Thurs 1st Mar – Sine, Cosine and Tangent ratios

LEARNING OBJECTIVE: To understand the three ratios – Sine Cosine and Tangent

SUCCESS CRITERIA: You will be able to find the angle in a triangle given any two sides

STARTER: Have a go at finding the marked lengths and angles in these triangles

LESSON:

• Show how the SINE of an angle is constant for the ratio opp/hyp
  
• Show how the COSINE of an angle is constant for the ratio adj/hyp
  
• Show how the TANGENT of an angle is constant for the ratio opp/adj
  

Examples showing how to use the above ratios to find the angle(s) in triangles

Have a go at Ex 12 H on Pages 283 and 284 then Ex 12l on page 286, then ex 12J on Page 288

PLENARY: QUESTION / PROBLEM to solve.

If I know the hypotenuse of a triangle is 15cm and its height is 12cm. Can I work out the angle of the triangle and then the length of the triangle.

Weds 29th Feb – sine, Cosine and Tangent ratios

LEARNING OBJECTIVE: TO understand the three ratios – Sine Cosine and Tangent

SUCCESS CRITERIA: You will be able to find the angle in a triangle given any two sides

STARTER: Work through Ex 12G on page 281using your calculator.

Discussion on any findings

LESSON: How to use sine and cosine on calculator to find length and/or height of triangles of any hypotenuse length and any angle

Lots of examples on IWB. Then have a go at the six questions on the IWB.

• Show how the SINE of an angle is constant for the ratio opp/hyp
  
• Show how the COSINE of an angle is constant for the ratio adj/hyp
  
• Show how the TANGENT of an angle is constant for the ratio opp/adj
  

Examples showing how to use the above ratios to find the angle(s) in triangles

Have a go at Ex 12 H on Pages 283 and 284 then Ex 12l on page 286, then ex 12J on Page 288

PLENARY: QUESTION / PROBLEM to solve.

If I know the hypotenuse of a triangle is 15cm and its height is 12cm. Can I work out the angle of the triangle and then the length of the triangle.

Tues Feb 28th – Intro to Trigonometry (continued)

LEARNING OBJECTIVE: Discover what sine and cosine values are

SUCCESS CRITERIA: You will be able to use sine and cosine values to work out the height and/or width of a right angled triangle

Example Notebook File.

STARTER: Use the Measurements in this Table which are for the length and width of triangles with a Hypotenuse of 100mm

Angle	Length	Height
0°	100mm	0mm
10°	98mm	17mm
20°	94mm	34mm
30°	87mm	50mm
40°	77mm	64mm
50°	64mm	77mm
60°	50mm	87mm
70°	34mm	94mm
80°	17mm	98mm
90°	0mm	100mm

 

Can you answer these questions

QUESTIONS:

1. Can you use your table to find the height of a triangle that has an angle of 30° and a hypotenuse length of 50cm
   
2. Can you use your table to find the height of a triangle that has an angle of 50° and a hypotenuse length of 30cm
   
3. Can you use your table to find the height of a triangle that has an angle of 60° and a hypotenuse length of 120cm
   
4. Can you use your table to find the length of a triangle that has an angle of 10° and a hypotenuse length of 5cm
   
5. Can you use your table to find the length of a triangle that has an angle of 80° and a hypotenuse length of 65cm
   
6. Can you use your table to find the height of a triangle that has an angle of 40° and a hypotenuse length of 1cm
   
7. Can you use your table to find the length of a triangle that has an angle of 70° and a hypotenuse length of 235cm
   
8. Can you use your table to find the height of a triangle that has an angle of 25° and a hypotenuse length of 112cm
   

LESSON:

CAN we use the table to the length of a small triangle that has a 1mm hypotenuse?

Discussion on Sine and Cosine on Calculator. What it represents. Making sure calculator is set to DEGREES.

Look at sin(10°), compare with table

Look at cos(50°). Compare with table

 

Work through Ex 12F on page 278 and Ex 12G on page 281using your calculator.

Discussion on any findings

 

How to use sine and cosine on calculator to find length and/or height of triangles of any hypotenuse length and any angle

Lots of examples on IWB. Then have a go at the six questions on the IWB

QUESTION / PROBLEM to solve.

If I know the hypotenuse of a triangle is 15cm and its height is 12cm. Can I work out the angle of the triangle and then the length of the triangle.

Give students 5/10 mins to try and solve this problem.

PLENARY: Checking answers throughout the lesson, Quick summary of lesson from students.

 
 

Mon Feb 27th - Introduction to Trigonometry

LEARNING OBJECTIVE: Discover what sine and cosine values are

SUCCESS CRITERIA: You will be able to use sine and cosine values to work out the height and/or width of a right angled triangle

STARTER: Try these four questions

EQUIPMENT NEEDED: Sharp Pencil, Ruler and Protractor & Calculator

LESSON: INVESTIGATION
Draw a right angled triangle that has an angle of 10° and a hypotenuse length of 10cm. Measure the length and height of the triangle and put the results into a table. Example Notebook File.

Repeat for triangles with 20°, 30°, 40°, 50°, 60°, 70° & 80°. Fill in the length and height for each triangle you draw. Try to be as accurate as you can and give answers to the nearest millimetre.

QUESTIONS:

1. Can you use your table to find the height of a triangle that has an angle of 30° and a hypotenuse length of 50cm
   
2. Can you use your table to find the height of a triangle that has an angle of 50° and a hypotenuse length of 30cm
   
3. Can you use your table to find the height of a triangle that has an angle of 60° and a hypotenuse length of 120cm
   
4. Can you use your table to find the length of a triangle that has an angle of 10° and a hypotenuse length of 5cm
   
5. Can you use your table to find the length of a triangle that has an angle of 80° and a hypotenuse length of 65cm
   
6. Can you use your table to find the height of a triangle that has an angle of 40° and a hypotenuse length of 1cm
   
7. Can you use your table to find the length of a triangle that has an angle of 70° and a hypotenuse length of 235cm
   
8. Can you use your table to find the height of a triangle that has an angle of 25° and a hypotenuse length of 112cm
   

Discussion on Sine and Cosine on Calculator. What it represents. Making sure calculator is set to DEGREES.

Work through Ex 12F on page 278 and Ex 12G on page 281using your calculator.

How to use sine and cosine on calculator to find length and/or height of triangles of any hypotenuse length and any angle

Lots of examples on IWB. Then have a go at the six questions on the IWB

QUESTION / PROBLEM to solve.

If I know the hypotenuse of a triangle is 15cm and its height is 12cm. Can I work out the angle of the triangle and then the length of the triangle.

Give students 5/10 mins to try and solve this problem.

PLENARY: Checking answers throughout the lesson, Quick summary of lesson from students.

 

Mon Feb 27th – Title of Lesson

Learning Objective:

Success Criteria:

Thurs 23rd Feb – Areas and Volumes of similar shapes

LEARNING
OBJECTIVE: TO discover the relationship between the linear enlargement and the area and volume enlargement ratios of similar shapes

SUCCESS
CRITERIA: You will understand what is meant by a similar shape And also understand how to use the linear scale factor of enlargement to work out the area and volume of similar shapes.

STARTER: Write down in a couple of sentences what you understand by the term similar shape. Think of both 2D and 3D shapes

LESSON: Discussion students answers to above starter, discussion on similar shapes.

Copy this table into your text book

Enlargement Scale Factor	Cuboid Dimensions		Total Surface Area	Volume
x 1	2cm x 3cm x 4cm
x 2
x 3
x 5
x 0.5

 
 

1. Work out the total surface area of the cuboid in the first row and put the result in your table
   
2. Do the same for th4e volume of your cuboid and put the result in your table.
   
3. Now double all the lengths of the cuboid and complete the 2^nd row of the table
   
4. Triple the ORIGINAL lengths of the cuboid and then complete the table for the 3^rd row.
   
5. Continue until all rows of your table are completed.
   

Can you spot the relationship between the linear scale factor and the Area scale factor (divide the surface areas by the surface area of the original cuboid in row 1)

Can you spot the relationship between the linear scale factor and the Volume Scale Factor (divide the volume by the volume of the original cuboid in row 1)

Can you summarise and generalise your findings.

Use this lesson (from screen 4) to show how these findings can help solve problems with areas of similar shapes

Use this lesson to show how you can use these findings to solve problems with volumes of similar shapes.

PLENARIES: Answers and Discussions to investigation work, Answer to Mymthas screens on IWB as we work thorugh problems. Summary discussion at end of lesson and get some idea of confidence from students.

Weds 22nd Feb – More work on Area and Volume Exam Questions

LEARNING OBJECTIVE: To Use the knowledge and formula for 2D and 3D shapes to solve exam problems

SUCCESS CRITERIA: You will be able to solve Grade A and A* type Questions

STARTER: Water Container Problem

LESSON: Solve Starter problem together on IWB.

Hand out More Exam Questions for Students to Attempt

PLENARY: Checking Answers, Checking with individuals and tables

Tues Feb 21st – More work on Area and Volume Higher Questions

LEARNING OBJECTIVE: To Use the knowledge and formula for 2D and 3D shapes to solve exam problems

SUCCESS CRITERIA: You will be able to solve Grade A and A* type Questions

STARTER: Paper Clip Problem

LESSON: Solve Starter problem together on IWB.

Hand out More Exam Questions for Students to Attempt

PLENARY: Checking Answers, Checking confidence at end of lesson.

Monday Feb 20th – Review & Feedback of Area and Volume Test

LEARNING OBJECTVIE: TO discover weaknesses' through test feedback and practice further questions

SUCCESS CRITERIA: You will be able to solve Higher level (A and A*) Questions on Area and Volume

STARTER: Hand out test results and give students 5 mins to talk about results, ask questions...

LESSON: Slowly work through all questions explaining how to solve and how to present questions in an exam.

Give Students a chance to write down model answers to ALL QUESTIONS covered on IWB

Exam Papers

Formula Sheet:

PLENARY:
Have a go at This Question

Thurs 9th Feb – Assessment on Area and Volume Exam questions

Hand out Exam Papers and paper to work on along with Formula Sheet

Students have all lesson to work on exam questions in exam conditions.

Calculators are allowed.

SHOW ALL STAGES OF WORKING OUT

ALWAYS INCLUDE THE UNITS IN YOUR ANSWERS

Weds 8th Feb – Consolidation and Revision of Volume and Surface Area work

LEARNING OBJECTIVE: You will have a chance to practice the skills learned in the last 5 lessons on surface area and Volume Questions

SUCCESS CRITERIA: You will be able to solve Surface area and volume questions

STARTER: Here are all the formulas you need to use for this section of work

• Area of Rectangle = Length x Width
  
• Area of a triangle = Base length x perpendicular height x ½
  
• Area of a trapezium = ½ x (a +b) x h, where a and b is the length of the parallel sides and h is perpendicular width of the trapezium
  
• Area of a circle = πr²
  
• Area of a Sector of a circle angle x° = x°/360 x πr²
  
• Volume of a cuboid = length x width x height
  
• Volume of a prism = Area of face x depth or area of base x height
  
• Volume of a Pyramid = 1/3 x area of base x perpendicular height
  
• Volume of a sphere = 4/3 x πr²
  
• Surface area of a Sphere 4 x πr²
  
• Curved Surface area of a cone = πrl, where l is the slant height of the cone
  

LESSON: Students to work through These questions during lesson in order to consolidate understanding of Surface Area and Volume Questions.

PLENARY: Checking answers with class/ individuals / groups as appropriate – Stopping class going over misconceptions errors that lost have.

HOMEWORK: Please repeat last two homeworks unless you got a GREEN

Have a go at the two new homeworks ALL DUE FOR FIRST MONDAY AFTER HALF TERM

 

 

 

Tues Feb 7th – more work on Total Surface Area of 3D Shapes

LEARNING OBJECTIVE: understand how to find the total surface area of a 3d object – cuboid, cylinder, cone, and pyramid

SUCCESS CRITERIA: You will be able to find the TSA of Cuboids, Cylinder, cones and pyramids

STARTER: Use screen 7 of this lesson.

Draw the Net and put on all the lengths for each of the Shapes.

YOU DO NOT HAVE TO WORK OUT ANY SURFACE AREAS FOR THESE QUESTIONS

Check answers on IWB With Students

LESSON: Look at screen 6 – Area of A triangular prism – on IWB

Use screen 8 to remind how to work out TSA of a cylinder

Use screens 1, 2 and 4 To look at TSA of Cones and Pyramids from this lesson

Continue working through this worksheet

KEYWORD: Apothem

PLENARY: Checking Answers, stopping class and going over questions. If time a past paper question

 
 

  

Mon Feb 6th – Total Surface area of 3d shapes - Cuboids, Cylinders, prisms

LEARNING OBJECTIVE: understand how to find the total surface area of a 3d object – cuboid, cylinder, cone, and pyramid

SUCCESS CRITERIA: You will be able to find the TSA of Cuboids, Cylinder, cones and pyramids

STARTER:

1. What is the total surface area of the following two cuboids
   
   1. Length 3cm, width 4cm height 6cm
      
   2. Length 5m, width 2m, height 3m
      
   3. 
      
2. My lounge is 4m by 5m and is 2.4m high. I want to paint all the walls (ignore doors and windows)
   

   How much will it cost me if the paint I require is £11.56 a litre and 1 litre will cover 5m²
   

LESSON: Discussion on Surface area including net of a 3d shape. Look at some Prisms to find TSA of, including cylinders.

Have a go at This Worksheet

PLENARY: Checking Answers. Stopping and going over problems with whole class/tables/small groups.