Dimension

level

Progression Point

Number

1.0 Standard

… They use materials to model addition and subtraction of subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects. They add and subtract by counting forward and backward using the numbers from 0 to 20.

1.25

·     counting forwards and backwards by 1 from starting points between 1 and 100

·     calculation of the next number when asked to add 1 or 2 to any natural number from 0 to 10

·     drawing of diagrams to show subtraction activities

1.5

·     addition and subtraction of two-digit multiples of ten by counting on and counting back

·     counting on from the larger of two collections to find their total

·     use of the number properties (commutative and associative) of addition in mental computation, and recognition of complements to ten; for example, 3 + 4 + 7 + 6 = 3 + 7 + 4 + 6 = 10 + 10 = 20

2.0 Standard

… They add and subtract one- and two-digit numbers by counting on and counting back. They mentally compute simple addition and subtraction calculations involving one- or two-digit natural numbers, using number facts such as complement to 10, doubles and near doubles. They use commutative and associative properties of addition and multiplication in mental computation (for example, 3 + 4 = 4 + 3 and 3 + 4 + 5 can be done as 7 + 5 or 3 + 9).

2.5

·     addition and subtraction of amounts of money including calculation of change from $10

·     use of strategies such as ‘near doubles’, ‘adding 9’ and ‘build to next 10’ to solve addition and subtraction problems

·     use of written methods for whole number problems of addition and subtraction involving numbers up to 99

3.0 Standard

… They estimate the results of computations and recognise whether these are likely to be over-estimates or under-estimates. They compute with numbers up to 30 using all four operations. They devise and use written methods for:

·     whole number problems of addition and subtraction involving numbers up to 999

They devise and use algorithms for the addition and subtraction of numbers to two decimal places, including situations involving money. They add and subtract simple common fractions with the assistance of physical models.

4.0 Standard

Students explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

Dimension

level

Progression Point

Number

1.5

·     ordering of money amounts in cents

·     counting by 2s, 5s and 10s from 0 to a given target, and recognition of the associated number patterns; for example,
7, 9, 11 …

1.75

·     counting by 1s, 10s and 100s from 0 to 1000

·     grouping of coins of the same denomination in sets of $1

2.0 Standard

Students model the place value of the natural numbers from 0 to 1000. They order numbers and count to 1000 by 1s, 10s and 100s. Students skip count by 2s, 4s and 5s from 0 to 100 starting from any natural number. They order money amounts in dollars and cents and carry out simple money calculations.

They add and subtract one- and two-digit numbers by counting on and counting back.

2.25

·     use of place value (as the idea that ‘ten of these is one of those’) to determine the size and order of whole numbers to hundreds

·     use of money as a model for grouping and unpacking lots of 10s

·     rounding of amounts of money up and down to the nearest dollar

2.5

·     addition and subtraction of amounts of money including calculation of change from $10

3.0 Standard

They devise and use algorithms for the addition and subtraction of numbers to two decimal places, including situations involving money.

4.0 Standard

They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money.

Dimension

level

Progression Point

Measurement

0.5

·     use of descriptive terms such as longer, taller and heavier to compare length and mass of pairs of familiar objects

1.0 Standard

At Level 1, students compare length, area, capacity and mass of familiar objects using descriptive terms such as longer, taller, larger, holds more and heavier. They make measurements using informal units such as paces for length, handprints for area, glasses for capacity, and bricks for weight.

1.25

·     informal measurement of length by making, describing and comparing personal units

1.5

·     use of uniform units for length; for example, cm as a unit for measuring length

·     informal measurement of area and mass by making, describing and comparing personal units  

1.75

·     informal measurement of capacity by making, describing and comparing personal units

2.0 Standard

At Level 2, students make, describe and compare measurements of length, area, volume, mass and time using informal units. They recognise the differences between non-uniform measures, such as hand-spans, to measure length, and uniform measures, such as icy-pole sticks. They judge relative capacity of familiar objects and containers by eye and make informal comparisons of weight by hefting. They describe temperature using qualitative terms (for example, cold, warm, hot). Students use formal units such as hour and minute for time, litre for capacity and the standard units of metres, kilograms and seconds.

2.25

·     use of formal units of measurement; for example, metres to measure length, and hour, minute and second for time

·     application of estimations using personal units, such as pace length and arm span, and comparison with measures using formal units, such as metres and centimetres

·     use of ruler and tape measure (linear scale) and trundle wheel (circular scale) to validate estimates of length

2.5

·     estimation and measurement of mass, volume and capacity of common objects; for example, kilogram of flour, litre of soft drink

2.75

·     calculation of area through multiplication of the length of a rectangle by its width

·     understanding of the distinction between discrete and continuous scales

3.0 Standard

At Level 3, students estimate and measure length, area, volume, capacity, mass and time using appropriate instruments. They recognise and use different units of measurement including informal (for example, paces), formal (for example, centimetres) and standard metric measures (for example, metre) in appropriate contexts. They read linear scales (for example, tape measures) and circular scales (for example, bathroom scales) in measurement contexts.

3.25

·     estimation and measurement of perimeter of polygons

·     conversion between metric measurements for length; for example, 0.27m = 27cm

·     estimation and measurement of angles in degrees to the nearest 10°

3.5

·     estimation and measurement of surface area; for example, use of square metres, and area of land; for example, use of hectares

·     awareness of the accuracy of measurement required and the appropriate tools and units

3.75

·     conversion between metric units; for example, L to mL, and understanding of the significance of thousands and thousandths in the metric system

4.0 Standard

At Level 4, students use metric units to estimate and measure length, perimeter, area, surface area, mass, volume, capacity time and temperature. They measure angles in degrees. They measure as accurately as needed for the purpose of the activity. They convert between metric units of length, capacity and time (for example, L–mL, sec–min).

Dimension

Level

Progression Point

Number

1.25

·     Drawing of diagrams to show sharing of up to 20 items

1.5

·     Counting by 2s, 5s and 10s from 0 to a given target …

2.0 Standard

... Students skip count by 2s, 4s and 5s from 0 to 100 starting from any natural number.

Students describe and calculate simple multiplication as repeated addition, such as 3 × 5 = 5 + 5 + 5; and division as sharing, such as 8 shared between 4.

They use commutative and associative properties of addition and multiplication in mental computation (for example, 3 + 4 = 4 + 3 and 3 + 4 + 5 can be done as 7 + 5 or 3 + 9).

2.25

·     Use of money as a model for grouping and unpacking lots of 10s

·     Use of written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition) and ‘how many?’ (quotition) processes

2.5

·     Automatic recall of number facts from 2, 5 and 10 multiplication tables

2.75

·     Representation of multiplication as a rectangular array and as the area of a rectangle

·     Use of fact families to solve division problems, for example 5 × 7 = 35, 35 ÷ 7 = 5

3.0 Standard

... Students compute with numbers up to 30 using all four operations.

They provide automatic recall of multiplication facts up to 10 × 10.

They devise and use written methods for: whole number problems of addition and subtraction involving numbers up to 999; multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70 ); division by a single-digit divisor (based on inverse relations in multiplication tables).

3.25

·     Appropriate selection and use of mental and written algorithms to add, subtract, multiply and divide (by single digits) natural numbers

·     Multiplication of fractions by fractions through use of the rectangle area model (grid)

3.75

·     Multiplication by increasing and decreasing by a factor of two; for example, 24 × 16 = 48 × 8 = 96 × 4 = 192 × 2 = 384 × 1 = 384

·     Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

·     Use of inverse relationship between multiplication and division to validate calculations

4.0 Standard

... Students explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

They add, subtract and multiply fractions and decimals (to two decimal places) …

4.25

·     Use of index notation to represent repeated multiplication

·     Division of fractions using multiplication by the inverse

4.75

·     Addition, multiplication and division of integers

5.75

·     Division and multiplication of numbers in index form, including application to scientific notation

Dimension

Level

Progression Point

Number

1.0 Standard

... Students form collections of sets of equal size.

1.25

·     Drawing of diagrams to show sharing of up to 20 items

1.5

·     Use of half and quarter as a descriptor; for example a quarter of a cake

1.75

·     Identification of half of a set of objects, including recognition of the need for ½ when sharing an odd numbers of objects

2.0 Standard

... Students describe simple fractions such as one half, one third and one quarter in terms of equal sized parts of a whole object, such as a quarter of a pizza, and subsets such as half of a set of 20 coloured pencils.

2.25

·     Use of fractions with numerators other than one; for example ¾ of a block of chocolate

2.5

·     Development and use of fraction notation and recognition of equivalent fractions such as
¹ / ₂ = ⁴ / ₈ , including the ordering of fractions using physical models

3.0 Standard

... Students develop fraction notation and compare simple common fractions such as³/₄ > ²/₃ using physical models.

They add and subtract simple common fractions with the assistance of physical models.

3.25

·     Multiplication of fractions by fractions using rectangle area model (grid)

3.5

·     Addition, subtraction and multiplication of fractions and decimals (to one decimal place) using approximations such as whole number estimates and technology to confirm accuracy

·     Representation of simple ratios as percentages, fractions and decimals

·     Ordering of integers (for example, positive and negative temperatures), positive fractions and decimals

3.75

·     Recognition of equivalent rates expressed as percentages, fractions and decimals

·     Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

4.0 Standard

... Students model integers (positive and negative whole numbers and zero), common fractions and decimals.

They place integers, decimals and common fractions on a number line.

They use decimals, ratios and percentages to find equivalent representations of common fractions (for example, ³ / ₄ = ⁹ / ₁₂ = 0.75 = 75% = 3 : 4 = 6 : 8).

They add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money.

4.25

·     Knowledge of decimal and percentage equivalents for ¹ / ₂ , ¹ / ₄ , ³ / ₄ , ¹ / ₃ ,² / ₃

·     Expression of single digit decimals as fractions in simplest form and conversion between ratio, fraction, decimal and percentage forms

·     Division of fractions using multiplication by the inverse

5.0 Standard

... Students write equivalent fractions for a fraction given in simplest form (for example, ² / ₃ = ⁴ / ₆ = ⁶ / ₉ = … ).

They know the decimal equivalents for the unit fractions ¹/₂ , ¹/₃ , ¹/₄ , ¹/₅ , ¹/₈ , ¹/₉and find equivalent representations of fractions as decimals, ratios and percentages (for example, a subset: set ratio of 4:9 can be expressed equivalently as ⁴/₉ = 0. 4 ≈ 44.44%).

They write the reciprocal of any fraction and calculate the decimal equivalent to a given degree of accuracy.