Grade 7 Quadratic Equations needing rearrangement Solve quadratic

Grade 7 Quadratic Equations (needing rearrangement) Solve quadratic equations that need rearrangement If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Lesson Plan Lesson Overview Objective(s) Solve quadratic equations that need rearrangement Grade Prior Knowledge Fraction operations (numerical) Algebraic manipulation (including factorising quadratics) Duration Provided algebraic skills are strong (expanding and factorising quadratics) content can be taught with practice time within 60 minutes. Resources Print slides: 4, 6, 8, 12, 15 7 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Recap key algebraic skills needed for solving quadratics (expanding brackets and factorising) Give students slide 4 and 6 printed. To work independently to complete (content should be recap of prior knowledge). Teacher circulation to check all are confident in these two key skills. Students can self mark their work using slide 5 and 7. 15 Concept of arc length being part of the circumference and area of a sector being part of the area of the full circle Give students slide 8 printed. Demonstrate two examples where the equation needs to be rearranged. Explain to students that whilst these examples may look more complex the same rules of algebra apply. Remind students of the rules of adding fractions for numbers and show them how the same method is used where the fractions contain algebraic terms. Allow students to practice 6 further questions given on their sheet. 20 Solve quadratic equations that need rearrangement in contextualised problems Give students slide 12. Allow students to attempt question on their own for 2 minutes. Review question together and model answer using slide 13 and 14. Stress the importance of making a conclusion. 10 Solve quadratic equations that need rearrangement in exam questions (from specimen papers) Give students slide 15. This includes 2 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show the marks are allocated. 15 Next Steps Assessment PLC/Reformed Specification/Target 7/Algebra/Quadratic Equations (needing Re-arrangement)

Key Vocabulary Algebraic Fraction Denominator Product Quadratic Solve

Expanding Brackets 2(x - 4) + 3(x + 5) 7(x + 5) 2 m(m + 3) 3(2 + t) 3 y(4 y – 3) x(x + 2) 5(y + 4 t – 2) (t + 4) 3(2 y – 5) x(x 2 + 2) (x – 5) (x + 3) 4(3 x + 2) 5(y – 2) -2(y – 3) (2 x + 1) (x – 4) (2 t – 3) (t + 5) Student Sheet 1

Expanding Brackets

Factorising 3 x + 6 x 2 - 8 x +7=0 x 2 + 7 x x 2 - 5 x = -6 3 e 2 + 5 e 8 y 2 – 4 xy 8 a 2 + 12 a 3 xy 2 – 6 xy Student Sheet 2 2 x 2 + 10 x + 12 6 x 2 + x - 2

Factorising 3 x + 6 x 2 + 7 x 3 e 2 + 5 e 8 y 2 – 4 xy x 2 - 8 x +7=0 3(x + 2) x(x + 7) e(3 e + 5) 4 y(2 y - x) (x – 7) (x – 1) x 2 - 5 x = -6 (x – 2) (x – 3) 2 x 2 + 10 x + 12 (2 x +4) (x + 3) 8 a 2 + 12 a 4 a(2 a + 3) 3 xy 2 – 6 xy 3 xy(y – 2) 6 x 2 + x - 2 (2 x -1) (3 x + 2)

Solving quadratics by rearranging DEMO Student Sheet 3 PRACTICE

Solving quadratics by rearranging We can be given an equation to solve which appears to be linear but is actually quadratic. Step 1: Multiply the whole equation by the denominator Step 2: Expand the brackets Step 3: Make the equation equal to zero Step 4: Factorise Step 4: Solve for x.

Solving quadratics by rearranging Step 1: Multiply the whole equation (every term) by BOTH denominators. Step 2: Expand the brackets Step 3: Make the equation equal to zero Step 4: Factorise Step 4: Solve for x. Step 5: Substitute values back in to equation to check they are correct.

Solving quadratics by rearranging a) x=3, x=2 b) x=3, x=-7 c) x=4, x=-1 d) x=-2, x=3 e) x=-0. 375, x=2 f) x=-0. 584, x=0. 684

Problem Solving and Reasoning Megan is training for a long-distance cycle race. One day she cycles for x hours in the morning, travelling a distance of 60 km. In the afternoon, she cycles for 1 hour more travelling the same distance, but her average speed is 2 km/h slower than in the morning. How many hours did Megan travel in the afternoon? Student Sheet 4

Problem Solving and Reasoning Megan is training for a long-distance cycle race. One day she cycles for x hours in the morning, travelling a distance of 60 km. In the afternoon, she cycles for 1 hour more travelling the same distance, but her average speed is 2 km/h slower than in the morning. How many hours did Megan travel in the afternoon? In the morning In the afternoon

Problem Solving and Reasoning Use difference between speeds in morning and afternoon to form an equation Solve the equation In the context of the question, we must ignore -5 as we cannot have negative time. Therefore Megan travelled 7 hours in the afternoon (6+1).

Exam Questions – Specimen Papers Student Sheet 5

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers