Which ones are you using?

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

2. Which ones are you using? LEARNING JOURNEY Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK Factorise: x2 – 5x – 14 Factorise: x2 – 10x + 24 Factorise: 16y2 + 20y 2) 1) 3) = (x – 4)(x – 6) = 4y(4y + 5) = (x – 7)(x + 2) Factorise: h2 – 81 Factorise and simplify: x2 + 4x – 5 x2 + 5x – 6 Factorise and simplify: 4) 6) 5) x2 – 25_ x2 + 5x = (h + 9)(h - 9) x + 5 x - 5 (x + 5)(x - 5) (x + 5)(x - 1) = = = = x x(x + 5) (x + 6)(x - 1) x + 6 EXTENSION Solve 2x2 – 32 = 0 (x + 4)(x – 4) = 0 x2 – 16 = 0 ÷ 2 x = -4 or x = 4

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Quadratic Formula + -b - 4ac 2 - x b = QUADRATIC FORMULA 2a EXAMPLES Solve the following equations by using the quadratic formula: (a) 2x2 + 3x - 20 = 0 (b) 5x2 - 11x - 4 = 0 a = 2 b = 3 c = -20 a = 5 b = -11 c = -4 - - x x 3 3 2 4 2 -20 (-11) 2 - x - x -11 4 5 -4 X = X = x 2 2 x 2 5 + + + + + + - - - - - - - + 3 9 160 + 11 121 80 X = X = 4 10 - 3 169 11 201 X = X = 4 10 - - 3 3 169 + 169 - 11 11 201 + 201 - OR X = X = OR X = X = 4 4 10 10 - 4 2.5 X = X = - 0.32 (2d.p.) 2.52 (2d.p.) X = X =

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Quadratic Formula TASK 1 (GRADE A) 1) Solve the following using the quadratic formula: (b) (a) 9 1 -2 5 1 3 -2 9 1 9 5 1 3 5 1 1 5 9 13 89 2 2 0.22 -9.22 -0.70 -4.30 (c) (d) 8 3 -1 3 2 -5 3 -1 2 -5 8 3 8 3 3 2 8 76 3 49 4 6 0.12 -2.79 1 -2.5

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills Quadratic Formula TASK 2 (GRADE A) • 1) Solve the following using the quadratic formula: • 2x + x - 8 = 0 • b) 3x + 5x + 1 = 0 • c) x - x − 10 = 0 • d) 5x + 2x - 1 = 0 • e) 7x+ 12x + 2 = 0 • f) 3x + 11x + 9 = 0 • g) 4x + 9x + 3 = 0 • h) 6x+ 22x + 19 = 0 • i) x + 3x – 6 = 0 • j) 3x - 7x + 1 = 0 k) 2x + 11x + 4 = 0 l) 4x + 5x - 3 = 0 m) 4x - 9x + 4 = 0 n) 7x + 3x - 2 = 0 o) 5x- 10x + 1 = 0 2 x = 1.77 or x = -2.27 2 x = -0.39 or x = -5.11 2 x = -0.23 or x = -1.43 2 x = 0.44 or x = -1.69 2 x = 3.7 or x = -2.7 2 x = 1.64 or x = 0.61 x = 0.29 or x = -0.69 2 x = 0.36 or x = -0.79 2 x = -0.19 or x = -1.53 2 x = 1.89 or x = 0.11 2 x = -1.23 or x = -2.43 2 x = -0.41 or x = -1.84 2 2 x = -1.39 or x = -2.27 x = 1.37 or x = -4.37 2 x = 2.18 or x = 0.15 2 EXTENSION (GRADE A) 1) Mavis is solving a quadratic equation using the quadratic formula. She correctly substitutes in values for a, b and c to get: What is the equation Mavis is trying to solve? x2 - 3x - 7 = 0 2) Junior uses the quadratic formula to solve: Sienna uses factorisation to solve: They both find something unusual in their solutions. Explain what this is.

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Quadratic Formula PLT Skills MINI-PLENARY – SPOT THE MISTAKES The student has solved the equation using the quadratic formula. Find the mistakes below: 4x2 - 5x - 3 = 0 a = 4 b = -5 c = -3 (-5) 2 - x - x 5 4 4 -3 X = x 2 4 + + + + -5 -25 48 - - - X = 6 -5 23 X = 6 -5 -5 23 + 23 - OR X = X = 6 6 - 1.63 (2d.p.) -0.03 (2d.p.) X = X =

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

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Quadratic Formula PLT Skills PLENARY ACTIVITY 1 – EXAM QUESTION (GRADE A) Solve the equation 4x2 - 5x - 3 = 0 c = -3 a = 4 b = -5 Give your answer correct to two decimal places. You must show your working. (-5) 2 - x - x -5 4 4 -3 X = x 2 4 + 5 25 48 + + + X = - - - 8 5 73 X = 8 5 5 73 + 73 - OR X = X = 8 8 - 0.44 (2d.p.) 1.69 (2d.p.) X = X = (3 marks)

10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Quadratic Formula PLT Skills PLENARY ACTIVITY 2 – DISCRIMINANT (GRADE A*) x2 + 3x + 5 = 0 2 a = 1 c = 5 b = 3 Find the discriminant b - 4ac of the equation and explain what the result tells us 2 b - 4ac 2 x x 1 - 4 5 = 3 - 20 9 = - 11 =

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

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

13. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? 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