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• VCMMG031

  Respond to a simple statement about location or direction

  Elaborations

  • following directional communication used in daily routine, for example, ‘put in’ to finish an activity, ‘sit down’, ‘stand up’ during an activity or program
  • following everyday language of location and direction through modelled daily routines, for example: looking upwards for ‘up’; using rhymes and chants that relate to movement; following a warm-up sequence for work or sport; unpacking their bag; washing their hands and setting up for lunch
  • exploring the concept of ‘inside’ and ‘outside’ during activities by putting objects ‘in’ and ‘out’ of a container and following routines and instructions that involve moving inside and outside locations

  VCMMG031 | Mathematics | Level B | Measurement and Geometry | Location and transformation

• VC2M4N05

  solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

  Elaborations

  • using physical or virtual materials to demonstrate the multiplicative relationship between the places
  • using materials such as place value charts, numeral expanders or sliders to recognise and explain why multiplying by 10 moves the digits one place to the left and dividing by 10 moves digits one place to the right
  • using a calculator or other digital tools to recognise and develop an understanding of the effect of multiplying or dividing numbers by tens, hundreds and thousands, recording sequences in a place value chart, in a table or spreadsheet, generalising the patterns noticed and applying them to solve multiplicative problems without a calculator

  VC2M4N05 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VCMNA001

  Respond to objects being counted and distributed

  Elaborations

  • experiencing number names and number sequence in everyday experiences, for example birthdays, distributing equipment, collecting materials
  • experiencing number and its use in stories, songs and rhythm, chosen for their interest and relevance to the student’s age
  • attending to number and counting in daily routines, for example cups of flour in the bowl, number of times an action or event is repeated or experienced
  • reacting to everyday situations where objects are counted, for example number of items on a plate or tray, steps to the door, eggs in the carton, bounces of a ball
  • being supported as they touch, feel or move over objects as they are being counted

  VCMNA001 | Mathematics | Level A | Number and Algebra | Number and place value

• VC2M3A03

  recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts

  Elaborations

  • using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts
  • recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives
  • practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts
  • systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns

  VC2M3A03 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M3M03

  recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events

  Elaborations

  • estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
  • planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
  • reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock
  • using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
  • exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars

  VC2M3M03 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M7N02

  represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

  Elaborations

  • relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
  • applying and explaining the connections between place value and expanded notations, for example, $7000=7\times {10}^3$ and $3750=3\times {10}^3+7\times {10}^2+5\times {10}^1$
  • applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, $48=6\times 8=2\times 3\times 2\times 2\times 2=3^1\times 2^4=3\times 2^4$
  • developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation

  VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M4N04

  count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines

  Elaborations

  • cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence ‘one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters … eight-quarters or two-wholes ...’
  • subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines
  • converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line
  • using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one

  VC2M4N04 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M10SP01

  apply deductive reasoning to formulate proofs involving shapes in the plane and use theorems to solve spatial problems

  Elaborations

  • distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
  • developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
  • applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
  • investigating proofs of geometric theorems and using them to solve spatial problems, for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes, and using visual proofs to justify solutions
  • using dynamic geometry software to find the quadrilateral that has a vertex on each side of a rectangle and has the shortest possible path, and proving that the path forms a parallelogram

  VC2M10SP01 | Mathematics | Mathematics Version 2.0 | Level 10 | Space

• VC2MFN03

  quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning

  Elaborations

  • establishing the language and process of counting, and understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are and that the last number counted answers the question of ‘How many?’; for example, saying numbers in sequence while playing and performing actions
  • using counting to compare the size of 2 or more collections of like items to justify which collection contains more or fewer items
  • using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
  • discussing how different cultures may have alternative ways of representing the count; for example, discussing how some people of the Asia region use an abacus or Chinese hand gestures
  • using body-tallying that involves body parts and one-to-one correspondence from counting systems of Aboriginal and/or Torres Strait Islander Peoples to count to 20

  VC2MFN03 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• VC2M9A01

  apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables

  Elaborations

  • representing decimals in exponential form; for example, 0.475 can be represented as $0.475=\frac{4}{10}+\frac{7}{100}+\frac{5}{1000}=4\times {10}^{-1}+7\times {10}^{-2}+5\times {10}^{-3}$ and 0.00023 as 23 × 10^-5
  • simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, $5^{-3}=\frac{1}{5^3}={\left(\frac{1}{5}\right)}^3=\frac{1}{125}$ and connecting terms of the sequence $125, 25, 5, 1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}$… to terms of the sequence $5^3, 5^2,5^1, 5^0, 5^{-1}, 5^{-2}, 5^{-3}$...
  • relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, $2^3÷2^5=2^{-2}=\frac{1}{2^2}=\frac{1}{4}$ and ${(3\times 5)}^2=3^2\times 5^2=9\times 25=225$
  • recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number $a$, $a^0=1$, $x^1=x, {r^2=r\times r, h}^3=h\times h\times h,$$y^4=y\times y\times y\times y$, and$\frac{1}{w}\times \frac{1}{w}=\frac{1}{w^2}=w^{-2}$
  • relating simplification of expressions from first principles and counting to the use of exponent laws; for example,
    ${\left(a^2\right)}^3=\left(a\times a\right)\times \left(a\times a\right)\times \left(a\times a\right)=a\times a\times a\times a\times a\times a=a^6$;
    $b^2\times b^3=\left(b\times b\right)\times \left(b\times b\times b\right)=b\times b\times b\times b\times b=b^5; \frac{y^4}{y^2}=\frac{y\times y\times y\times y}{y\times y}=\frac{y^2}{1}=y^2$and${\left(5a\right)}^2=\left(5\times a\right)\times \left(5\times a\right)=5 \times 5\times a\times a=25\times a^2=25a^2$
  • applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, $\frac{{\left(2xy\right)}^3}{{xy}^4}=\frac{8x^3{y}^3}{x{y}^4}=8x^2{y}^{-1}$
  • relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^-12 grams and one terabyte = 10¹² bytes

  VC2M9A01 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra