dice. Students should relate probability to events in their daily life, e.g. "it is very likely to rain today".
Click to download a PDF of second-tier material relating to Level 2 Probability (74KB)
