We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately...

We are learning to:- Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately solve quadratic equations by completing the square. (Grades A-A*).

Always aim high!LESSON OBJECTIVES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner

PLT Skills Which ones are you using?

AUTHORWhere are we in our journey?

Real life cross/curricular

links?www.mistrymaths.co.uk

http://www.mistrymaths.co.uk/

BRAIN IN GEAR


Self Manager


Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

Work out the following Mathematical anagrams:TASK

EXTENSIONDevelop your own Mathematical anagrams as above as a creative thinker.

DURAATICQ

NOETIFFICCE

GEARERRAN

EXAMPLEDITDIONA can be rearranged to make ADDITION

Quadratic

Coefficient

Rearrange

Write in standard form: 57.6

STARTER


Self Manager


Creative Thinker

Team Worker


using?PLT Skills

EXTENSION

TASK1) 2) 3)

5)

4)

6)

Solve:2x + 5y = 153x - 2y = 13

Distance = 925milesSpeed = 74mphTime = ……….minutes

Write the bearing.

Find the sum of one exterior angle in an regular decagon and one exterior angle in a regular hexagon?

Area shaded black?

8mWork out the perimeter

15cm

8cm

N

4cm

= 5.76 x 101

= 92574 = 12.5hours

750

Area of circle – Area of triangleΠ x r x r -

8 x 42

b x h2

= 3.14 x 7.5 x 7.5 -= 176.625 -16=160.6cm2

075°4x + 10y = 3015x - 10y = 65+19x = 95

x = 5 10 + 5y = 15

5y = 5

y = 1

8m

Π x d4 + r + r

= 3.14 x 164 + 8 + 8

=28.56m

Decagon → 36010 =36° Hexagon → 360

6 =60°


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsCOMPLETING THE SQUARE

EXAMPLE 1)ax + bx + c 2 = x + b

22( - b

2( )2+ c

(a)Rewrite the following in the form (x a) b+- +-

2

x + 6x - 112 (b) x - 8x + 52

Write down the formula first(x + ) – ( ) + cb

2b2

2 2

b = 6 c = -11

Substitute in the values for b and c(x + 6

2 )2 – ( 62 )2 + - 11

(x + 3)2 – (3 )2 - 11(x + 3)2 – 9 - 11(x + 3)2 - 20

Write down the formula first(x + ) – ( ) + cb

2b2

2 2

b = -8 c = 5

Substitute in the values for b and c(x + -8

2 )2 – (-82 )2 + 5

(x - 4)2 – (-4)2 + 5(x - 4)2 – 16 + 5(x - 4)2 - 11


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsTASK 1 (GRADE A)

1) 2) 3) 4)

5) 6) 7) 8)

COMPLETING THE SQUARE

Rewrite the following in the form (x a) b+- +-2

x + 4x - 22 x + 12x - 72 x - 6x + 52 x - 8x + 112

x + 2x - 92 x + 10x + 62 x - 14x - 122 x - 20x + 152


Self Manager


Creative Thinker

Team Worker




22( - b

2( )2+ c

Solve by completing the square. Leave your answer in the form a +-

x - 6x – 3 = 02

bx - 6x – 3 = 02

Write down the formula first(x + ) – ( ) + c = 0b

2b2

2 2

b = -6 c = -3

Substitute in the values for b and c(x + -6

2 )2 – (-62 )2 + - 3 = 0

(x - 3)2 – (-3)2 - 3 = 0(x - 3)2 – 9 - 3 = 0(x - 3)2 - 12 = 0

(x - 3)2 - 12 = 0(x - 3)2 =12x - 3 = 12+-x = 3 +- 12

4 32 3


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsTASK 2 (GRADE A*)

1) 2) 3) 4)

5) 6) 7) 8)


x + 2x – 5 = 02 x - 6x + 4 = 02 x + 10x + 7 = 02 x - 4x - 2 = 02

x + 12x + 3 = 02 x - 14x – 4 = 02 x - 2x - 7 = 02 x + 8x - 11 = 02

Solve the following by completing the square. Leave your answers in surd form.

10


Self Manager


Creative Thinker

Team Worker




22( - b

2( )2+ c

Solve by completing the square. Give your answer to 2 decimal places.

x + 2x – 9 = 02

x + 2x – 9 = 02

Write down the formula first(x + ) – ( ) + c = 0b

2b2

2 2

b = 2 c = -9

Substitute in the values for b and c(x + 2

2 )2 – ( 22 )2 + - 9 = 0

(x + 1)2 – ( 1 )2 - 9 = 0(x + 1)2 – 1 - 9 = 0(x + 1)2 - 10 = 0

(x + 1)2 - 10 = 0(x + 1)2 = 10x + 1 = 10+-x = -1+-

x = -1+ 10 x = -1 - 10x = 2.16 x = -4.16


Self Manager


Creative Thinker

Team Worker



1) 2) 3) 4)

5) 6) 7) 8)


x + 2x – 3 = 02 x - 4x + 2 = 02 x + 10x + 12 = 02 x - 6x - 13 = 02

x + 10x + 15 = 02 x - 16x – 13 = 02 x - 2x - 21 = 0

2 x + 2x - 9 = 02

Solve the following by completing the square. Round your answers to 2d.p. where appropriate.


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsEXTENSION 1 (GRADE A*)

1) 2) 3)

5) 6) 7)



2x + 4x – 8 = 02 2x + 12x – 20 = 02 3x - 12x + 9 = 02

5x + 30x = 452 x + 3x – 2 = 02 x - 5x = -32

Divide by 2 throughout Divide by 2 throughout Divide by 3 throughout

Divide by 5 and change RHS = 0 Make RHS = 0


Self Manager


Creative Thinker

Team Worker




Rearrange the following statements to give the complete solution, using the method of completing the square to the equation: ax + bx + c = 02

H, C, B, E, D, J, A, F, G, I


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsMINI-PLENARY 1 – BINGO


Draw a 3 x 3 grid as shown below:

Place any nine answers below into the grid (repeats forbidden)-8 -3 D 6

-4.5 4 -2 A 2 B -9 -10

C 7 -50 3


Self Manager


Creative Thinker

Team Worker




Find the value of ? below:

x + 4x + 5 = 02

(x + ?) + 1 = 02

2


Self Manager


Creative Thinker

Team Worker





x + 14x + 48 = 02

(x + ?) - 1 = 02

7


Self Manager


Creative Thinker

Team Worker





x - 6x - 16 = 02

(x + ?) - 25 = 02

-3


Self Manager


Creative Thinker

Team Worker




Which is answer is correct in surd form:

x + 4x + 3 = 02

A) x = -2 1-+ B) x = 2 1-+

C) x = -2 7-+ D) x = -2 7-+


Self Manager


Creative Thinker

Team Worker





x - 20x - 44 = 02

(x + ?) - 144 = 02

-10


Self Manager


Creative Thinker

Team Worker





x - 16x + 64 = 02

(x + ?) = 02

-8


Self Manager


Creative Thinker

Team Worker





x - 8x + 7 = 02

C) x = 4 9-+

B) x = -4 9-+A) x = -4 23-+

D) x = 4 23-+


Self Manager


Creative Thinker

Team Worker





x - 9x + 20 = 02

(x + ?) + 40.25 = 02

-4.5


Self Manager


Creative Thinker

Team Worker





x - 8x + 18 = 02

(x - 4) + ? = 02

-2


Self Manager


Creative Thinker

Team Worker





x + 4x + 7 = 02

(x + 2) + ? = 02

3


Self Manager


Creative Thinker

Team Worker





x - 4x - 12 = 02

C) x = -2 16-+

B) x = -2 8-+A) x = 2 8-+

D) x = 2 16-+


Self Manager


Creative Thinker

Team Worker





x + 6x + 15 = 02

(x + 3) + ? = 02

6


Self Manager


Creative Thinker

Team Worker





x + 12x + 27 = 02

(x + 6) + ? = 02

-9


Self Manager


Creative Thinker

Team Worker





x - 18x + 31 = 02

(x - 9) + ? = 02

-50


Self Manager


Creative Thinker

Team Worker





x + 10x + 24 = 02

C) x = -5 1-+

B) x = 5 1-+A) x = -5 -1-+

D) x = -5 49-+


Self Manager


Creative Thinker

Team Worker





x - 12x + 40 = 02

(x - 6) + ? = 02

4


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsMINI-PLENARY 2 – ASSESSING UNDERSTANDING

Bogdar rewrites the expression x + px + q by completing the square. He correctly does this and gets (x – 7) – 52. What are the values of p and q?


2

2

(x – 7) – 522

= (x – 7)(x – 7) – 52

= x2 + 49 - 7x - 7x - 52

= x2 - 14x - 3

p q

p = -14 and q = -3

DISCOVERY


Self Manager


Creative Thinker

Team Worker


using?PLT Skills

LINK BACK TO OBJECTIVES

- Accurately solve quadratic equations by completing the square.

What grade are we

working at?

PLENARY ACTIVITY 1 – CONNECT 4


Self Manager


Creative Thinker

Team Worker



Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose.

PLENARY ACTIVITY 1 – CONNECT 4 ANSWERS


Self Manager


Creative Thinker

Team Worker




{-3, -1}

{4, -2}

{-2, 6}

{8, -6}

{-2, -10}

{12, -4}

{7, -9}

{5, 3}

{-3, -7}

{3, -1}

{-1, 5}

{1.27, -17.27}

{4.83, -6.83}

{9.16, 2.84}

{5.56, -7.56}

{-1.28, -11.72} {11.52, -2.52}

{-5.61, 1.61}

{-7, 1}

{-5.45, -0.55} {-1}

{-3.41, -0.59}

{-5.41, -2.59}

{-8.36, 0.36}

{-6.74, -0.74}

{-2, 0}

{-3.73, -0.27}

{4.41, 1.59}

{6.32, -0.32}

{7.16, 0.84}

{9, -1}

{9.24, 0.76}

{11.08, -1.08}

{11.57, 0.43}

{3.45, -1.45}

{5.32, -1.32}

PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION


Self Manager


Creative Thinker

Team Worker


using?PLT Skills

(a) Find the values of a and b such that:


1) x + 6x – 3 = (x + a) + b2 2

(2 marks)

(b) Hence, or otherwise, solve the equation: giving your answers in surd form.

x + 6x – 3 = 02

(3 marks)

(x + ) – ( ) + c = 0b2

b2

2 2 b = 6 c = -3

(x + 62 )2 – ( 6

2 )2 + - 3 = 0

(x + 3)2 – ( 3 )2 - 3 = 0

(x + 3)2 – 9 - 3 = 0(x + 3)2 - 12 = 0

a ba = 3 and b = -12

(x + 3)2 - 12 = 0

12

(x + 3)2 - 12 = 0(x + 3)2 = 12x + 3 = 12+-x = -3+-

4x = -3+- 3

2x = -3+- 3

Draw your brain

What have you learnt?

In your brain, write or draw everything you can remember about solving quadratic equations by completing the square. It can be a skill or a

reflection, or something else that might be prominent in your brain.

What grade are we

working at?

Where are we in our

journey?

.

How well do you understand the task?

I don’t understand

I nearly understand

I fully understand

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

SELF ASSESSMENT Plenary

Activity

www.mistrymaths.co.uk


SELF ASSESSMENT Plenary

Activity

On your post it notes…

Think about how you can improve your

work.

WWW (What Went Well)

EBI (Even Better If)

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

www.mistrymaths.co.uk



Self Manager


Creative Thinker

Team Worker


using?PLT SkillsTASK 1 (GRADE A)

1) 2) 3) 4)

5) 6) 7) 8)


Rewrite the following in the form (x a) b+- +-2

x + 4x - 22 x + 12x - 72 x - 6x + 52 x - 8x + 112

x + 2x - 92 x + 10x + 62 x - 14x - 122 x - 20x + 152


Self Manager


Creative Thinker

Team Worker



1) 2) 3) 4)

5) 6) 7) 8)


x + 2x – 5 = 02 x - 6x + 4 = 02 x + 10x + 7 = 02 x - 4x - 2 = 02

x + 12x + 3 = 02 x - 14x – 4 = 02 x - 2x - 7 = 02 x + 8x - 11 = 02



Self Manager


Creative Thinker

Team Worker



1) 2) 3) 4)

5) 6) 7) 8)


x + 2x – 3 = 02 x - 4x + 2 = 02 x + 10x + 12 = 02 x - 6x - 13 = 02

x + 10x + 15 = 02 x - 16x – 13 = 02 x - 2x - 21 = 0

2 x + 2x - 9 = 02

Solve the following by completing the square. Round your answers to 2d.p. where appropriate.


Self Manager


Creative Thinker

Team Worker



1) 2) 3)

5) 6) 7)



2x + 4x – 8 = 02 2x + 12x – 20 = 02 3x - 12x + 9 = 02

5x + 30x = 452 x + 3x – 2 = 02 x - 5x = -32


Self Manager


Creative Thinker

Team Worker




Rearrange the following statements to give the complete solution, using the method of completing the square to the equation: ax + bx + c = 02


Self Manager


Creative Thinker

Team Worker


using?PLT SkillsMINI-PLENARY 2 – ASSESSING UNDERSTANDING

Bogdar rewrites the expression x + px + q by completing the square. He correctly does this and gets (x – 7) – 52. What are the values of p and q?


2

2

PLENARY ACTIVITY 1 – CONNECT 4


Self Manager


Creative Thinker

Team Worker




PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION


Self Manager


Creative Thinker

Team Worker


using?PLT Skills

(a) Find the values of a and b such that:


1) x + 6x – 3 = (x + a) + b2 2

(2 marks)

(b) Hence, or otherwise, solve the equation: giving your answers in surd form.

x + 6x – 3 = 02

(3 marks)

We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately...

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Transcript of We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately...