# 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

Level Six

Integrated

Units of Work

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

Level Six

Number and Algebra

Problem solving activities

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).

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Units of Work

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

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

Use algebraic skills to solve a problem involving three variables.

Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).

Level Six

Number and Algebra

Problem solving activities

Generate linear and quadratic patterns

Make predictions using a rule

Use a systematic method to solve a problem

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

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).

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

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

Level Six

Number and Algebra

Problem solving activities

Use algebra to simplify expressions

Use geometry to assist their algebra.

Level Six

Number and Algebra

Problem solving activities

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).

Level Six

Number and Algebra

Problem solving activities

Use guessing to make conjectures

Solve a problem using algebraic expressions

Level Six

Number and Algebra

Problem solving activities

Use guessing to make conjectures

Solve a problem using algebraic expressions

Level Six

Number and Algebra

Problem solving activities

Use guessing to make conjectures

Solve a problem using algebraic expressions