Topic 11 Year 9 Mathematics
|No of lessons||8|
|When is it happening||Term 2|
|What will students learn||
Understand that every right-angled triangle is similar to a right-angled triangle drawn within a unit circle.
Be able to find the length of catheti in right-angled triangles from a given angle and the length of the hypotenuse, including through using sine and cosine functions. Understand that the relationship between the opposite and adjacent is held constant by a set angle
Be able to directly find the length of the opposite from the adjacent and given angle (and vice versa).
Be able to find any angle in a right-angled triangle from two known sidelengths.
|Key Knowledge that students should know at the end of 'Topic'||This is the knowledge that students will meet for the first time in this topic||Students consider a right-angle triangle drawn within a unit circle, and whether every right-angled triangle is similar to one drawn like this. Students revisit similar shapes to find missing side lengths. Common side lengths of right-angled triangles with a unit hypotenuse are given. Students use ratio tables to find side lengths with different hypotenuses. Students graph the lengths of the opposite and adjacent to uncover trig graphs. Calculator trig functions are introduced. Students generalise the relationship between the hypotenuse and other side lengths. The relationship between the opposite and adjacent is left untouched so far, and is looked at the following week. The relationship between the opposite and adjacent is explored. Multiple representations are looked at, such as gradient and graphical representations. Another lesson is spent on looking at generalising the relationship between all three sides of a right-angled triangle. The final piece of the right-angled trig puzzle is placed as students look at working out angles from given side lengths. Inverse trig functions are introduced. Generalisation is looked at a third and final time. Students see different arrangements of key trig formulae and look at ways of deciding which formula to use.|
|This is knowledge that students may have met before but will need to deepen their understanding||Students consider a right-angle triangle drawn within a unit circle, and whether every right-angled triangle is similar to one drawn like this. Students revisit similar shapes to find missing side lengths.|
|Key Skills that students should be able to demonstrate at the end of 'Topic'||This is the skills that students will meet for the first time in this topic||Using a calculator, manipulate algebra expressions|
|This is skills that students may have met before but will need to develop||Using Sin, cos and tan|
|Key vocabulary that students should know and understand|
|The Big Question||Can you find missing lengths and angles of a right angled triangle using Trigonometry?|
Key questions that students should be able to answer at the end of the 'Topic'
|Can you find missing side lengths of similar shapes?|
|Can you identify the opposite and adjacent of a right-angled triangle in relation to another given angle?|
|Can you estimate sine and cosine values?|
|Can you find lengths of opposites and adjacent from a hypotenuse and a given angle in a right-angled triangle?|
|Can you calculate the length of an opposite from and adjacent and given angle (or vice versa)?|
|Can you rearrange formulae?|
|Can you find the angles in right-angled triangles from two side lengths, using inverse trig functions?|
|Can you find all the sides lengths and angle sizes of a right-angled triangle from a given side length and any other piece of information?|