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Enhancing Mathematical Learning Skills through Expanding Brackets

In this lesson, students will enhance their mathematical learning skills by accurately expanding and simplifying single brackets. They will also apply enterprise skills such as creativity, independence, and reflection. The lesson objectives are to enhance mathematical learning skills and accurately expand and simplify single brackets.

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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 and simplify. (Level 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: Simplify Expression Product 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: 4, 1, -2, -5, ….. Increase 150kg by 60%. + 7 150kg + 90kg 10% = 15kg 45 24 10 5 3 5 1 11 2 8 56 12 7 12 x6 x6 240kg = 90kg 60% = 28 80 8 24 12 6 4 2 7 142 2) Simplify: 9b + 3c + 3b – 7c -3 -3 -3 -3n 12b + 7 = - 4c 3) Work out the following: -3 x 20 + 7 20th Term = X 2 X 3 20th Term = -53 (a) (b) + ÷ X 2 X 3 2) Use a calculator to write the following as percentages: 2 9 10 2 5 x = = (a) 45 out of 80 = = = 56.3% (1d.p.) 100 = X 4) Work out the following: 240 seconds x x (b) 24 out of 142 4minutes £56 of of (b) 100 16.9% (1d.p.) = ÷ ÷ X £16 100 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 and simplify: (d) (a) (c) (b) b(5b - 6) - b(3b – 4) 4(v – 3w) - 2(4v – w) a(a + 4b) - b(2a – 5b) 3(2g + 3h) + 2(4g – h) 6g 8g 4v - 9h - 12w 8v + 2h - + + 2w = = 14g - 4v + 7h - 10w = = - 4b - 6b + 2 2 2 2 2 2 2b 5b a a 2 2ab 4ab = - + 5b 3b 5b + + = - 2b = + 2ab =

  6. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 1 (LEVEL 6) 1) Expand the following brackets and simplify: 4a 2a 30p + 4b 2b 12q + 9p + + + 3q + = = (b) (d) (a) (c) (e) (f) 2(3x – 2y) + 6(2x + y) 7(2e + t) + 2(e – 3t) 7(4u – 3k) + 5(2u – k) 4(a + b) + 2(a + b) 5(m - x) + 3(2m + x) 6(5p + 2q) + 3(3p + q) 6a 39p + 6b + 15q = = 2e - 14e 7t - 6x 4y 12x + 6t + + + 6y = = 16e 18x + t + 2y = = - 5m - - 5x 21k 10u + 28u 5k 3x 6m + + = = 11m 38u - 2x - 26k = =

  7. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 2 (LEVEL 6) 1) Expand the following brackets and simplify: - 5m 24h 3m 8g + 5n 2n - 4g - - + 2h = = (b) (c) (a) (d) 8(g + 3h) - 2(2g + h) 7(d + 2e) - 3(2d – 3e) 5(m + n) - (3m + 2n) 6(2 – 3x) - 3(2 – 5x) 4g 2m + 3n + 22h = = - 7d + 14e 6d 12 18x 6 - 9e - + + 15x = = - 3x d 6 + 23e = =

  8. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS TASK 3 (LEVEL 6) 1) Expand the following brackets and simplify: 2r 2h 2 2 dh 7mn - + 2mn + + dh + + = = (b) (a) (c) (d) (e) (f) y(4x – 2y) + x(7y + 5x) e(5e + 4f) - f(2e + 3f) k(4k – 2t) - t(3k + 7t) j(j + 7r) - r(2r – 9j) d(d + h) + h(2h + d) m(3m + 7n) + n(2m – 4n) 2 7t 2 5x 4n 3f 2 2 + 2dh + 9mn = = - 4xy 2 2y - 4ef - 7xy 2ef + + + = = + 11xy + 2ef = = 2 2 2 2 2 2 2 2 2 2 2 3m 5e 4k 4k 5x 3m 5e j d d j 2 2 2 2 2 2 - 2y - 7t - 4n - 3f + 2h - 2r 7jr - = 9jr + + - 2kt - - 3kt = + 16jr = = - 5kt

  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 6) – NAUGHTS AND CROSSES GAME In pairs, create three of your own naughts and crosses grids on expanding brackets and simplifying as shown below. Best out of three to win.

  10. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? EXPANDING BRACKETS EXTENSION (LEVEL 6) 1) Match the following expressions with their respective answers: EXPRESSIONS ANSWERS 8(x + 2) + 7(x – 3) – 5(x – 4) 9 + 6(x – 5) + (3x – 8) 2(x + 3) –7(x – 1) – (4x + 15) 7x – (3x + 2) + (2x – 7) + 10 6(2x + 5) – 4(3x – 4) – (2x + 7) + 2x 9x – 29 – 9x – 2 10x + 15 6x + 1 39

  11. 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: (b) (a) j(j + 7r) - r(2r – 9j) 6(2 – 3x) - 3(2 – 5x) - 12 18x 6 - 2r 7jr - - = 15x 9jr - + = + 33x 6 = + 16jr = 2 2 j j 2 - 2r

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

  13. 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)

  14. 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

  15. Expand and simplify: 2(x+5) + 2(x+5) 4x+20

  16. Expand and simplify: 3(x+2) + 2(x+6) 5x+18

  17. Expand and simplify: 5(x+2) + 3(x+5) 8x+25

  18. Expand and simplify: 6(x+7) + 2(x+2) 8x+46

  19. Expand and simplify: 3(y+3) + 3(y+6) 6y+27

  20. Expand and simplify: 3(x+8) + 2(x-5) 5x+14

  21. Expand and simplify: 5(x+4) + 3(x-2) 8x+14

  22. Expand and simplify: 4(x+6) + 2(x-2) 6x+20

  23. Expand and simplify: 5(x+7) + 4(x-2) 9x+27

  24. Expand and simplify: 6(x+2) + 4(x-3) 10x

  25. Expand and simplify: 3(x-2) + 2(x+4) 5x+2

  26. Expand and simplify: 4(x-1) + 2(x+3) 6x+2

  27. Expand and simplify: 5(x-3) + 4(x+6) 9x+9

  28. Expand and simplify: 6(x-4) + 4(x+5) 10x-4

  29. Expand and simplify: 6(x-3) + 4(x+3) 10x-6

  30. Expand and simplify: 3(x-2) + 2(x-3) 5x-12

  31. Expand and simplify: 5(x-4) + 3(x-5) 8x-35

  32. Expand and simplify: 8(x-3) + 4(x-6) 12x-48

  33. Expand and simplify: 9(x-3) - 5(x-4) 4x-7

  34. Expand and simplify: 10(x-6) - 7(x-9) 3x+3

  35. Expand and simplify: m(n+g) + g(g+7m) g +8mg 2 +mn

  36. Expand and simplify: t(m+w) + w(w+6t) w +7tw 2 +mt

  37. Expand and simplify: 4r(a+6) + a(a+7r) a +11ar 2 +24r

  38. Expand and simplify: 8t(d+9) + d(d+5t) d +13dt 2 +72t

  39. Expand and simplify: 8y(z-2) - y(y-7z) -y +15yz 2 -16y

  40. What level 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 expanding single brackets and simplifying. It can be a skill or a reflection, or something else that might be prominent in your brain.

  41. 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

  42. 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

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