LESSON PLAN
Teacher’s name:
Unit title:
DIONDA JONAS
Subject title: MATHEMATICS
Date:
2D AND 3D SHAPE
Class: YEAR 8
Shaping our Children’s future
Week No.:
Week 17
Topic:
Quadrilaterals and polygons
Lesson Objectives:
Identify and describe the hierarchy of quadrilaterals.
Number of Students:
2
Relevance of the lesson:
Resources and Materials: Learners Book, notebooks, mini whiteboards
Days and Dates:
Stages and Time
Starter
10 Minutes
Activities
From Learners Book
‘Getting Started’
Learners should have little difficulty with most of the material. However, before learners attempt these
questions, I will discuss what they remember about the names of various parts of a circle. Some learners
may have forgotten what a vertex is (plural: vertices). I will give a brief discussion on faces, edges and
vertices of cubes and cuboids.
Main
If the learners had no difficulty with the starter, the next face will be that
30 Minutes
I will:


Give each pair of learners several pieces of blank paper.
Ask each pair of learners to write the names of as many quadrilaterals as they can think of on
separate pieces of paper. Learners should also sketch each quadrilateral and label or list its
properties. For example, for a parallelogram:
Differentiation





opposite sides are parallel
opposite sides are equal length
opposite angles are equal
Ask learners to sort, organise or group the quadrilaterals by their properties and then ask them to
share their ideas with the class. Learners should be able to justify how they have organised the
quadrilaterals.
Establish the hierarchy of quadrilaterals and the definition of each quadrilateral, discussing the
necessary and sufficient properties. For example, learners should recognise that any rectangle is
also a parallelogram, although not all parallelograms are rectangles.
Otherwise:
I will tell learners that ‘I will read out one line of description at a time and I will allow them enough time (2
minutes 30 seconds) to draw all possible quadrilaterals that the descriptions could relate to or write down
the answer in words’
What quadrilaterals am I describing?
1. This quadrilateral has two pairs of parallel sides (square, rectangle, parallelogram, rhombus)
2. All angles in this quadrilateral are 90o (square, rectangle)
3. All sides in this quadrilateral are equal in length (square, rhombus)
4. This quadrilateral has order four rotational symmetry (square)
5. This quadrilateral has no lines of symmetry (trapezium, parallelogram)
6. This quadrilateral has order two rotational symmetry (rectangle, rhombus, parallelogram)
7. Opposite sides in this quadrilateral are equal in length (square, rectangle, parallelogram, rhombus)
8. This quadrilateral has two pairs of sides of equal length (square, rectangle, parallelogram, rhombus,
kite)
9. This quadrilateral has one line of symmetry (kite, isosceles, trapezium)
Learners facing difficulties
might need to leave their
Learners Book open so they
can see the seven
quadrilaterals together in
the introduction
Extension
0 Minutes
Plenary
10 Minutes
Line of Symmetry
Learners will be asked to write the numbers 1 to 8 down the left – hand side of their whiteboard
Then I will tell them ‘that I will say the name of a regular polygon, learners will write down how many lines
of symmetry that shape has.
I will then say the names, giving about 10 seconds for learners to think and write down a number.
It is expected for learners to
get 6 to 8 answers. If
anyone get fewer than that,
the learner can be asked to
revised the lesson, the
1 Octagon (8), 2 Decagon (10), 3 Square (4), 4 Hexagon (6), 5 Equilateral triangle (3), 6 Pentagon (5), 7
Heptagon (7), 8 Nonagon (9).
Learners can self-mark or peer mark their boards.
names of polygons and their
number of sides as extra
homework. The learners can
then be retested later.
Instead of asking them for
lines of symmetry, thy can
be asked for the order of
rotational symmetry.
Topic:
Quadrilaterals and polygons
Lesson Objectives:
Understand that the number of sides of a regular polygon is equal to the number of lines of symmetry and the order of rotation.
Relevance of the lesson:
Resources and Materials: Learners Book, Slides, Exercise Books, workbook, Regular polygons drawn on paper, Scissors
Days and Dates:
Stages and Time
Starter
15 Minutes
Activities
Words such as hierarchy, lines of symmetry, quadrilateral, regular polygon, and rotational symmetry are
write on slide or on the board and the leaners are asked to produce questions whose answer is the word
provided.
- A system in which things are arranged in order of their importance
- A line that divides a shape into two parts, where to parts is the mirror image of the other
- A flat shape with four straight sides
- A 2D shape with three or more straight sides. All the sides are equal in length
- A shape has rotational symmetry if, in one full turn, it fits exactly onto its original position at least
twice
For learners who require
more support, they are
informed that triangles have
numerous centres, defined
in different ways such as
centroid, circumcentre and
orthocentre. The centre of
the triangle found in this
activity is called the incentre.
Each learner is given an equilateral triangle drawn on a piece of paper.
And I will:
- Ask learners to cut out the equilateral triangle.
Learners requiring more
support may incorrectly
state that a shape has an
Main
30 Minutes
Differentiation
-
Extension
Then ask learners to fold the triangle to show the three lines of symmetry. The lines of symmetry
order of rotational
should meet to show the centre of the triangle. Ask learners to use a sharp pencil or compass point
symmetry of zero.
placed firmly on the centre of the triangle, and turn the triangle to show the rotational symmetry.
-
Ask learners:
How many lines of symmetry does an equilateral triangle have?
What is the order of rotational symmetry of an equilateral triangle?
-
Then provide learners with other regular polygons such as a regular quadrilateral (square), a
regular pentagon and a regular hexagon and ask them to repeat this activity.
-
Ask learners:
What do you notice about the relationship between the number of sides of the polygon, the number
of lines of symmetry and the order of rotational symmetry?
Is this true for a rectangle? Why not?
How many lines of symmetry would a regular decagon (10 sides) have and what is its order of
For those who need more challenges, they will be asked to give their own explanations to the term
0 Minutes
Plenary
5 Minutes
Workbook Exercise 8.1
All shapes will look identical
after having completed one
complete turn.
Topic:
Area, perimeter and circumference of a circle
Lesson Objectives:
Understand π as the ratio between a circumference and a diameter.
Recall and use the formula for the circumference of a circle
Relevance of the lesson:
Resources and Materials: Learners Book, Slides, Exercise Books, Circular objects (e.g. tins, lids, cups), String or tape measures for the circumference measurement, Resource
Sheet 8.2, Rulers; string; felt pens; notebooks; calculators (and perhaps Resource Sheet 8.2 ;)
Days and Dates:
Stages and Time
Starter
Activities
Activity: Calculating the value of Pi
Rulers; string; felt pens; notebooks; calculators (and perhaps Resource Sheet 8.2 ;)
25 Minutes

We Introduce learners to the constant pi (π). Explain that pi is the exact ratio of the circumference
of a circle to its diameter. Learners should understand that pi is approximately 3.14, but that the
exact value of pi cannot be written in numeric form, as it is a decimal with infinitely many decimal
places, and hence we use the symbol π to represent this number.

Here, we want learners to calculate the value of pi for themselves and use it to derive the formula
for circumference.
We make sure that there is a variety of cylindrical objects available, such as straight-sided cans and
bottles. It is easier for learners to do this activity in pairs. One learner can hold the object and the
other one can measure it.


We ask learners to find the diameter of a cylindrical object. Some learners may find it easier to
place two books or two rulers, one either side of the object. If they line them up so they are parallel,
they can measure the perpendicular distance between them.

Next, we ask learners to use a piece of string to measure the circumference of the same object.
Some learners may find it helpful to wrap the string around the object they are measuring and
mark, with felt pen, where the string overlaps. Then they can measure the distance between the
marks on the string.
Differentiation
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Now they divide the measurement of the circumference by the diameter of the circle. Learners
repeat this, with circles of various sizes. Encourage them to record their results in a table. Learners
should realise that the value (circumference divided by the diameter) is always about the same.
Once leaners have established that the answer is always ‘a bit more than 3’, explain that although
mathematicians have calculated this value, called pi, very accurately, in this unit we will use
rounded value 3.14 or 3.142 (to 2 or 3 decimal places)
We will show learners the symbol for pi, π, and explain that this stands for the value of the
circumference divided by the diameter for all circles.
Write on the board C/d = π. Then you can either ask learners to make C the subject of the formula
or show them that they can arrange this to get C= πd
Resource Sheet 8.2 will be used to support this activity or for homework. Learners will use coins
and roll them along a straight line.
Main
Activity: Calculating Diameter, radius, Circumference, area of a circle.
15 Minutes

Here, learners work in pairs for this activity. Give each pair of learners several circular objects (e.g.
tins, lids, cups) and ask them to measure the circumference and diameter of each circle.

Select learners to share one of their results with the class and tabulate the results on the board:
Diameter
…
Extension
0 Minutes
Circumference
…

Once several results have been recorded ask learners:
Is there a relationship between the diameter and the circumference?

If learners cannot see a relationship, extend the table to create a third column, where learners
should calculate circumference ÷ diameter. Learners should notice that the circumference is
approximately three times the length of the diameter.
From this, learners should derive the formula for the circumference of a circle, C = πd. Give learners a
selection of questions where they are required to use the formula to find the circumference, diameter or
radius of a circle. For example:
 Find the circumference of a circle with diameter 12.4cm.
 Find the circumference of a circle with radius 79mm.
 Find the diameter of a circle with circumference 178m.
 Find the radius of a circle with circumference 2km.
Plenary
10 Minutes
After checking learners’ answers, we discuss the different methods leaners used to work out the answer.
Learners will also be asked that they should imagine that they were to calculate or workout the difference
in the circumference of two different circles. This time once circle has a radius of 6 cm and the other one a
diameter of 6 cm. What method will they use? (No calculation. They should just explain)
Topic:
Area of trapezia and parallelograms
Lesson Objectives:
Use knowledge of rectangles, squares and triangles to derive the formulae for the area of parallelograms and trapezia. Use the formulae to calculate
the area of parallelograms and trapezia.
Relevance of the lesson:
Resources and Materials: Learners Book, Slides, Exercise Books, graph paper,
Days and Dates:
Stages and Time
Starter
20 Minutes
Activities
Each learner is given a sheet of centimetre squared paper. Learners are asked to draw a parallelogram,
ensuring horizontal edges are in line with the squared paper, e.g.
Differentiation
Although this task is set out
so that the parallel lines are
horizontal, learners requiring
more support need to
recognise that parallel lines
can go in any direction (e.g.
vertical or with a diagonal
slope).
Learners are asked to find the area of the parallelogram by dividing it into a rectangle and two congruent
triangles. Support learners to see that they can turn their shape into a rectangle by moving one of the
triangles, e.g.
Learners are then asked:
Can you use this diagram to write the formula for finding the area of a parallelogram?

Learners will show they are generalising (TWM.02) when they notice the area of a parallelogram
can be found in the same way as a rectangle, by multiplying the base by the perpendicular height.
They should use this to derive the formula for the area of a parallelogram: A = b × h, where b is
the base and h is the perpendicular height.
Learners are then asked to use the formula to find the area of parallelograms which are not drawn on a
square grid.
Main
Work Book Exercise 8.2
Each learner is given an isosceles trapezium drawn on centimetre squared paper with horizontal base
10cm and parallel edge 6cm:
20 Minutes
Learners are asked to find the area of the trapezium by dividing it into a rectangle and two congruent
triangles. Learners are supported to see that they can turn their shape into a rectangle by moving and
reflecting one of the triangles, e.g.
Learners are also made to notice that this rectangle has the same height as the original trapezium, but now
1
has horizontal width 8cm. The formula for the area of a trapezium show to learners: A = (a + b) × h, where
2
a and b are the parallel sides of the trapezium and h is the perpendicular height.
Learners are then asked to discuss with a partner and explain how the formula is derived. They should
1
recognise that the (a + b) is the mean of the two parallel sides of the trapezium.
2
Learners are asked to draw other trapezia on centimetre squared paper (including non-isosceles trapezia).
They should find the area of each by dividing them into a rectangle and two triangles and then confirm that
using the formula for the area gives the same result.
Learners should then use the formula to find the area of trapezia which are not drawn on a square grid.
Work Book Exercise 8.2
Extension
0 Minutes
Plenary
10 Minutes
Learners Book Exercise 8.2
Topic:
3D SHAPES
Lesson Objectives:
Understand and use Euler’s formula to connect number of vertices, faces and edges of 3D shapes.
Use knowledge of area and volume to derive the formula for the volume of a triangular prism. Use the formula to calculate the volume of triangular
prisms.
Relevance of the lesson:
Resources and Materials: Learners Book, Slides, Exercise Books, Models or pictures of polyhedra
Days and Dates:
Stages and Time
Starter
25 Minutes
Activities
Differentiation
Learners are given a selection of polyhedra (e.g. solid shapes, boxes, or pictures of a cube, triangular
prism, etc.). They should identify the number of vertices, faces and edges for each shape and record their
results in a table:
Learners may incorrectly
think that Euler’s formula
applies to all 3D shapes.
Ensure learners know that
Euler’s formula applies only
to polyhedra (3D shapes
with plane faces). It does
not apply to, for example, a
cylinder.
Shape
Cube
…
Vertices
8
Faces
6
Edges
12
Learners are selected to share their results and write these on the board. Once several results have been
recorded, ask learners to discuss with a partner what they notice about the results.
Learners are then introduce to Euler’s formula V + F – E = 2 and asked to confirm that this formula is true
for the polyhedra in their table.
They are then asked to use Euler’s formula to find missing information about polyhedral, such as:
 How many edges does a polyhedron with eight vertices and six faces have?
 What 3D shapes could this be?
 How many faces does a polyhedron with eight edges and five vertices have?
 What 3D shape could this be?
Resources:
Models or pictures of polyhedra
Main
In pairs, learners are asked to discuss and recall how to find the volume of cubes and cuboids. Then shown
the right-angled triangular prism below:
20 Minutes
Learners are then asked:
 What is the volume of this triangular prism?
 What is your method?
 Write a formula for the volume of any triangular prism.
Learners will show they are generalising when they derive the formulae for the volume of a triangular
prism.
volume of triangular prism = length × width × perpendicular height
2
Learners are then shown that the volumes of cubes, cuboids and triangular prisms can be found by finding
the area of the cross-section and then multiplying by the length of the prism:
volume of prism = area of cross section × length
Extension
0 Minutes
Plenary
Work Book exercise 8.2
5 Minutes
Learners Book Exercise 8.3
Home Work Book 5A to 5E