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• 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

• 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

• 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

• VCMMG287

  Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites

  Elaborations

  • establishing and using formulas for areas such as trapeziums, rhombuses and kites

  VCMMG287 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG293

  Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning

  Elaborations

  • establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites
  • identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry

  VCMMG293 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• 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

• VCMMG289

  Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume

  Elaborations

  • investigating the relationship between volumes of rectangular and triangular prisms

  VCMMG289 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG292

  Develop the conditions for congruence of triangles

  Elaborations

  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence

  VCMMG292 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMNA272

  Use index notation with numbers to establish the index laws with positive integral indices and the zero index

  Elaborations

  • evaluating numbers expressed as powers of positive integers

  VCMNA272 | Mathematics | Level 8 | Number and Algebra | Number and place value

• VCMNA273

  Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies and make estimates for these computations

  Elaborations

  • using patterns to assist in finding rules for the multiplication and division of integers
  • using the number line to develop strategies for adding and subtracting rational numbers
  • making an estimate for the total of a family weekly grocery bill with consideration of accuracy of the estimate, or for problems involving the circumference and area of a circle

  VCMNA273 | Mathematics | Level 8 | Number and Algebra | Number and place value

• VCMNA284

  Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution

  Elaborations

  • solving real life problems by using variables to represent unknowns

  VCMNA284 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VCMNA283

  Plot linear relationships on the Cartesian plane with and without the use of digital technologies

  Elaborations

  • completing a table of values, plotting the resulting points and determining whether the relationship is linear
  • finding the rule for a linear relationship

  VCMNA283 | 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

• 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

• 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

• VCMNA280

  Factorise algebraic expressions by identifying numerical factors

  Elaborations

  • recognising the relationship between factorising and expanding
  • identifying the greatest common divisor (highest common factor) of numeric and algebraic expressions and using a range of strategies to factorise algebraic expressions

  VCMNA280 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VCMNA278

  Solve problems involving profit and loss, with and without digital technologies

  Elaborations

  • expressing profit and loss as a percentage of cost or selling price, comparing the difference
  • investigating the methods used in retail stores to express discounts

  VCMNA278 | Mathematics | Level 8 | Number and Algebra | Money and financial mathematics

• VCMNA274

  Investigate terminating and recurring decimals

  Elaborations

  • recognising terminating, recurring and non-terminating decimals and choosing their appropriate representations

  VCMNA274 | Mathematics | Level 8 | Number and Algebra | Real numbers

• 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

• 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