1. Quadratic Equations (needing rearrangement)
Grade 7
Quadratic Equations (needing rearrangement)
Solve quadratic equations that need rearrangement
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Solve quadratic equations that need rearrangement
Grade 7
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
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 how the marks are allocated.
Next Steps
Assessment
PLC/Reformed Specification/Target 7/Algebra/Quadratic Equations (needing Re-arrangement)

3. Key Vocabulary
Algebraic Fraction Denominator Product Quadratic Solve

4. Expanding Brackets 2(x - 4) + 3(x + 5) 5(y – 2) -2(y – 3) 2m(m + 3)
5(y + 4t – 2)
x(x2 + 2)
(t + 2) (t + 4)
(x – 5) (x + 3)
(2x + 1) (x – 4)
(2t – 3) (t + 5)
Multiply Out – AQA foundation
Student Sheet 1

5. Expanding Brackets

6. Factorising 3x + 6 x2 + 7x 3e2 + 5e x2 - 8x +7=0 x2 - 5x = -6
8y2 – 4xy
8a2 + 12a
3xy2 – 6xy
6x2 + x - 2
Student Sheet 2

7. Factorising x2 - 8x +7=0 3x + 6 x2 + 7x 3e2 + 5e x2 - 5x = -6
8y2 – 4xy
8a2 + 12a
3xy2 – 6xy
2x2 + 10x + 12
4y(2y - x)
(2x +4) (x + 3)
4a(2a + 3)
6x2 + x - 2
3xy(y – 2)
(2x -1) (3x + 2)

8. Solving quadratics by rearranging
DEMO
PRACTICE
Student Sheet 3

9. 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.

10. 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.

11. 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

12. 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

13. 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

14. 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).

15. Exam Questions – Specimen Papers
Student Sheet 5

16. Exam Questions – Specimen Papers

17. Exam Questions – Specimen Papers