Education Technology
Students factorise and expand algebraic expressions including monic quadratic expressions; simplify algebraic products and quotients using index laws and apply the four operations to simple algebraic fractions with numerical denominators. They solve linear simultaneous equations, using algebraic and graphical techniques, explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials.
Linear and non-linear relationships

### Standard ACMNA238

Solve problems involving parallel and perpendicular lines

### Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

#### Activity: Amazing Locus

Students are presented with a challenging problem and provided with the tools to help break it down to see the relatively simple, yet amazing, solution. The problem requires students to calculate gradients, gradients of perpendicular lines, the equation of a line given point and gradient and finally solve a set of equations simultaneously.
• ACMNA238
• ACMNA237

### Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

#### Activity: String Graphs Part3

This is part three of a four part series. In this activity students find the points of intersection between consecutive straight lines. (Simultaneous Equations). Students use a range of techniques: by-hand, graphically and using CAS. Students then formulate equations to summaries the consecutive points of intersection.
• ACMNA237

### Standard ACMNA214

Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

### Standard ACMNA238

Solve problems involving parallel and perpendicular lines

### Standard ACMNA296

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

### Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

#### Activity: Circumcentre

Coordinate Geometry - Students calculate gradients, perpendicular gradients, equations to lines (given point and gradient), solve simultaneous equations and calculate the distance between two points, and much more! This activity is part of a series on coordinate geometry and includes companion video tutorials and lots of extension opportunities.

• ACMNA214
• ACMNA238
• ACMNA296
• ACMNA237

### Standard ACMNA234

Substitute values into formulas to determine an unknown

### Standard ACMMG243

Formulate proofs involving congruent triangles and angle properties

### Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

#### Activity: Centroid

This activity is aligned with the Circumcentre and Orthocentre activities forming a natural progression for the Euler line activity. Students calculate gradients, equations to lines, solve equations simultaneously and use the calculator's tools to check their answers.
• ACMNA234
• ACMMG243
• ACMNA237

### Standard ACMNA238

Solve problems involving parallel and perpendicular lines

### Standard ACMNA296

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

### Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

#### Activity: Orthocentre

Coordinate Geometry - Students calculate midpoints, gradients, perpendicular lines and use simultaneous equations to help determine the location of the orthocentre. A really cool property of the orthocentre is revealed in the extension component of the activity.

• ACMNA238
• ACMNA296
• ACMNA237