Transcript Length, area and volume BAA

Situation
Choose the activity(ies) that best suit
your students’ learning needs.
A short activity to get students
thinking about the information in a
Warm
up – ideal for the beginning
question
of the lesson
What are
Four questions to encourage
students to think about alternative
the possibilities?
questions using the same
information
Four questions to encourage
students to use higher order
Thinkingthinking
harder
skills to consider question
alternatives
Some
Three more questions to practise
theto
same
more
tryapproach in different
contexts
An opportunity for students to
assess and reflect on their
Reflection
progress, including the grade they
are working at
Content covered
Test
Key points which can be printed
and used
at home or in pairs in the
yourself
cards
classroom
Length, area and volume BAA*
Situation – Content covered
Reflection
C
Length, area and volume
Solve perimeter and area problems involving shapes
involving circles
C
Length, area and volume
Use Pythagoras’ theorem
C
Length, area and volume
Solve perimeter and area problems involving shapes
involving circles
B
Length, area and volume
Use trigonometry to solve right-angled triangles
A*
Length, area and volume
Use trigonometry in three dimensions
A*
Length, area and volume
Find the volume of the frustum of a truncated cone
A
Length, area and volume
Calculate the lengths of circular arcs
A
Length, area and volume
Calculate the areas of sectors
A
Length, area and volume
Calculate the surface areas of cylinders, cones and spheres
A
Length, area and volume
Solve area and volume problems in similar shapes
A
Length, area and volume
Solve problems involving surface area and volume
A
Length, area and volume
Calculate the volumes of spheres, cones and pyramids
Length, area and volume BAA*
Situation – Warm up
Answers
The shape is made up of a semi-circle
of radius 4 cm and an isosceles triangle.
O is the centre of the circle.
1. What is the length of OC?
2. What is the length of AO?
3. What size is ABO?
4. Make up a simple question about this situation.
Length, area and volume BAA*
Situation – What are the possibilities?
Answers
The shape is made up of a semi-circle
of radius 4 cm and an isosceles triangle.
O is the centre of the circle.
Question 3
Three kinds of marks can be
given:
1. What can you work out from this information?
2. What is the area of the shape?
(4 marks)
3. Make up a mark scheme for this question.
4. Write your own exam-style question about this situation.
Prompts
B for something being correct,
irrespective
Question 4 of method
Use the Prompts button to help
M
for carrying
out unfamiliar
a correct step
students
who are
with this style of question.
A for a correct answer
Use the Thinking prompts
button to help students be more
creative with their questions.
Thinking
prompts
Length, area and volume BAA*
Situation – Thinking harder
Answers
The shape is made up of a semi-circle
of radius 4 cm and an isosceles triangle.
O is the centre of the circle.
1. What if the shape was 3-D, what would be the volume of the cone?
2. What if the shape was 3-D, what would be the surface area of the cone?
3. If the shape was 3-D, and the cone was made using a sector of a circle, what
would the radius of that circle be?
4. If the shape was 3-D, what would be the surface area of the whole shape?
Length, area and volume BAA*
Situation – Some more to try
Answers
1. The diagram shows a sector of a circle.
The arc length is 10 cm. What size is x?
2. The diagram shows a square-based
pyramid with base sides 10 cm and
height 12 cm.
What angle does plane CDX make with
the base?
3. The diagram shows a frustum of a cone.
The radii of the top and bottom are
3 cm and 5 cm respectively.
Calculate the volume of the frustum.
Length, area and volume BAA*
Situation – Reflection
Click below the button to reveal
the grades.

I can

Use Pythagoras’ theorem
Solve perimeter and area problems involving shapes
involving circles
Use trigonometry to solve right-angled triangles
Calculate the areas of sectors
Calculate the surface areas of cylinders, cones
and spheres
Self assess
• Find or write some evidence to support your assessment.
• Write down your next steps.
• You may wish to use the Test yourself cards.
Length, area and volume BAA*

C
C
B
A
A
Situation – Test yourself cards
These cards contain
some of the key
terms and skills you
will need to answer
length, area and
volume questions.
Copy down the
ones you need to
practise or ask
your teacher for a
printout.
What is Pythagoras’ theorem?
What is a sector?
a2 + b2 = c2 in a right-angled triangle,
with c on the longest side.
Part of a circle, like a slice of pizza.
How do you work out angles
using trigonometry?
How do you know when to use tangent?
Divide the appropriate lengths, then use the The hypotenuse is not involved – you do not
inverse sin, cos or tan buttons.
know it or need to find it.
When do you use sine?
When do you use cosine?
When you are given or are finding
the hypotenuse and the side opposite
the angle.
When you are given or are finding the
hypotenuse and the side next to the angle.
How do you work out areas of sectors?
How do you work out surface area?
You find the fraction of the whole circle
using the angle and it is the same fraction
of πr².
Add up the areas of all the shapes on
the surface.
Length, area and volume BAA*
Situation – Answers for Warm up
1. 4 cm
2. 7.5 cm
3. 61.9°
4. Possible simple questions include:
– How long is OB? [answer 4 cm]
– What is the total length of the shape? [answer 12 cm]
– What is the size of AOB? [answer 90°]
Length, area and volume BAA*
Situation – Answers for What are the possibilities?
1. In addition to those in Warm up slide question 4, some suggestions include:
– The length of the arc of the semi-circle
– The perimeter of the triangle
2. and 3.
AO
= √(8.5² – 4²)
= 7.5 cm
Area of triangle
=  × 8 × 7.5
= 30 cm²
Area of semi-circle
=  × π × 4²
= 25.13 cm²
Total area
= 30 + 25.13
= 55.13 cm²
1 mark
1 mark
1 mark
1 mark
4. Possible exam questions, in addition to those in Warm up question 4, are:
– Work out the perimeter of this shape. [2 marks, grade B]
Length, area and volume BAA*
Situation – Answers for Thinking harder
1. 125.7 cm³
2. 106.8 cm²
3. 8.5 cm
4. 207.3 cm²
Length, area and volume BAA*
Situation – Answers for Some more to try
Click on the question to reveal the
solution.
79.6°
1. The diagram shows a sector of a circle.
The arc length is 10 cm. What size is x?
2. The diagram shows a square-based
pyramid with base sides 10 cm and
height 12 cm.
67.4°
What angle does plane CDX make with
the base?
3. The diagram shows a frustum of a cone.
The radii of the top and bottom are
3 cm and 5 cm respectively.
410.5 cm3
Calculate the volume of the frustum.
Length, area and volume BAA*
Situation – Prompts
Think of a
really easy
question…
Think of a
really short
question…
Think of a really
obvious question…
Think of a
really hard
question…
Think of a
really boring
question…
Think of a really
strange question…
Length, area and volume BAA*
Situation – Thinking prompts
Could I make a
question with
fractions in it?
Is there a question
that would mean
adding some of the
numbers?
Is there a
question that
would mean
dividing?
Could I make a
question with an
answer less than 1?
Could I make a
question worth 5
marks?
Is there a
question that
would involve the
number 90?
Could I make a
question worth 2
marks?
Is there a question
that would involve
multiplication?
Length, area and volume BAA*