Achievement Objectives |
Learning Outcomes |
Unit title |
GM5-9 |
- 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 |
GM5-9
GM5-4
NA5-4 |
- 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 |
GM5-10
NA5-4 |
- 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 |
GM5-10 |
- 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 |
GM5-10 |
- state and explain Pythagoras' theorem
- use Pythagoras' theorem to find the unknown sides of right angled triangles
|
Pythagoras' Theorem |
GM5-10 |
- 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 |
GM5-10 |
- 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 |
GM5-10 |
- measure lengths and angles accurately
- find the height of objects using trigonometry
|
Dizzy Heights |
GM5-10 |
- use cos to solve problems involving right-angled 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 |
GM5-10 |
- use sin to solve problems involving right-angled 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 |
GM5-10 |
- use tan to solve problems involving right-angled 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 |