Achievement Objectives 
Learning Outcomes 
Unit title 
GM59 
 find the scale factors for length, area and volume
 identify the centre point of an enlargement
 place similar objects to show a negative enlargement

Russian Boxes 
GM59 GM54 NA54 
 use scale factors to investigate areas being enlarged
 use scale factors to investigate volumes being enlarged
 solve real life context problems involving scale factors

Scale Factors for Areas and Volumes 
GM510 NA54 
 measure the lengths of the sides of sets of similar right angled triangles and find the ratio of sides
 investigate the relationship between these ratios and the angle size
 use calculators or tables to find the sine, cosine and tangent of angles

Introducing Trigonometry 
GM510 
 label right angle triangles with respect to a given angle.
 use trigonometric ratios to calculate the length of opposite and adjacent sides in right angled triangles
 use trigonometric ratios to calculate the size of angles in right angled triangles

Using Trigonometry 
GM510 
 state and explain Pythagoras' theorem
 use Pythagoras' theorem to find the unknown sides of right angled triangles

Pythagoras' Theorem 
GM510 
 find lengths of objects using Pythagoras' Theorem
 understand how similar triangles can be used to prove Pythagoras' Theorem
 understand that Pythagoras' Theorem can be thought of in terms of areas on the sides of the triangle

Gougu Rule or Pythagoras' Theorem 
GM510 
 describe and demonstrate how trigonometry can be used to find the height of a tall building or tree
 describe and demonstrate how trigonometry can be used to find the height of a high hill, or other high object where one cannot stand directly beneath the highest part
 describe in broad terms how trigonometry might be used to find the distance between the earth and the moon

Trigonometric applications outside the classroom 
GM510 
 measure lengths and angles accurately
 find the height of objects using trigonometry

Dizzy Heights 
GM510 
 use cos to solve problems involving rightangled triangles
 solve equations of the form cos(θ) = a, for a between –180° and 360°
 state the value of cos(θ) in special cases
 graph y = cos(θ)

Investigating the Idea of Cos 
GM510 
 use sin to solve problems involving rightangled triangles
 solve equations of the form sin(θ) = a, for a between –180° and 360°
 state the value of sin(θ) in special cases
 graph y = sin(θ)
 describe some of the ways in which the sine, cosine and tangent functions are related

Investigating the Idea of Sin 
GM510 
 use tan to solve problems involving rightangled triangles
 solve equations of the form tan(θ) = a, for a between –180° and 360°
 state the value of tan(θ) in special cases
 graph y = tan(θ)

Investigating the Idea of Tan 