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• VCMNA277

  Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies

  Elaborations

  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
  • calculating population growth rates in Australia and Asia and explaining their difference
  • finding one of distance travelled, time taken or average speed given the other two quantities

  VCMNA277 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMMG290

  Solve problems involving duration, including using 12- and 24-hour time within a single time zone

  Elaborations

  • identifying regions in Australia and countries in Asia that are in the same time zone

  VCMMG290 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMNA275

  Investigate the concept of irrational numbers, including π

  Elaborations

  • understanding that the real number system includes irrational numbers

  VCMNA275 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMMG291

  Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology

  Elaborations

  • understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
  • establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
  • exploring tiling patterns in art and design

  VCMMG291 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMSP300

  Investigate the effect of individual data values including outliers, on the range, mean and median

  Elaborations

  • using displays of data to explore and investigate effects
  • exploring the effect of outliers on the range for different sets of data by comparing its value with and without outliers included

  VCMSP300 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMNA276

  Solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital technologies

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts, and GST
  • using percentages to calculate population increases and decreases
  • using percentage error to compare relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VCMNA276 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMSP297

  Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the differences between convenience, judgemental and simple random sampling from a population

  VCMSP297 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMNA279

  Extend and apply the distributive law to the expansion of algebraic expressions

  Elaborations

  • applying the distributive law to the expansion of algebraic expressions using strategies such as the area model

  VCMNA279 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VCMNA285

  Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs

  Elaborations

  • investigating different combinations of length and width of a rectangle for a fixed area, and drawing the corresponding graph
  • using graphs to analysing change in the value of a currency against another currency over a specified period

  VCMNA285 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VCMNA281

  Simplify algebraic expressions involving the four operations

  Elaborations

  • understanding that the laws used with numbers can also be used with algebra

  VCMNA281 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VCMSP294

  Identify complementary events and use the sum of probabilities to solve problems

  Elaborations

  • identifying the complement of familiar events
  • understanding that probabilities range between 0 to 1 and that calculating the probability of an event allows the probability of its complement to be found

  VCMSP294 | Mathematics | Level 8 | Statistics and Probability | Chance

• VCMMG286

  Choose appropriate units of measurement for area and volume and convert from one unit to another

  Elaborations

  • choosing units for area including mm², cm², m², hectares, km², and units for volume including mm³, cm³, m³
  • recognising that the conversion factors for area units are the squares of those for the corresponding linear units
  • recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units

  VCMMG286 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG288

  Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other

  Elaborations

  • investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
  • investigating the area of circles using a square grid or by rearranging a circle divided into sectors
  • solving problems given one of radius, diameter, circumference or area of a circle, then the other quantities are determined from this

  VCMMG288 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMSP296

  Represent events in two-way tables and Venn diagrams and solve related problems

  Elaborations

  • using Venn diagrams and two-way tables to calculate probabilities for events, satisfying 'and', 'or' and 'not' conditions
  • understanding that representing data in Venn diagrams or two-way tables facilitates the calculation of probabilities
  • collecting data to answer the questions using Venn diagrams or two-way tables

  VCMSP296 | Mathematics | Level 8 | Statistics and Probability | Chance