Creative Thinker Effective Participator Independent Enquirer Reflective Learner

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills LESSON OBJECTIVES Self Manager Team Worker Which ones are you using? Always aim high! We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills? ) - Accurately solve quadratic equations by completing the square. (Grades A-A*). Where are we in our journey? AUTHOR www. mistrymaths. co. uk Real life cross/curricular links?

Creative Thinker Effective Participator PLT Skills Independent Enquirer Reflective Learner BRAIN IN GEAR Self Manager Team Worker Which ones are you using? EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: DURAATICQ Quadratic NOETIFFICCE Coefficient GEARERRAN Rearrange EXTENSION Develop your own Mathematical anagrams as above as a creative thinker.

Effective Participator PLT Skills TASK 1) Write in standard form: 57. 6 1 = 5. 76 x 10 N 4) Independent Enquirer Reflective Learner = 075° 5) 925 74 3) 4 cm 8 cm = 12. 5 hours 15 cm Solve: 2 x + 5 y = 15 3 x - 2 y = 13 4 x + 10 y = 30 + 15 x - 10 y = 65 = 95 19 x x = 5 10 + 5 y = 15 5 y = 5 EXTENSION Team Worker Which ones are you using? STARTER 2) Distance = 925 miles Speed = 74 mph 750 Time = ………. minutes Write the bearing. Self Manager y= 1 Area shaded black? Area of circle – Area of triangle Πxrxr - bxh 2 8 x 4 2 = 3. 14 x 7. 5 = 176. 625 - 16 = 160. 6 cm 2 6) 8 m Creative Thinker 8 m Work out the perimeter = Πxd +r+r 4 3. 14 x 16 +8+ 4 8 =28. 56 m 360 =60° Hexagon → Find the sum of one exterior angle in an regular decagon 6 360 and one exterior angle in a regular hexagon? Decagon → 10 =36°

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE ax + bx + c 2 = Self Manager Team Worker Which ones are you using? (x + ) - ( ) + c b 2 2 EXAMPLE 1 Rewrite the following in the form (x +- a) 2 +- b 2 2 (a) x + 6 x - 11 (b) x - 8 x + 5 b = 6 c = -11 Write down the formula first 2 2 (x + b 2 ) – ( b 2 ) + c Substitute in the values for b and c (x + 26 )2 – ( 26 )2 + - 11 (x + 2 2 – ) ( ) 3 3 - 11 2 3 ) – 9 - 11 2 3 ) - 20 b = -8 c = 5 Write down the formula first 2 2 (x + b 2 ) – ( b 2 ) + c Substitute in the values for b and c 2 -8 )2 5 – ) (x + -8 ( 2 2 + 2 2 – ) ( x ( - 4) -4 + 5 2 (x - 4 ) – 16 + 5 2 (x - 4 ) - 11

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 1 (GRADE A) Self Manager Team Worker Which ones are you using? Rewrite the following in the form (x +- a)2 +- b 1) x + 4 x - 2 2) x 2 + 12 x - 7 3) x 2 - 6 x + 5 4) x 2 - 8 x + 11 5) x 2 + 2 x - 9 6) x 2 + 10 x + 6 7) x 2 - 14 x - 12 2 8) x - 20 x + 15 2

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE ax + bx + c 2 = Self Manager Team Worker Which ones are you using? (x + ) - ( ) + c b 2 2 EXAMPLE 2 2 Solve x - 6 x – 3 = 0 by completing the square. Leave your answer in the form a +- b 2 (x - 3 ) - 12 = 0 x 2 - 6 x – 3 = 0 b = -6 c = -3 2 x ) ( 3 = 12 Write down the formula first 2 2 x - 3 = +- 12 (x + b 2 ) – ( b 2 ) + c = 0 x = 3 +- 12 Substitute in the values for b and c 2 -3=0 ) (x + -62 )2 – ( -6 2 + 2 2 – ( ) x ( - 3) -3 - 3 = 0 2 (x - 3 ) – 9 - 3 = 0 2 (x - 3 ) - 12 = 0 4 3 2 3

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 2 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Leave your answers in surd form. 2 2 x - 4 x - 2 = 0 x + 10 x + 7 = 0 x + 2 x – 5 = 0 x 6 x + 4 = 0 4) 3) 2) 1) 5) x 2 + 12 x + 3 = 0 6) x 2 - 14 x – 4 = 0 7) x 2 - 2 x - 7 = 0 2 8) x + 8 x - 11 = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE ax + bx + c 2 = Self Manager Team Worker Which ones are you using? (x + ) - ( ) + c b 2 2 EXAMPLE 3 2 Solve x + 2 x – 9 = 0 by completing the square. Give your answer to 2 decimal places. 2 (x + 1 ) - 10 = 0 x 2 + 2 x – 9 = 0 b = 2 c = -9 2 + 1) x ( = 10 Write down the formula first 2 2 x +1 = +- 10 (x + b 2 ) – ( b 2 ) + c = 0 x = -1+- 10 Substitute in the values for b and c (x + 22 )2 – ( 22 )2 + - 9 = 0 x = -1 + 10 x = -1 - 10 2 2 – ( ) x ( + 1) 1 -9=0 2 (x + 1 ) – 1 - 9 = 0 2 (x + 1 ) - 10 = 0 x = 2. 16 x = -4. 16

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 3 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Round your answers to 2 d. p. where appropriate. 1) x 2 + 2 x – 3 = 0 2) x 2 - 4 x + 2 = 0 3) x 2 + 10 x + 12 = 0 4) x 2 - 6 x - 13 = 0 5) x 2 + 10 x + 15 = 0 6) x 2 - 16 x – 13 = 0 7) x 2 - 2 x - 21 = 0 2 8) x + 2 x - 9 = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE EXTENSION 1 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Leave your answers in surd form. 1) 2 x + 4 x – 8 = 0 2) 2 x 2 + 12 x – 20 = 0 5) 5 x 2 + 30 x = 45 2 6) x + 3 x – 2 = 0 2 Divide by 2 throughout Divide by 5 and change RHS = 0 Divide by 2 throughout 3) 3 x 2 - 12 x + 9 = 0 Divide by 3 throughout 2 x 7) - 5 x = -3 Make RHS = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE EXTENSION 2 (GRADE A*) Self Manager Team Worker Which ones are you using? Rearrange the following statements to give the complete solution, using the 2 method of completing the square to the equation: ax + bx + c = 0 H, C, B, E, D, J, A, F, G, I

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE Self Manager Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO Draw a 3 x 3 grid as shown below: Place any nine answers below into the grid (repeats forbidden) -8 -3 D 6 -4. 5 4 -2 A 2 B -9 -10 C 7 -50 3

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 + 4 x + 5 = 0 Find the value of ? below: (x + ? ) + 1 = 0 2 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 + 14 x + 48 = 0 Find the value of ? below: (x + ? ) - 1 = 0 7 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 6 x - 16 = 0 Find the value of ? below: (x + ? ) - 25 = 0 -3 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE Self Manager Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO x 2 + 4 x + 3 = 0 Which is answer is correct in surd form: A) x = -2 +- 1 B) x = 2 +- 1 C) x = -2 +- 7 D) x = -2 +- 7

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 20 x - 44 = 0 Find the value of ? below: (x + ? ) - 144 = 0 -10 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 16 x + 64 = 0 Find the value of ? below: (x + ? ) = 0 -8 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE Self Manager Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO x 2 - 8 x + 7 = 0 Which is answer is correct in surd form: A) x = -4 +- 23 B) x = -4 +- 9 C) x = 4 +- 9 D) x = 4 +- 23

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 9 x + 20 = 0 Find the value of ? below: (x + ? ) + 40. 25 = 0 -4. 5 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 8 x + 18 = 0 Find the value of ? below: (x - 4) + ? = 0 -2 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 + 4 x + 7 = 0 Find the value of ? below: (x + 2) + ? = 0 3 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE Self Manager Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO x 2 - 4 x - 12 = 0 Which is answer is correct in surd form: A) x = 2 +- 8 B) x = -2 +- 8 C) x = -2 +- 16 D) x = 2 +- 16

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 + 6 x + 15 = 0 Find the value of ? below: (x + 3) + ? = 0 6 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 + 12 x + 27 = 0 Find the value of ? below: (x + 6) + ? = 0 -9 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 18 x + 31 = 0 Find the value of ? below: (x - 9) + ? = 0 -50 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE Self Manager Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO x 2 + 10 x + 24 = 0 Which is answer is correct in surd form: A) x = -5 +- -1 B) x = 5 +- 1 C) x = -5 +- 1 D) x = -5 +- 49

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE x 2 - 12 x + 40 = 0 Find the value of ? below: (x - 6) + ? = 0 4 Team Worker Which ones are you using? MINI-PLENARY 1 – BINGO 2 Self Manager

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? MINI-PLENARY 2 – ASSESSING UNDERSTANDING PLT Skills. COMPLETING THE SQUARE Bogdar rewrites the expression x 2 + px + q by completing the square. He correctly does this and gets (x – 7)2 – 52. What are the values of p and q? 2 (x – 7) – 52 = x 2 + 49 - 7 x - 52 = x 2 - 14 x - 3 p q p = -14 and q = -3

Creative Thinker PLT Skills Effective Participator Independent Enquirer Reflective Learner DISCOVERY Self Manager Team Worker Which ones are you using? LINK BACK TO OBJECTIVES - Accurately solve quadratic equations by completing the square. What grade are we working at?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLENARY ACTIVITY 1 – CONNECT 4 PLT Skills. COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose.

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLENARY ACTIVITY 1 – CONNECT 4 ANSWERS PLT Skills. COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose. {-5. 45, -0. 55} {11. 08, -1. 08} {-2, 0} {4, -2} {-8. 36, 0. 36} {5, 3} {7. 16, 0. 84} {-1. 28, -11. 72} {11. 52, -2. 52} {-1} {4. 83, -6. 83} {-2, -10} {6. 32, -0. 32} {3, -1} {-2, 6} {3. 45, -1. 45} {-1, 5} {9, -1} {11. 57, 0. 43} {5. 32, -1. 32} {9. 24, 0. 76} {8, -6} {-5. 41, -2. 59} {-3. 73, -0. 27} {-7, 1} {9. 16, 2. 84} {-5. 61, 1. 61} {12, -4} {7, -9} {-3. 41, -0. 59} {1. 27, -17. 27} {-6. 74, -0. 74} {-3, -7} {4. 41, 1. 59} {5. 56, -7. 56}

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION PLT Skills. COMPLETING THE SQUARE 1) (a) Find the values of a and b such that: x 2 + 6 x – 3 = (x + a)2 + b b = 6 c = -3 b 2 (x + 2 ) – ( 2 ) + c = 0 2 (x + 3 ) – 9 - 3 = 0 2 (x + 26 )2 – ( 26 )2 + - 3 = 0 (x + 3 ) - 12 = 0 2 2 (x + 3 ) – ( 3 ) - 3 = 0 a b a = 3 and b = -12 (2 marks) (b) Hence, or otherwise, solve the equation: x 2 + 6 x – 3 = 0 giving your answers in surd form. 2 (x + 3 ) - 12 2 (x + 3) x +3 x =0 = 12 = +- 12 = -3 +- 12 x = -3 +- 4 3 x = -3 +- 2 3 (3 marks)

What have you learnt? Draw your brain In your brain, write or draw everything you can remember about solving quadratic equations by completing the square. It can be a skill or a reflection, or something else that might be prominent in your brain. Where are we in our journey? What grade are we working at?

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Which ones are you Enterprise Skills. SELF ASSESSMENT Plenary using? Activity How well do you understand the task? . I don’t understand I nearly understand www. mistrymaths. co. uk I fully understand

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. SELF ASSESSMENT Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www. mistrymaths. co. uk Responsible Citizen Team Worker Which ones are you using?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 1 (GRADE A) Self Manager Team Worker Which ones are you using? Rewrite the following in the form (x +- a)2 +- b 1) x + 4 x - 2 2) x 2 + 12 x - 7 3) x 2 - 6 x + 5 4) x 2 - 8 x + 11 5) x 2 + 2 x - 9 6) x 2 + 10 x + 6 7) x 2 - 14 x - 12 2 8) x - 20 x + 15 2

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 2 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Leave your answers in surd form. 2 2 x - 4 x - 2 = 0 x + 10 x + 7 = 0 x + 2 x – 5 = 0 x 6 x + 4 = 0 4) 3) 2) 1) 5) x 2 + 12 x + 3 = 0 6) x 2 - 14 x – 4 = 0 7) x 2 - 2 x - 7 = 0 2 8) x + 8 x - 11 = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE TASK 3 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Round your answers to 2 d. p. where appropriate. 1) x 2 + 2 x – 3 = 0 2) x 2 - 4 x + 2 = 0 3) x 2 + 10 x + 12 = 0 4) x 2 - 6 x - 13 = 0 5) x 2 + 10 x + 15 = 0 6) x 2 - 16 x – 13 = 0 7) x 2 - 2 x - 21 = 0 2 8) x + 2 x - 9 = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE EXTENSION 1 (GRADE A*) Self Manager Team Worker Which ones are you using? Solve the following by completing the square. Leave your answers in surd form. 1) 2 x + 4 x – 8 = 0 2) 2 x 2 + 12 x – 20 = 0 5) 5 x 2 + 30 x = 45 2 6) x + 3 x – 2 = 0 2 3) 3 x 2 - 12 x + 9 = 0 2 x 7) - 5 x = -3

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills. COMPLETING THE SQUARE EXTENSION 2 (GRADE A*) Self Manager Team Worker Which ones are you using? Rearrange the following statements to give the complete solution, using the 2 method of completing the square to the equation: ax + bx + c = 0

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? MINI-PLENARY 2 – ASSESSING UNDERSTANDING PLT Skills. COMPLETING THE SQUARE Bogdar rewrites the expression x 2 + px + q by completing the square. He correctly does this and gets (x – 7)2 – 52. What are the values of p and q?

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLENARY ACTIVITY 1 – CONNECT 4 PLT Skills. COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose.

Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker Which ones are you using? PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION PLT Skills. COMPLETING THE SQUARE 1) (a) Find the values of a and b such that: x 2 + 6 x – 3 = (x + a)2 + b (2 marks) (b) Hence, or otherwise, solve the equation: x 2 + 6 x – 3 = 0 giving your answers in surd form. (3 marks)