Stage 5.3

Outcomes

Numbers and Algebra
- Ratios and Rates
  - MA5.3-4NA
    Draws, interprets and analyses graphs of physical phenomena
    - Solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
      - Interpret distance/time graphs when the speed is variable
        
        Play Activities 26
        
        Examples
      - Describe qualitatively the rate of change of a graph using terms such as 'increasing at a decreasing rate'
        
        Play Activities 5
        
        Examples
- Linear Relationships
  - MA5.3-8NA
    Uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line
    - Find the midpoint and gradient of a line segment (interval) on the Cartesian plane (ACMNA294)
      - Use the concept of an average to establish the formula for the midpoint, M, of the interval joining two points (x1,y1) and (x2,y2) on the Cartesian plane: M(x,y) = (x1 + x2 / 2, y1 + y2 / 2)
        
        Play Activities 2
        
        Examples
    - Solve problems using various standard forms of the equation of a straight line
      - Find the equation of a line passing through two points
        
        Play Activities 6
        
        Examples
- Non-Linear Relationships
  - MA5.3-9NA
    Sketches and interprets a variety of non-linear relationships
    - Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)
      - Find x- and y-intercepts, where appropriate, for the graph of y = ax squared + bx + c, given a, b and c
        
        Play Activities 4
        
        Examples
      - Determine the equation of the axis of symmetry of a parabola using: CCT the midpoint of the interval joining the points at which the parabola cuts the x-axis the formula x = -b/2a
        
        Play Activities 3
        
        Examples
Measurement and Geometry
- Volume
  - MA5.3-14MG
    Applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids
    - Solve problems involving the volumes of right pyramids, right cones, spheres and related composite solids (ACMMG271)
- Circle Geometry
  - MA5.3-17MG
    Applies deductive reasoning to prove circle theorems and to solve related problems
    - Prove and apply angle and chord properties of circles (ACMMG272)
    - Prove and apply tangent and secant properties of circles
      - Apply tangent and secant properties of circles to find unknown angles and lengths in diagrams
        
        Play Activities 7
        
        Examples
Statistics and Probability
- Single Variable Data Analysis
  - MA5.3-18SP
    Uses standard deviation to analyse data
    - Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)
      - Investigate the meaning and calculation of standard deviation using a small set of data
        
        Play Activities 5
        
        Examples