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: • Finding connections between different words. (Which PLT skills?) • Accurately solve quadratic simultaneous equations. (Grade A*) AUTHOR www.mistrymaths.co.uk

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

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK Solve the following simultaneous equations: 6x + y = 27 4x + y = 11 2) 6x + y = 26 2x - y = 6 1) - + 2x = 16 Signs different (-) Signs different (+) 8x = 32 x = 8 x = 4 Substitute in x = 8 Substitute in x = 4 32 + y = 11 8 - y = 6 y = -21 y = 2 EXTENSION Solve the following simultaneous equation: 3x – 5y = 5 5x – 3y = 15 x 3 1) Substitute in x = 3.75 x 5 11.25 - 5y = 5 9x – 15y = 15 - 5y = -6.25 - 25x – 15y = 75 y = 1.25 -16x = -60 x = 3.75

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills QUADRATIC SIMULTANEOUS EQUATIONS EXAMPLE 1 Solve the following quadratic simultaneous equation. 1 2 Rearrange equation for substitution Make both brackets = 0 Substitute for into equation x x Substitute back into one of the original equations to find x When x When Factorise quadratic

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills QUADRATIC SIMULTANEOUS EQUATIONS EXAMPLE 2 Solve the following quadratic simultaneous equation. 1 2 When both equations are given in term of y, make = Rearrange to make the equation = 0 When +3 +3 -2 -2 Factorise quadratic When Make both brackets = 0 Substitute back into one of the original equations to find

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills QUADRATIC SIMULTANEOUS EQUATIONS TASK (GRADE A*) Solve these pairs of simultaneous equations: 1) (a) • = -4, y = 1 • 𝒙 = -2, y = 2 • = 1, y = 2 • 𝒙 = -2, y = -1 (b) • = 3, y = 2 • 𝒙 = -2, y = 3 2) (b) (a) (c) • = 3, y = 4 • 𝒙 = 4, y = 3 • = 0, y = 3 • 𝒙 = -3, y = 0 • = 3, y = 3 • 𝒙 = 1, y = -1 3) (b) (a) (c) • = 2, y = 5 • 𝒙 = -2, y = -3 • = -1, y = -2 • 𝒙 = 4, y = 3 • = 3, y = -2 • 𝒙 = -2, y = 3 • = -3, y = -3 • 𝒙 = 1, y = 1 4) (a) (b) • = 2, y = -1 • 𝒙 = 3, y = 1 • = -2, y = -1 • 𝒙 = 1, y = 2 (c) (d) • = -2, y = 1 • 𝒙 = 3, y = 6 (e) (f) • = 1, y = -4 • 𝒙 = 4, y = 2 (g) • = 4, y = 5 • 𝒙 = -5, y = -4

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills QUADRATIC SIMULTANEOUS EQUATIONS EXTENSION (GRADE A*) 2 1) (a) Solve the simultaneous equations: y = x + 3x – 4 and y = 5x – 5 (b)Which of the sketches below represents the graphs of the equations in part (a)? Explain your choice. = 1, y = 0 As straight line just touches the curve (i) (iii) (ii)

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills QUADRATIC SIMULTANEOUS EQUATIONS MINI-PLENARY Spot the mistake below: 1 2 Rearrange equation for substitution Substitute back into one of the original equations to find Substitute for into equation When -3– = -4 -3 -3 -1 -1 When Make both brackets = 0

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

10. PLENARY ACTIVITY GRADE A* EXAM QUESTION Solve the simultaneous equations. x = 3 + 2y x + 2y = 27 Do not use trial and improvement. You must show your working. 1 2 2 2 Substitute for into equation Make both brackets = 0 x x Substitute back into one of the original equations to find x x When ÷6 -3 -3 +1 +1 When Factorise quadratic (6 marks)

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 solving quadratic simultaneous 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