Transcript Slide 1

Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Finding connections between different words. (Which
PLT skills?)
- Accurately finding the area of a triangle using sine.
(Grades A/A*)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
BRAIN IN GEAR
PLT Skills
Self
Manager
Team
Worker
Which ones are you using?
EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
CEASELN
Scalene
RAEA
Area
DINDCLUE GALEN
Included Angle
EXTENSION
Develop your own Mathematical anagrams as above as a
creative thinker.
Creative
Thinker
PLT Skills
Effective
Participator
TASK
1) Find the area of:
7cm
4cm
Independent
Enquirer
Reflective
Learner
STARTER
standard form
5
= 7.1 x 10
100°
90°
111°
x = 115°
3x - 4
x + 11
2x - 8
2x + 1 + 3x - 4 + 2x - 8 + x + 11= 360
= 360
8x
÷8
EXTENSION
-
100
Pentagon
1
adds to =
( 100 ) 3
540°
x = 540°- 100°- 124°- 111°- 90°
2x + 1
x
5) Value of:
Reciprocal
3)
÷8
6x4
Area of a triangle =
2
Area of a triangle = 12cm2
124°
Which ones are you using?
2) Write 710000 in
6cm
x
Team
Worker
Work out x:
5cm
4) Work out x:
Self
Manager
3
2
1
=
103
1
=
1000
Power
Root
6m
6m
4m
5m
x
Work out x:
x
5
x
x
10
4
10
x5
=
4
=
= 12.5m
= 45°
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF A TRIANGLE
Self
Manager
Which ones are you using?
INTRODUCTION – PROOF
B
c
A
o
a
θ
b
1
xbxh
2
1 xb
x a x sin θ
Area of a triangle =
2
1
ab sin θ
Area of a triangle =
2
Area of a triangle =
H
h
D
Team
Worker
C
A
sin θ =
sin θ =
opposite
hypotenuse
h
a
h = a x sin θ
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF A TRIANGLE
Self
Manager
Which ones are you using?
EXAMPLE 1
Find the area of the triangle below giving your answer to 3 s.f. :
B
a 5cm
C
36° θ
9cm
b
1
ab sin θ
2
1 x
Area of a triangle =
5 x 9 x sin 36°
2
Area of a triangle =
Area of a triangle = 13.2cm2
Team
Worker
A
Creative
Thinker
Effective
Participator
PLT Skills AREA OF
TASK 1 (GRADE A)
Independent
Enquirer
Reflective
Learner
A TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
1) Find the areas of the triangles below giving your answers to 3 s.f. :
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF A TRIANGLE
Self
Manager
Which ones are you using?
EXAMPLE 2
Find the missing side a below giving your answer to 3 s.f. :
B
Area = 8.2cm 2
aa
C
36°
θ
7cm
b
A
1
ab sin θ
2
1
8.2 = 2 x a x 7 x sin 36
8.2 = a x 3.5 x sin 36
Area of a triangle =
8.2
3.5 x sin 36 = a
a = 3.99cm
Team
Worker
Creative
Thinker
Effective
Participator
PLT Skills AREA OF
TASK 2 (GRADE A)
Independent
Enquirer
Reflective
Learner
A TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
1) Find the missing lengths in the triangles below giving your answers to 3 s.f. :
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF A TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
EXAMPLE 3
Find the area of the triangle below giving your answer to 3 s.f. :
B
c 10cm
14cm a
θA
A
20cm
1
b
ab sin θ
2
1
bc sin θ
Area of a triangle =
2
1 x 20 x
10 x sin 40.54
Area of a triangle =
2
Area of a triangle =
Area of a triangle = 65.0cm2
Cannot use the
formula until we
calculate a missing
angle for θ
C
Use the cosine rule to find θ
b² + c² - a²
cos A =
2bc
2
20 + 10 2 - 142
=
cos θ
2 x 20 x 10
304
cos θ =
400
- 1 304
θ = cos 400
θ = 40.54°
Creative
Thinker
Effective
Participator
PLT Skills AREA OF
TASK 3 (GRADE A*)
Independent
Enquirer
Reflective
Learner
A TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
1) Find the missing lengths in the triangles below giving your answers to 3 s.f. :
(a)
(b)
(d)
(e)
(c)
(f)
Creative
Thinker
Effective
Participator
Independent
Enquirer
PLT Skills AREA OF A
EXTENSION (GRADE A*)
Reflective
Learner
TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
1) Calculate the area of triangle PQR without a calculator:
Q
It does not matter
which side given you
take to be a or b
a 6cm
P
45°
R
7√2cm b
1
ab sin θ
2
1
x 6 x 7√2 x sin 45
Area of a triangle =
2
1
x 6 x 7√2 x √2
Area of a triangle =
2
2
Area of a triangle =
42√2 √2
4
Area of a triangle = 42 x 2
4
Area of a triangle =
Area of a triangle = 21cm 2
Creative
Thinker
Effective
Participator
Independent
Enquirer
PLT Skills AREA OF A
EXTENSION (GRADE A*)
Reflective
Learner
TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
2) Calculate the area of the kite below :
b
25cm
a
1
ab sin θ
2
1
bc sin θ
Area of a triangle =
2
1 x 25 x
40 x sin 133.43
Area of a triangle =
2
Area of a triangle =
θ
60cm
Area of a triangle = 363.1074cm2
40cm
c
Splits into two
congruent triangles
Cannot use the
formula until we
calculate a missing
angle for θ
Area of kite = 726.21cm2
Use the cosine rule to find θ
b² + c² - a²
cos A =
2bc
2
2
2
40
25
60
+
cos θ =
2 x 25 x 40
-1375
cos θ =
2000
- 1 -1375
θ = cos 2000
θ = 133.43°
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
AREA OF A TRIANGLE
Self
Manager
Team
Worker
Which ones are you using?
MINI-PLENARY – SPOT THE MISTAKES
1) Find the area of the triangle
1
ac sin θ
2
800cm
1 x
Area of a triangle =
8 x 11 x sin 67°
2
Area of a triangle =
Area of a triangle = 40.5cm2
2) Find the length of c
1
ac sin θ
2
1
84 = 2 x 16 x c x sin 32
84 = c x 8 x sin 32
Area of a triangle =
sin
÷
84 x 8 x cos 32 = c
c = 19.8cm
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
DISCOVERY
Self
Manager
Team
Worker
Which ones are you using?
LINK BACK TO OBJECTIVES
- Accurately finding the area of a triangle
using sine.
What grade
are we
working at?
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills AREA OF A TRIANGLE Which ones are you using?
PLENARY ACTIVITY– ASSESSING UNDERSTANDING (GRADE A)
Applying the skills and knowledge you have acquired today, work
out the area of the shape below:
1
ab sin θ
2
1 x
Area of a triangle A =
9 x 13 x sin 60°
2
D
Area of a triangle A =
7m
B
85°
Area of a triangle A = 50.7m2
C
1
ad sin θ
2
1 x
Area of a triangle B =
7 x 13 x sin 85°
2
Area of a triangle B =
13m
60°
9m
A
A
Area of a triangle B = 45.3m2
B
Area of full shape = 50.7 + 45.3
Work out the area of each triangle
and add the answers together
Area of full shape = 96m2
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about finding
the area of a triangle using sine. It can be a skill or a reflection, or
something else that might be prominent in your brain.
Where are we
in our
journey?
What grade
are we
working at?
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
www.mistrymaths.co.uk
I fully
understand
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
Enterprise Skills SELF ASSESSMENT 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