Mathematics Developmental Continuum P-10

Number

To view all information on the current Victorian Curriculum go to the VCAA site (http://victoriancurriculum.vcaa.vic.edu.au)

This version of the Mathematics Developmental Continuum is being updated. Currently the organization of the Indicators of Progress is aligned to the outdated VELS curriculum.

VELS levels correspond to school year levels as follows:

  • VELS Level 1 - Foundation
  • VELS Level 2 - Years 1 and 2
  • VELS Level 3 - Years 3 and 4
  • VELS Level 4 - Years 5 and 6
  • VELS Level 5 - Years 7 and 8
  • VELS Level 6 - Years 9 and 10
Mathematics Standards and Progression Points Indicator of Progress

 

At Level 1, students form small sets of objects from simple descriptions and make simple correspondences between those sets. They count the size of small sets using the numbers 0 to 20. They use one-to-one correspondence to identify when two sets are equal in size and when one set is larger than another. They form collections of sets of equal size. They use ordinal numbers to describe the position of elements in a set from first to tenth. 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.

 

 

 

At Level 2, 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 form patterns and sets of numbers based on simple criteria such as odd and even numbers. They order money amounts in dollars and cents and carry out simple money calculations. They 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. 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 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).

 

 

 

At Level 3, students use place value (as the idea that ‘ten of these is one of those’) to determine the size and order of whole numbers to tens of thousands, and decimals to hundredths. They round numbers up and down to the nearest unit, ten, hundred, or thousand. They develop fraction notation and compare simple common fractions such as 3 /4 > 2 / 3 using physical models. They skip count forwards and backwards, from various starting points using multiples of 2, 3, 4, 5, 10 and 100.

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 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).

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.

 

 

 

 

At Level 4, students comprehend the size and order of small numbers (to thousandths) and large numbers (to millions). They 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 create sets of number multiples to find the lowest common multiple of the numbers. They interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4).

Students identify square, prime and composite numbers. They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers. They recognise and calculate simple powers of whole numbers (for example, 24 = 16).

Students 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 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) and apply these operations in practical contexts, including the use of money. They use estimates for computations and apply criteria to determine if estimates are reasonable or not.

 

At Level 5, students identify complete factor sets for natural numbers and express these natural numbers as products of powers of primes (for example,
36 000 = 25 × 32 × 53).

They 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, 1/9 and 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.

Students use knowledge of perfect squares when calculating and estimating squares and square roots of numbers
(for example, 202 = 400 and 302 = 900 so √700 is between 20 and 30). They evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9). They know simple powers of 2, 3, and 5 (for example, 26 = 64, 34 = 81, 53 = 125). They calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √(9/16) = 3/4). They calculate cubes and cube roots of perfect cubes (for example, 3√64 = 4). Using technology they find square and cube roots of rational numbers to a specified degree of accuracy (for example, 3√200 = 5.848 to three decimal places).

Students express natural numbers base 10 in binary form, (for example, 4210 = 1010102), and add and multiply natural numbers in binary form (for example, 1012 + 112 = 10002 and 101 2 × 112 = 11112).

Students understand ratio as both set: set comparison (for example, number of boys : number of girls) and subset: set comparison (for example, number of girls : number of students), and find integer proportions of these, including percentages (for example, the ratio number of girls: the number of boys is 2 : 3 = 4 : 6 = 40% : 60%).

Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding
(for example, 925 ÷ 34 ˜ 900 ÷ 30 = 30).

Students use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors. They use approximations to π in related measurement calculations
(for example, π × 52 = 25π = 78.54 correct to two decimal places).

They use technology for arithmetic computations involving several operations on rational numbers of any size.

 

At Level 6, students comprehend the set of real numbers containing natural, integer, rational and irrational numbers. They represent rational numbers in both fractional and decimal (terminating and infinite recurring) forms (for example, 14/ 25 = 1.16, = 47/99 ). They comprehend that irrational numbers have an infinite non-terminating decimal form. They specify decimal rational approximations for square roots of primes, rational numbers that are not perfect squares, the golden ratio f , and simple fractions of p correct to a required decimal place accuracy.

Students use the Euclidean division algorithm to find the greatest common divisor (highest common factor) of two natural numbers 9 (for example, the greatest common divisor of 1071 and 1029 is 21 since 1071 = 1029 × 1 + 42, 1029 = 42 × 24 + 21 and 42 = 21 × 2 + 0).

Students carry out arithmetic computations involving natural numbers, integers and finite decimals using mental and/or written algorithms (one- or two-digit divisors in the case of division). They perform computations involving very large or very small numbers in scientific notation (for example, 0.0045 × 0.000028 = 4.5 × 10-3 × 2.8 × 10-5 = 1.26 × 10-7).

They carry out exact arithmetic computations involving fractions and irrational numbers such as square roots
(for example, √18 = 3√2, √( 3/2 ) = (√6)/2) and multiples and fractions of p (for example p + p/4 = 5/4). They use appropriate estimates to evaluate the reasonableness of the results of calculations involving rational and irrational numbers, and the decimal approximations for them. They carry out computations to a required accuracy in terms of decimal places and/or significant figures.
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