# NA6-5: Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

Teaching resources for this Achievement Objective

This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Cosine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. We note that the Cosine Rule is a generalisation of Pythagoras’ Theorem. Note that this...

solve triangles using the Cosine Rule plan a practical exercise involving measurement understand what a generalisation is

Units of Work

Geometry and Measurement

Level Six

This is a problem from the number and algebra strand.

Use algebra when necessary Construct, 3 by 3 arrays of numbers according to a given rule Devise and use problem solving strategies to explore situations mathematically (be systematic).

Problem solving activities

Number and Algebra

Level Six

Solve a problem in a number of ways, including using algebraic expressions

Problem solving activities

Number and Algebra

Level Six

solve a problem in a number of ways, including using algebraic expressions

Problem solving activities

Number and Algebra

Level Six

This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Sine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. Finally we compare the use of the Sine Rule and the Cosine Rule. Note that this unit may...

solve triangles using the Sine Rule understand what a conjecture is solve triangles using the Cosine Rule know when it is appropriate to use the Sine Rule and when to use the Cosine Rule

Units of Work

Number and Algebra

Level Six

Determine the maximum area of a regular polygon with a given perimeter Appreciate the concept of limit as it applies to the area of regular n-gons and circle that both have the same perimeter

Problem solving activities

Number and Algebra

Level Six

Determine the maximum area of a rectangle with a given perimeter Consider how the area of a quadrilateral changes as its shape changes Interpret a relationship from a graph

Problem solving activities

Number and Algebra

Level Six

Use algebraic skills to solve a problem involving three variables. Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).

Problem solving activities

Number and Algebra

Level Six

Generate linear and quadratic patterns Make predictions using a rule Use a systematic method to solve a problem

Problem solving activities

Number and Algebra

Level Six

This is a problem from the number and algebra strand.

Determine the maximum area of a regular polygon with a given perimeter Appreciate the concept of limit as it applies to the area of regular n-gons and circle that both have the same perimeter

Problem solving activities

Number and Algebra

Level Six

Find and use patterns to solve a problem (algebraically or by using a table)

Problem solving activities

Number and Algebra

Level Six

Find a rule for a quadratic pattern Justify or explain the rule for a quadratic pattern Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a table, use algebra).

Problem solving activities

Number and Algebra

Level Six

Solve a problem in a number of ways, including using algebraic expressions.

Problem solving activities

Number and Algebra

Level Six

use algebraic equations to determine the maximum area of a rectangle with a given partial perimeter.

Problem solving activities

Number and Algebra

Level Six

Here we look for patterns in number problems and use algebra as an efficient means of solving general problems.

show that they can understand a complicated problem investigate special cases of a problem make conjectures use special cases as a framework for a general proof produce proofs that require algebra

Units of Work

Number and Algebra

Level Six

Use algebra to simplify expressions Use geometry to assist their algebra.

Problem solving activities

Number and Algebra

Level Six

Solve simultaneous equations Devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment, draw a diagram, use smaller cases, use algebra).

Problem solving activities

Number and Algebra

Level Six

Use guessing to make conjectures Solve a problem using algebraic expressions

Problem solving activities

Number and Algebra

Level Six

Use guessing to make conjectures Solve a problem using algebraic expressions

Problem solving activities

Number and Algebra

Level Six

Use guessing to make conjectures Solve a problem using algebraic expressions

Problem solving activities

Number and Algebra

Level Six