By the end of this topic you will be able to answer this question and other similar problems.
During the topic you will explore the relationships between the sides of right-angled triangles and use the knowledge gained to solve problems involving the sides and angles of right-angled triangles.
Filed under: 3rd Year | Tagged: National 5, trigonometry |
H tends to infinity 
Monday 31 May, Period 6
Work in groups to compare sides in right-angled triangles. All start with a 30º-60º-90º triangle, any size.
Note and discuss findings.
Problem solving starter leading to properties of triangles.
Some very quick to spot opp 1/2 length of hyp.
Looked at adj/hyp.
Challenge for period to be able to draw a 30º-60º-90º triangle without a protractor – nearly all succeeded.
Tuesday 1 June, period 1
Recap what we discovered yesterday and then look at right triangles with different angles in groups.
Create a table of ratios for angles 5º to 85º from class results. Use the table to calculate lengths and angles.
Table successfully created as a class. Most results fairly accurate.
Table used to estimate angles in various triangles.
Thursday 3 June, period 3
Calculating angles & sides using trig tables.
Use 3 d.p. trig tables and class generated examples on board.
Introduce SOH CAH TOA mnemonic.
Class making excellent progress. Move onto using calculator trig functions next lesson.
Monday 7 June, period 6
Calculating angles using the calculator trig functions.
Start with recap on show-me boards.
Class worked examples using trig tables then move onto calculator.
Stress steps and working out, i.e.
• select ratio
• substitute values
• solve for angle
Use exercise on p200 of Central Maths as practice questions.
Tuesday 8 June, period 1
Todays lesson is all about consolidating your trig calculations.
Starter questions:
Complete angle practice questions from Central Maths then onto calculating sides.
Wednesday 9 June, period 3
Recap calculations covered yesterday.
Starter questions based on photographs of real life triangle contexts.
Work out how to solve a length problem where the missing length is in the denominator.
Practice all ‘3’ trig calculations using Central Maths p204.
Monday 14 June, period 6
Check questions set as homework then recap trig calculations to date.
Look at moon crater depth problem.
Exercise on trig problem solving.
Some pupils trying to complete the sum from memory rather than solving algebra step using algebra skills.
More practice of mixed examples needed.
Tuesday 15 June, period 1
Starter question: two trig calculations from pupils’ Int1 exam answer papers.
Further worked examples then Trigonometry calculations worksheet.
God discussion on exam solutions from Understanding Standards.
Practice of mixed examples completed.
Homework: Complete Q2&3 on both sides of the worksheet for Thursday 17 June
Wednesday 16 June, period 3
Starter question:
Todays focus will be trig problem solving questions.
Decent progress by those present yesterday.
The effect of missing a period to attend the Construction course was clearly evident.
Completed MiA 3³ Ex10.1 Q4-8
Thursday 17 June, period 5
Further problem solving trig sums from MiA 3³ Ex10.1 & 10.2.
Aim to head outside to calculate the height of the school weather permitting.
Wet outside no no outdoor trig today.
Worked on problems from Ex10.1 -10.2
Monday 21 June, period 6
Math4Real “Sine Ratio” video and supporting worksheets (“Tick or Trash”, followed by GCSE exam questions)
Although this video and worksheets only focuses on the sine ratio the problems and activities are good and can be applied to all three ratios.
Homework: …..
No homework issued as I forgot to copy sheets!
Will be issued on Wednesday instead due to pupils absent tomorrow.
All tasks complete. Good discussion on example solutions to problems.
Tuesday 22 June, period 1
Peer & self assessment of trig skills.
Class will be given 10 minutes to prepare then asked to collectively create two sets of three questions assessing the basic trig calculations covered in this topic.
Success criteria discussed and time limit.
Class complete first set of three sums then mark and provide written and verbal feedback to each other (what was good and what can be done to improve/move forward to next level).
Class then complete second set of sums, taking on board previous advice. Feedback process is repeated.
Class discussion followed by self assessment on whether success criteria met.
I am really pleased with the class’ response to this task.
Very good quality feedback given following discussion about useful feedback.
Almost all pupils assessed themselves as having met the success criteria, i.e. ‘passed’. Those absent last week on Amsterdam trip understandably identified that they needed more practice.
I will definitely use this assessment strategy again!
Three pupils agreed to create examples of model solutions for display in the classroom.
Wednesday 23 June, period 3
Practical assessment – calculate height of school at highest point, flagpole and street light.
Whole class to go outside, groups of 3, each with a tape measure and clinometer.
Discuss results and potential errors at end.
The class achieved very good results overall.
We calculated that the school was approximately 13m high, flagpole – 8m and streetlight 5m.
Main cause of error was in use of or dodgy clinometers!
Thursday 24 June, period 5
No Maths today, we are all going to the hall to watch a play related to the EcoSchools project.
Monday 28 June, period 6
Trig problem solving cooperative group task.
Each group issued with a set of 5 clue cards to solve trig problem within time limit (5 mins).
Problems rotate round class.
Discuss solutions at the end.