Solve quadratic equations using the formula Grades 7/8 Quadratic Equations Solve quadratic equations using the formula If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk

Lesson Plan Lesson Overview Progression of Learning Objective(s) Solve quadratic equations using the formula Grade 7/8 Prior Knowledge Solving quadratics by factorising. Duration 60 minutes (variable; may take longer or extend into second lesson). Resources Slides 9 onwards are printable versions of some of the earlier slides. Equipment Calculator Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Introduction Three quadratic equations; give these to students to tackle. They should be able to complete the first two easily by factorising, but will be stuck with the third. This becomes a presentation of solution using the formula. 15 Factorising Differentiated practice. “Silver” questions introduce negative co-efficients; “Gold” questions need to be rearranged. It is quite likely that students will need more than the 20 minutes allocated. PRINT SLIDE 9 20 Reasoning Four differentiated problem questions. Best tackled by students working in pairs or groups if excessive teacher intervention is to be avoided. PRINT SLIDE 10 Examination style question. PRINT SLIDE 11 Plenary Matching exercise. May be done as a card sort. CLICKING ON EACH ELEMENT IN THE SLIDE COLOURS IT; THERE ARE THREE COLOURED GROUPS. PRINT/CUT OUT SLIDE 12 10 Next Steps Surds, rationalising denominators. Assessment PLC/Reformed Specification/Target 7/Algebra/Quadratic Equations (quadratic formula)

Key Vocabulary Coefficient Formula Round off Simplify Solve/solution

Quadratic Equations; formula Solve x² + 7x + 12 = 0 x² + 8x + 12 = 0 x² + 9x + 12 = 0 a = 1 b = 9 c = 12 −9+ 81−48 = −1.63 9 9 ×1×12 2 ×1 −9− 81−48 = −7.37 2

Click on “Bronze”, “Silver” or “Gold” to see answers for that section Quadratic Equations; formula Solve these quadratic equations by using the formula Give your answers to three significant figures (note that the examination paper will specify rounding; this is a “clue” that means “use the formula” BRONZE SILVER GOLD x² + 5x + 2 = 0 x² + 10x + 7 = 0 2x² + 14x + 13 = 0 2x² + 11x + 7 = 0 x² + 7x + 1 = 0 x² − 6x + 3 = 0 x² + x − 5 = 0 3x² − 14x + 13 = 0 2x² − 4x − 9 = 0 x² − 7x + 2 = 0 3x² + 2x = 3 x(x + 5) = 1 2x² = 3x + 4 5x2 = x + 1 2(1 − x2) = 9x x = −4.56 or x = −0.438 x = −9.24 or x = −0.757 x = −5.90 or x = −1.10 x = −4.77 or x = −0.734 x = −6.85 or x = −0.146 x = 0.551 or x = 5.45 x = −2.79 or x = 1.79 x = 1.28 or x = 3.39 x = −1.35 or x = 3.35 x = 0.298 or x = 6.70 x = −1.39 or x = 0.721 x = −5.19 or x = −0.193 x = −0.851 or x = 2.35 x = −0.358 or x = 0.558 x = −4.71 or x = 0.212 Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Quadratic Equations; formula Reasoning BRONZE SILVER The area of the square is the same as the area of the rectangle. Find x. Solve the equation 2x3 + 2x2 − 8x = 0. x 3 5.63 −2.56 or 1.56 x x + 5 SILVER GOLD The area of the rectangle is 130cm2. Find x. Solve the equation 2x2 + x = 50. (x + 5)cm2 −5.26 or 4.76 5.44 (x + 7)cm2 Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Examination style question. Quadratic Equations; formula Examination style question. 3x + 2 The area of the pentagon is 156. (a) Show that x2 + 2x − 30 = 0. (b) Find the length of PQ. Give your answer to three significant figures. 2x + 1 x x + 10 Q R S T P

Quadratic Equations; formula Sort into groups… x2 + 6x + 2 = 0 x2 − 6x + 9 = 0 x2 − 2x + 6 = 0 x y x y y x

Solve these quadratic equations by using the formula Quadratic Equations; formula Solve these quadratic equations by using the formula Give your answers to three significant figures (note that the examination paper will specify rounding; this is a “clue” that means “use the formula” BRONZE SILVER GOLD x² + 5x + 2 = 0 x² + 10x + 7 = 0 2x² + 14x + 13 = 0 2x² + 11x + 7 = 0 x² + 7x + 1 = 0 x² − 6x + 3 = 0 x² + x − 5 = 0 3x² − 14x + 13 = 0 2x² − 4x − 9 = 0 x² − 7x + 2 = 0 3x² + 2x = 3 x(x + 5) = 1 2x² = 3x + 4 5x2 = x + 1 2(1 − x2) = 9x

Quadratic Equations; formula Reasoning BRONZE SILVER The area of the square is the same as the area of the rectangle. Find x. Solve the equation 2x3 + 2x2 − 8x = 0. x 3 x x + 5 SILVER GOLD The area of the rectangle is 130cm2. Find x. Solve the equation 2x2 + x = 50. (x + 5)cm2 (x + 7)cm2

Examination style question. Quadratic Equations; formula Examination style question. 3x + 2 The area of the pentagon is 156. (a) Show that x2 + 2x − 30 = 0. (b) Find the length of PQ. Give your answer to three significant figures. 2x + 1 x x + 10 Q R S T P

Quadratic Equations; formula Sort into groups… x2 + 6x + 2 = 0 x2 − 6x + 9 = 0 x2 − 2x + 6 = 0 x y x y y x