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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
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Cosine Rule

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
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Difference magic squares

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).
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Diophantus I

Level Six
Number and Algebra
Problem solving activities

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

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Diophantus II

Level Six
Number and Algebra
Problem solving activities

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

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I'm So Sorry I Ate Chocolate

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
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Karen's second tiles

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
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Peter's third string

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
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Pigs, goats and sheep

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).
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Pizza toppings 2

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
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Polygonal strings

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
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Rectangular milk crate

Level Six
Number and Algebra
Problem solving activities

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

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Square milk crates

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).
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The lady's age

Level Six
Number and Algebra
Problem solving activities

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

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The old chicken run problem

Level Six
Number and Algebra
Problem solving activities

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

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Triangular number links

Level Six
Number and Algebra
Problem solving activities
Use algebra to simplify expressions
Use geometry to assist their algebra.
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Weighing time

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).
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What is s?

Level Six
Number and Algebra
Problem solving activities
Use guessing to make conjectures
Solve a problem using algebraic expressions
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What is s and t?

Level Six
Number and Algebra
Problem solving activities
Use guessing to make conjectures
Solve a problem using algebraic expressions
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What is t?

Level Six
Number and Algebra
Problem solving activities
Use guessing to make conjectures
Solve a problem using algebraic expressions