Middle School Mathematics Year 7 to 10

Middle School Mathematics Year 7-10

Year 7 Mathematics

Number and Algebra

Number and place value

  1. Investigate index notation and represent whole numbers as products of powers of prime numbers (VCMNA238)
  2. Investigate and use square roots of perfect square numbers (VCMNA239)
  3. Apply the associative, commutative and distributive laws to aid mental and written computation and make estimates for these computations (VCMNA240)
  4. Compare, order, add and subtract integers (VCMNA241)

Real numbers

  1. Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (VCMNA242)
  2. Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (VCMNA243)
  3. Multiply and divide fractions and decimals using efficient written strategies and digital technologies (VCMNA244)
  4. Express one quantity as a fraction of another, with and without the use of digital technologies (VCMNA245)
  5. Round decimals to a specified number of decimal places (VCMNA246)
  6. Connect fractions, decimals and percentages and carry out simple conversions (VCMNA247)
  7. Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (VCMNA248)
  8. Recognise and solve problems involving simple ratios (VCMNA249)

Money and financial mathematics

  1. Investigate and calculate ‘best buys’, with and without digital technologies (VCMNA250)

Patterns and algebra

  1. Introduce the concept of variables as a way of representing numbers using letters (VCMNA251)
  2. Create algebraic expressions and evaluate them by substituting a given value for each variable (VCMNA252)
  3. Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (VCMNA253)
  4. Design and implement mathematical algorithms using a simple general purpose programming language (VCMNA254)

Linear and non-linear relationships

  1. Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (VCMNA255)
  2. Solve simple linear equations (VCMNA256)
  3. Investigate, interpret and analyse graphs from real life data, including consideration of domain and range (VCMNA257)

Measurement and Geometry

Using units of measurement

  1. Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258)
  2. Calculate volumes of rectangular prisms (VCMMG259)

Shape

  1. Draw different views of prisms and solids formed from combinations of prisms (VCMMG260)

Location and transformation

  1. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (VCMMG261)

Geometric reasoning

  1. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (VCMMG264)
  2. Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (VCMMG265)
  3. Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (VCMMG263)
  4. Classify triangles according to their side and angle properties and describe quadrilaterals (VCMMG262)

Statistics and Probability

Chance

  1. Construct sample spaces for single-step experiments with equally likely outcomes (VCMSP266)
  2. Assign probabilities to the outcomes of events and determine probabilities for events (VCMSP267)

Data representation and interpretation

  1. Identify and investigate issues involving numerical data collected from primary and secondary sources (VCMSP268)
  2. Construct and compare a range of data displays including stem-and-leaf plots and dot plots (VCMSP269)
  3. Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (VCMSP270)
  4. Describe and interpret data displays using median, mean and range (VCMSP271)

 

Year 8 Mathematics

Number and Algebra

Number and place value

  1. Use index notation with numbers to establish the index laws with positive integral indices and the zero index (VCMNA272)
  2. 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 (VCMNA273)

Real numbers

  1. Investigate terminating and recurring decimals (VCMNA274)
  2. Investigate the concept of irrational numbers, including π (VCMNA275)
  3. Solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital technologies (VCMNA276)
  4. Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies (VCMNA277)

Money and financial mathematics

  1. Solve problems involving profit and loss, with and without digital technologies (VCMNA278)

Patterns and algebra

  1. Extend and apply the distributive law to the expansion of algebraic expressions (VCMNA279)
  2. Factorise algebraic expressions by identifying numerical factors (VCMNA280)
  3. Simplify algebraic expressions involving the four operations (VCMNA281)
  4. Use algorithms and related testing procedures to identify and correct errors (VCMNA282)

Linear and non-linear relationships

  1. Plot linear relationships on the Cartesian plane with and without the use of digital technologies (VCMNA283)
  2. Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (VCMNA284)
  3. Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs (VCMNA285)

Measurement and Geometry

Using units of measurement

  1. Choose appropriate units of measurement for area and volume and convert from one unit to another (VCMMG286)
  2. Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (VCMMG287)
  3. 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 (VCMMG288)
  4. Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (VCMMG289)
  5. Solve problems involving duration, including using 12- and 24-hour time within a single time zone (VCMMG290)

Geometric reasoning

  1. 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 (VCMMG291)
  2. Develop the conditions for congruence of triangles (VCMMG292)
  3. Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (VCMMG293)

Statistics and Probability

Chance

  1. Identify complementary events and use the sum of probabilities to solve problems (VCMSP294)
  2. Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’ (VCMSP295)
  3. Represent events in two-way tables and Venn diagrams and solve related problems (VCMSP296)

Data representation and interpretation

  1. Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation (VCMSP297)
  2. Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (VCMSP298)
  3. Explore the variation of means and proportions of random samples drawn from the same population (VCMSP299)
  4. Investigate the effect of individual data values including outliers, on the range, mean and median (VCMSP300)

 

Year 9 Mathematics

Number and Algebra

Real numbers

  1. Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (VCMNA301)
  2. Apply index laws to numerical expressions with integer indices (VCMNA302)
  3. Express numbers in scientific notation (VCMNA303)

Money and financial mathematics

  1. Solve problems involving simple interest (VCMNA304)

Patterns and algebra

  1. Extend and apply the index laws to variables, using positive integer indices and the zero index (VCMNA305)
  2. Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (VCMNA306)
  3. Apply set structures to solve real-world problems (VCMNA307)

Linear and non-linear relationships

  1. Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (VCMNA308)
  2. Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (VCMNA309)
  3. Sketch linear graphs using the coordinates of two points and solve linear equations (VCMNA310)
  4. Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (VCMNA311)

Measurement and Geometry

Using units of measurement

  1. Calculate the areas of composite shapes (VCMMG312)
  2. Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)
  3. Solve problems involving the surface area and volume of right prisms (VCMMG314)
  4. Investigate very small and very large time scales and intervals (VCMMG315)

Geometric reasoning

  1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (VCMMG316)
  2. Solve problems using ratio and scale factors in similar figures (VCMMG317)

Pythagoras and trigonometry

  1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (VCMMG318)
  2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (VCMMG319)
  3. Apply trigonometry to solve right-angled triangle problems (VCMMG320)

Statistics and Probability

Chance

  1. List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (VCMSP321)
  2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’ (VCMSP322)
  3. Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (VCMSP323)

Data representation and interpretation

  1. Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (VCMSP324)
  2. Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (VCMSP325)
  3. Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (VCMSP326)

 

Year 10 Mathematics

Number and Algebra

Real numbers

  1. Solve simple problems involving inverse proportion (VCMNA327)

Money and financial mathematics

  1. Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (VCMNA328)

Patterns and algebra

  1. Factorise algebraic expressions by taking out a common algebraic factor (VCMNA329)
  2. Simplify algebraic products and quotients using index laws (VCMNA330)
  3. Apply the four operations to simple algebraic fractions with numerical denominators (VCMNA331)
  4. Expand binomial products and factorise monic quadratic expressions using a variety of strategies (VCMNA332)
  5. Substitute values into formulas to determine an unknown and re-arrange formulas to solve for a particular term (VCMNA333)
  6. Implement algorithms using data structures in a general-purpose programming language (VCMNA334)

Linear and non-linear relationships

  1. Solve problems involving linear equations, including those derived from formulas (VCMNA335)
  2. Solve linear inequalities and graph their solutions on a number line (VCMNA336)
  3. Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology (VCMNA337)
  4. Solve problems involving gradients of parallel and perpendicular lines (VCMNA338)
  5. Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate (VCMNA339)
  6. Solve linear equations involving simple algebraic fractions (VCMNA340)
  7. Solve simple quadratic equations using a range of strategies (VCMNA341)
  8. Solve equations using systematic guess-check-and-refine with digital technology (VCMNA342)

Measurement and Geometry

Using units of measurement

  1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (VCMMG343)

Geometric reasoning

  1. Formulate proofs involving congruent triangles and angle properties (VCMMG344)
  2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (VCMMG345)

Pythagoras and trigonometry

  1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (VCMMG346)

Statistics and Probability

Chance

  1. Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (VCMSP347)
  2. Use the language of ‘if ….then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (VCMSP348)

Data representation and interpretation

  1. Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range (VCMSP349)
  2. Construct and interpret box plots and use them to compare data sets (VCMSP350)
  3. Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data (VCMSP351)
  4. Use scatter plots to investigate and comment on relationships between two numerical variables (VCMSP352)
  5. Investigate and describe bivariate numerical data, including where the independent variable is time (VCMSP353)
  6. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (VCMSP354)

 

(Source: VCAA)

Acceler8 VCE Maths Tutoring
The Mathematics Tutoring Specialist
Melbourne, Victoria, Australia.