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Enhancing Mathematical Learning Skills through Expanding Brackets

This lesson aims to enhance students' mathematical learning skills by accurately expanding single brackets. Students will also engage in creative problem-solving activities and develop entrepreneurial skills.

patriciajmiller
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Enhancing Mathematical Learning Skills through Expanding Brackets

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  1. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Real life cross/curricular links? Where are we in our journey? Which ones are you using? Enterprise Skills LESSON OBJECTIVES Always aim high! We are learning to: • Enhance our Mathematical learning skills. (Which Enterprise skills?) • Accurately expand single brackets. (Levels 5-6) AUTHOR www.mistrymaths.co.uk

  2. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker LEARNING JOURNEY Enterprise Skills Which ones are you using?

  3. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker BRAIN IN GEAR Enterprise Skills Which ones are you using? EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Expand Term Variable EXTENSION Develop your own Mathematical anagrams as above as a creative entrepreneur.

  4. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker STARTER Enterprise Skills Which ones are you using? TASK EXTENSION 1) 1) Find the nth term and 20th term of: 8, 3, -2, -7, ….. Decrease 120kg by 30%. + 8 120kg – 36kg 10% = 12kg 32 25 9 11 1 2 7 3 2 10 80 14 8 14 x3 x3 84kg = 36kg 30% = 40 78 10 18 14 7 2 6 9 145 2) Simplify: 2b + 7c + 8b – 4c -2 -2 -2 -5n 10b + 13 = + 3c 3) Work out the following: -5 x 20 + 13 20th Term = X 2 X 7 20th Term = -87 (a) (b) + ÷ X 2 X 7 2) Use a calculator to write the following as percentages: 4 7 18 6 3 x = = (a) 32 out of 78 = = = 41.0% (1d.p.) 100 = X 4) Work out the following: 180 seconds x x (b) 25 out of 145 3minutes £81 of of (b) 100 17.2% (1d.p.) = ÷ ÷ X £18 70 seconds = =

  5. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS EXAMPLES 1) Expand the following brackets: (b) (a) (d) (c) (f) (g) (e) (h) -3(x + y) 5(2w – 4) -(4x – 9) 6(a + b) 5w + 3(w – 4m) 2(3m – 4n) – 7n p(3q + 7) -4(2d – 8e) 10w - 3pq 20 7p 6a 6b + = + = = - -3x -4x 3y 9 -8d + 32e = = + = - 5w 3w = 12m - 6m - 8n + 7n = 6m 8w - - = = 12m 15n

  6. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 2 (LEVEL 5) TASK 1 (LEVEL 5) 1) Match pairs and find the odd one out: 1) Expand the following brackets: (a)3(y + 1) = (b) 4(x + 2) = (c) 2(x – 6) = (d) 5(y – 9) = (e) 6(a + b) = (f) 3(f + d) = (g) 2(k – m) = (h) 6(j – p) = (i) 10(2x + y) = (j) 10(3a – 2b) = 3y + 3 4x + 8 2x - 12 5y - 45 6a + 6b 3f + 3d 2k – 2m 6j – 6p 20x + 10y 30a – 20b

  7. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 3 (LEVEL 5) – NAUGHTS AND CROSSES GAME In pairs, create three of your own naughts and crosses grids on expanding brackets as shown below. Best out of three to win.

  8. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) Draw a 3 x 3 grid as shown below: Place any nine numbers below into the grid (repeats forbidden)

  9. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 3(x+1)=3x+? 3

  10. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 5(x+2)=?x+10 5

  11. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 10(x+7)=10x+? 70

  12. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 3(x+6)=3x+? 18

  13. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 6(-7+x)=?+6x -42

  14. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 5(2x+11)=?x+55 10

  15. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 3(4x+10)=?x+30 12

  16. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) ?(x+2)=6x+12 6

  17. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) ?(2x+1)=4x+2 2

  18. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 2(t-12)=2t+? -24

  19. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 3(?x+3)=12x+9 4

  20. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 2 5d(3+2d)=?d+10d 15

  21. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) ½ (6x+10)=3x+? 5

  22. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 7(t-3)=?t-21 7

  23. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) ?(4z-5)=36z-45 9

  24. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 4 (LEVEL 5) 8(y+3)=8y+? 24

  25. (e) a(2b + c) Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker (d) (e) (d) (f) (b) (a) (c) (f) (e) (a) (b) (f) (d) (c) (g) (i) (b) (h) (a) (j) (i) (h) (c) (g) s(t + u) 12x - 4(3y + 2x) 4h + 5(2h + 3s) 6(4g + 3h) 2(2m – 3n) – 8n 16p - 3(3q – 4p) -(7 – 2x) -(3p + 4) -2(d - f) -(q - p) -(a + b) 3(5j – 2k) 8(a + b + c) 10(13 – 5n) e(5 + 2f) 4(3d + 2) 9(m - n) 5(p + q) -3(g + 2) -4(6d – 3f) 7(d + f) – 2d -5(2h + 3i) 3w + 2(w + x) -3(-2j + k) Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 5 (LEVELS 5 - 6) 1) Expand the following brackets: 5p + 5q st + su 2ab + ac 9m – 9n 12d + 8 15j – 6k 5e + 2ef 130 – 50n 24g + 18h 8a + 8b + 8c 2) Expand the following brackets: -a - b -q + p -3g - 6 -3p - 4 -7 + 2x -10h – 15i -2d + 2f -24d + 12f 6j – 3k 3) Expand the following brackets: = 7d + 7f – 2d = 4h + 10h + 15s = 3w + 2w + 2x = 5d + 7f = 14h + 15s = 5w + 2x = 12x – 12y - 8x = 16p – 9q + 12p = 4m – 6n – 8n = 4x – 12y = 4m – 14n = 28p – 9q

  26. EXTENSION 1 (LEVELS 5 - 6) – CATCHPHRASE 3(x + 1) 7(x + y) 3(3x + 3) 5(x + 8) 8(2 + y) x(x + 3) 12(x + 3) 4(9 + x) 7(4 + y) 17(2 + x) 2x(x + 2) 2y(x + y) 2(1 – x) z(z + 5) 18(x + 1 – y) 2(x + 7) 9(2x + 4) 2x(x + 5) 3(1 – 2x) 8(8x + 5) 4y(y + 1) x(x + 9) 4(3x + 4) 9(x) 12(x – 3)

  27. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS EXTENSION 2 (LEVEL 6) 1) Expand the following brackets: 2) Show that: a(b + c) + b(a + c) + c(a + b) always equals the same as 2(ab + bc + ac) (a) y(y + 5) = (b) p(p – 4) = (c) b(b + c) = (d) q(2q + 4) = (e) t(2t – 3s) = (f) 2a(a + 3b) = (g) 2s(3s – 2t) = (h) 4q(2q + 3p) = (i) q2(3q + 2p) = (j) d2(4d - 2e) = 2 3 2 2 2 2 2 3 2 2 8q + 12pq 2q + 4q 2a + 6ab 6s - 4st b + bc 2t - 3st 3q + 2pq p - 4p y + 5y 4d - 2d e a(b + c) + b(a + c) + c(a + b) ac + bc + ab + ac ab + bc + = 2ab + 2ac + 2bc = 2(ab + bc + ac) = 2 2

  28. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS MINI-PLENARY ACTIVITY – SPOT THE MISTAKE Find the mistakes: 1) 3(x + 6) = 3x + 6 2) 9(p + 4) = p + 36 3) 5(x² - 3) = 5x² - 15 4) c(c + 4) = c² + 4 + c 5) –3(x + 1) = -3x + 3 6) 6(x + 5) = 6x + 11 7) 8(w + 3) = w + 24 8) 2(x² - 4) = 2x² + 8 9) f(e + 4) = ef + 4e 2 minutes End

  29. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker • LINK BACK TO OBJECTIVES • Accurately expand single brackets. What level are we working at? DISCOVERY Enterprise Skills Which ones are you using?

  30. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker A H S M T B S E S U R T Enterprise Skills Which ones are you using? EXPANDING BRACKETS PLENARY ACTIVITY (BINGO)

  31. A C E B D F H J G I K M O L N P R T Q S U W Y V X

  32. Expand 2(x+5) 2x+10

  33. Expand 9(t+2) 9t+18

  34. Expand 6(2x+3) 12x + 18

  35. Expand 7(3x+2) 21x + 14

  36. Expand 5(6x-5) 30x - 25

  37. Expand 6(x+y) 6x + 6y

  38. Expand 5(3d+3) 15d + 15

  39. Expand b(2c+d) 2bc + bd

  40. Expand 5(3j - 4m) 15j – 20m

  41. Expand -(w+y) -w - y

  42. Expand -(8-2f) -8 + 2f

  43. Expand -3(4d-2) -12d + 6

  44. Expand 3(a+b+c) 3a + 3b + 3c

  45. Expand m(n+8) mn + 8m

  46. Expand g(h+9) gh + 9g

  47. Expand -p(m+2) -mp – 2p

  48. Expand y(t+m) yt + ym

  49. Expand r(m-2d) mr – 2dr

  50. Expand y(y+7) y + 7y 2

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