Monday, 30 April 2012

Tues May 1st – Finding an angle using the Cosine Rule, Area of a triangle

LEARNING OBJECTIVE: Discover how to use the cosine rule to find a missing angle

SUCCESS CRITERIA: You will be able to use the cosine rule to find the missing angle in a triangle

HINT: You have to use the re-arranged cosine rule to find the missing angle when you have all three sides of the triangle and NONE of the angles

STARTER: SOLVE THIS PROBLEM

The hour hand of a clock is 6.2 cm long, the minute hand is 4.5 cm long.

What is the distance between the ends of the hands at exactly 7 o'clock

LESSON: Use above example to revise using cosine rule to find a length then work through this lesson to look at using a re-arranged version of the cosine rule to find out an angle of a triangle when you know all three lengths but none of the angles.

Now have a go at Q2 page 488, then q6 onwards on page 488

In last 15 mins briefly look at formula for area of a triangle using this lesson Screen 4 onwards.

PLENARY: Checking answers, checking confidence of students on Sine Rule, Cosine Rule and Area of a triangle Rule

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Wednesday, 25 April 2012

Thurs Apr 26th – The Sine Rule – The Ambiguous Case

LEARNING OBJECTVIE: You will discover that the sine rule can give two answers, and how to choose which answer?

SUCCESS
CRITERIA: You will understand how to deal with ambiguous case solutions when using the Sine Rule

  1. DEFINITION: Ambiguous:- am·big·u·ous/amˈbigyo͞oəs/ (Adjective)
  2. 1. Open to more than one interpretation; having a double meaning.

    2. Unclear or inexact because a choice between alternatives has not been made

    LESSON:

    Have a look at Question 2b, page 484 from Yesterday. Why do we get the wrong answer?

    Work through this Lesson - Ambiguous case (screens 8 & 9) then work through as much of exercise 22G as you can.

    PLENARY: Checking answers throughout the lesson, Get students to explain Ambiguity that can arise using the Sine Rule


     
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Tuesday, 24 April 2012

Weds Apr 25th Understanding how and when to use the sine rule to solve problems

LEARNING OBJECTIVE: To understand and use the Sine Rule to solve triangle problems

SUCCESS CRITERIA: You will be able to remember and write down the SINE RULE and use it to solve problems

STARTER: Use your calculator to write down to 3DP these values,

  1. Sine 30°
  2. Sin 60°
  3. Sin 45°
  4. Sin 0°
  5. Sin 90°
  6. Sin 1°
  7. Sin 99°
  8. Sin 45.6°

    Find the value of these to 1 dp

  9. Sin-1(.4226)
  10. Sin-1(1)
  11. Sin-1(0)
  12. Sin-1(.5)
  13. Sin-1(0.8746)
  14. Sin-1(0.23344)
  15. Sin-1(0.99027)
  16. What angle has a sin value of 0.996194
  17. What angle has a sin value of 0.22495

LESSON: Short discussion on TRIGONOMETRY and what students can remember about it.

Work through this Lesson on The Sine Rule (Don't do Screens 8 & 9)

Have a go at Questions 1 & 2 on page 484

Ambiguous case (screens 8 & 9) then rest of exercise 22G

PLENARY: Checking Answers, have a look at an Exam Pro question if time.
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Monday, 23 April 2012

Tues Apr 24th – Using the quadratic formula to solve equations

LEARNING OBJECTIVE: Discover other methods of solving quadratics when they will not factorise – quadratic Formula

SUCCESS CRITERIA: You will be able to solve quadratics that do not factorise

ENGAGEMENT ACTIVITY:

Quadratic formula Song, Solving a Quadratic using the formula (Example)

LESSON: work through Ex 20J page 446 of Higher Text Book.

PLENARIES: Checking answers to Exercises in book as we work through them, confidence feedback from students
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Thursday, 19 April 2012

Mon Apr 23rd – Solving Quadratics using the quadratic Formula

ENGAGEMENT
ACTIVITY: Looking at these Exam Questions

LESSON: Questions Number 2 in the exam questions cannot be solved using the techniques we know at the moment, we will have to use the Quadratic Formula to solve this

  1. Quadratic Formula Lesson,
  2. Extra Questions – Ex 20J page 446 of Higher Text Book.

PLENARIES: Use MyMthas screens for lots of practice, Checking answers to Exercises in book as we work through them, confidence feedback from students
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Wednesday, 18 April 2012

Thurs Apr 19th – Solving Quadratics that do not factorise – Competing the Square and Quadratic Formula

LEARNING OBJECTIVE: Discover other methods of solving quadratics when they will not factorise

SUCCESS CRITERIA: You will be able to solve quadratics that do not factorise.

Engagement Activity:

Use your calculator to write down the solution to the following problems to 2decimal places.

a. 3 - √23,    b. 3+ √23

a. 6 - √35,     b. 6+ √35

a. -33 - √41,     b. -3+ √41

a. -8 - √17,     b. -8+ √17

a. -9 - √75,     b. -9+ √75

Completing the square Calculator

LESSON:

Have 20 mins to try and complete these equations you started yesterday. Give the answers BOTH in surd form and the two solutions to 2dp.

  1. x2 + 14x – 5 = 0 , Complete this square (x + 7) 2
  2. x2 -6x + 3 = 0 , Complete this square (x - 3) 2
  3. x2 +6x + 7 = 0 , Complete this square (x + 3) 2
  4. x2 - 4x - 1 = 0 , Complete this square (x - 2) 2
  5. x2 + 3x + 3 = 0 , Complete this square (x + 1½ ) 2
  6. x2 - 5x – 5 = 0 , Complete this square (x – 2½)2
  7. x2 + x - 1 = 0 , Complete this square (x + ½)2
  8. x2 + 8x - 6 = 0 , Complete this square (x + 4) 2
  9. x2 + 2x -1 = 0 , Complete this square (x + 1) 2
  10. x2 -2x - 7 = 0 , Complete this square (x - 1) 2

Exam Questions

PLENARIES: Checking Answers throughout the lesson, feedback from Students on Confidence
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Tuesday, 17 April 2012

Weds 18th Apr – Solving quadratic Equations that do not factorise – Completing the square Method

LEARNING OBJECTIVE: Discover other methods of solving quadratics when they will not factorise

SUCCESS CRITERIA: You will be able to solve quadratics that do not factorise.

ENGAGEMENT ACTIVITIES:

Can You expand these equations

  1. (x+2)2
  2. (x-4)2
  3. (x+5)2
  4. (x- 3)2
  5. (x+1.5)2
  6. (x – 3.5)2

LESSON

Look at the following quadratics,

  1. Can you factorise them?
  2. If no, can you guess a solution using trial and improvement methods?

x2 + 4x – 8 = 0

x2 - 8x – 4 = 0


  1.  Look at (x+2)2 and the expression x2 + 4x + 2 –

    How are they different?

    What can we do to make this equation balance correctly?

    (x+2)2 = x2 + 4x + 2

    Examples

    1. x2 + 8x - 7
    2. x2 - 14x - 11
    3. x2 + 7x - 4

    Can you write the following equations in this form

    (x + a)2 –b or (x - a)2 –b

  2. x2 + 14x – 1 = (x+7) 2- 50
  3. x2 - 6x + 3 = (x-3) 2 -6
  4. x2 + 6x + 7 = (x+3) 2 -2
  5. x2 - 4x – 1 = (x-2) 2 -5
  6. x2 + 3x + 3 = (x + 1.5) 2+0.75
  7. x2 - 5x – 5 = (x-2.5) 2 -11.25
  8. x2 + x – 1 = (x+0.5) 2 -1.25
  9. x2 + 8x – 6 = (x+4) 2 -22
  10. x2 + 2x -1 = (x+1) 2 -2
  11. x2 - 2x – 7 = (x-1) 2 -8

    Look at these pairs of equations, can you complete the square and then solve the equations (leave your answer in surd form)

  12. x2 + 14x – 5 = 0 , (x + 7)2
  13. x2 -6x + 3 = 0 ,(x - 3)2
  14. x2 +6x + 7 = 0 ,(x + 3)2
  15. x2 - 4x - 1 = 0 ,(x - 2)2
  16. x2 + 3x + 3 = 0 ,(x + 1½ )2
  17. x2 - 5x – 5 = 0 ,(x - 3)2
  18. x2 + x - 1 = 0 ,(x + ½)2
  19. x2 + 8x - 6 = 0 ,(x + 4)2
  20. x2 + 2x -1 = 0 ,(x + 1)2
  21. x2 -2x - 7 = 0 ,(x - 1)2
     

PLENARY: Checking answers, stopping class and going over problems when stuck.
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Saturday, 14 April 2012

Mon Apr 16th/Tues Apr 17th – work through Practice Paper 1 Model answers

LEARNING OBJECTVIE: To revise exam topics and discover more exam techniques

SUCCESS CRITERIA: You will improve your grade in the next practice paper

STARTER: Hand out exam scripts to students give them a chance to look thorugh, compare answers, ask questions....

Put statistics on IWB showing grades

LESSON: Work through questions giving model answers and hints/tips/guidance to answering questions

Practice Paper 1

Practice Paper 1 mark scheme

PLENARY: Check on Student confidence
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