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SEVEN CIRCLES
In here there are activities
for years 7 to 9. Each year
develops a different aspect.
Year 7
Constructing the 7 circles
Finding shapes
Properties of shapes
Using notation
A CONVERSATION on POLYGONS
SEVEN CIRCLES
Before we start you are going to have a 2 minute
conversation. With you partner discuss as many
properties of as many different polygons that you can
recall. After two minutes we will discuss and list what you
have found. Try to use the mathematical language on the
next slide.
Objective: To be to construct the 7 circles and to be
able to discover polygons from circles and to
use correct notation (you may use colour as
well) and mathematical language to describe
them.
Have a go at reproducing this pattern. Use a radius
of 6cm, starting from the centre of the A3
paper.
What properties does the 7 circle pattern have?
Using the points where the circles meet as vertices,
find & draw these polygons.
Equilateral Triangle
Hexagon
Isosceles Triangle
Rectangle
Right Angled Triangle
Trapezium
Extension
Kite
Right Angled Trapezium
Pentagon
Angles:
Sum of the exterior angles
3 equal angles each ___degrees
No equal angles
Opposite angles are equal
4 equal angles each ___degrees
Right Angle
One pair of equal angles
5 equal angles each___degrees
All angles add to
1 pair of opposite angles are equal
6 equal angles each___degrees
Sides:
One pair of parallel sides
Names of Shapes:
Two pairs of parallel sides
Two pairs of opposite sides are equal
Triangles
Kite
Isosceles
Rhombus
Right Angled Triangle Hexagons
Scalene
Equilateral
Triangle
Pentagons
Quadrilaterals
Regular
Square
Parallelogram
Rectangle
Trapeziums
Total number of sides
Conventions:
One pair of adjacent sides are equal
Two pairs of adjacent sides are equal
No sides are equal
2 sides are equal
All sides are equal
Diagonals:
Use arrows to show lines are parallel
Diagonals cross at right angles
Use marks to show lines of equal length
Diagonals are of equal length
Use arcs to show angles are equal
Diagonals bisect each other
Use this to show a right angle
Symmetry:
Lines of Symmetry
Order of Rotational Symmetry
Year 8
Constructing the 7 circles
Finding shapes
Proving the properties of shapes
Using notation
A CONVERSATION on POLYGONS
SEVEN CIRCLES
Before we start you are going to have a 2 minute
conversation. With you partner discuss as many
properties of as many different polygons that you can
recall. After two minutes we will discuss and list what you
have found. Try to use the mathematical language on the
next slide.
Objective: To be to construct the 7 circles and to be
able to discover polygons from circles and to
prove why that property is true.
Have a go at reproducing this pattern. Use a radius
of 6cm, starting from the centre of the A3
paper.
Using the points where the circles meet as vertices,
find & draw these polygons. Without using a
ruler or protractor write down as many
properties of the polygon as you can and
explain how you know that property is true.
Use correct notation and mathematical
language (see next slide).
Equilateral Triangle
Hexagon
Isosceles Triangle
Rectangle
Right Angled Triangle
Trapezium
Kite
Right Angled Trapezium
Pentagon
Any other shapes?
Angles:
Sum of the exterior angles
3 equal angles each ___degrees
No equal angles
Opposite angles are equal
4 equal angles each ___degrees
Right Angle
One pair of equal angles
5 equal angles each___degrees
All angles add to
1 pair of opposite angles are equal
6 equal angles each___degrees
Sides:
One pair of parallel sides
Names of Shapes:
Two pairs of parallel sides
Two pairs of opposite sides are equal
Triangles
Kite
Isosceles
Rhombus
Right Angled Triangle Hexagons
Scalene
Equilateral
Triangle
Pentagons
Quadrilaterals
Regular
Square
Parallelogram
Rectangle
Trapeziums
Total number of sides
Conventions:
One pair of adjacent sides are equal
Two pairs of adjacent sides are equal
No sides are equal
2 sides are equal
All sides are equal
Diagonals:
Use arrows to show lines are parallel
Diagonals cross at right angles
Use marks to show lines of equal length
Diagonals are of equal length
Use arcs to show angles are equal
Diagonals bisect each other
Use this to show a right angle
Symmetry:
Lines of Symmetry
Order of Rotational Symmetry
Year 9
Constructing the 7 circles
Finding shapes
Finding Perimeters & Areas
Using notation
SEVEN CIRCLES
A CONVERSATION on POLYGONS
Before we start you are going to have a 2 minute
conversation. With you partner recall how to find the
perimeter and area of as many different shapes as you
can. After two minutes we will discuss and list what you
have found.
Objective: To be to construct the 7 circles and find
the area and perimeter of the polygons listed
below.
Have a go at reproducing this pattern. Use a radius
of 6cm, starting from the centre of the A3
paper.
What is the area and circumference of on circle.
(Show all working).
C
B
A
D
Using the points where the circles meet as vertices,
find & draw these polygons. Without using a
ruler or protractor find the lengths of each side
of the shape and their angles.
Now find the perimeter and area of these polygons Equilateral Triangle
Hexagon
Isosceles Triangle
Rectangle
Right Angled Triangle
Trapezium
Kite
Right Angled Trapezium
Pentagon
Any other shapes?
Extension
Find the above in terms of 𝜋 & 𝑟 .
Find the perimeter & area of A, B, C & D.
Year 10
Constructing the 7 circles
Finding shapes
Finding Equations of lines
Using notation
SEVEN CIRCLES
A CONVERSATION on POLYGONS
Before we start you are going to have a 2 minute
conversation. With you partner recall the general
equation for a straight line, what m & c represent and
how to find the equation of a linear line. After two
minutes we will discuss and list what you have found.
Objective: To be to construct the 7 circles, draw in a
set of axes and find the equation of the lines
that are required to make the shape.
Have a go at reproducing this pattern. Use a radius
of 6cm, starting from the centre of the A3
paper.
Draw in the axes & think carefully about the
numbers that go on the axes. (Surds perhaps).
Using the points where the circles meet as vertices,
find & draw these polygons. Without using a
ruler or protractor find the lengths of each side.
Now find the equation of the lines that make up the
sides of the polygonEquilateral Triangle
Hexagon
Isosceles Triangle
Rectangle
Right Angled Triangle
Trapezium
Kite
Right Angled Trapezium
Pentagon
Any other shapes?
Extension
Place the origin not at the centre.
Year 11
Constructing the 7 circles
Finding areas and perimeters of
shapes made from curves
Using notation
SEVEN CIRCLES
A CONVERSATION on POLYGONS
Before we start you are going to have a 2 minute
conversation. With you partner recall the general
equation for a straight line, what m & c represent and
how to find the equation of a linear line. After two
minutes we will discuss and list what you have found.
Objective: To be to construct the 7 circles, draw in a
set of axes and find the equation of each
circle.
Have a go at reproducing this pattern. Use a radius
of 6cm, starting from the centre of the A3
paper.
Draw in the axes & think carefully about the
numbers that go on the axes.
Find the equation of each circle.
Extension
Place the origin not at the centre.
OTHER IDEAS
PROBABILITY
PROBABILTY - the 7 circles are now a dart
board, where A is 12 points, B is 6 points, C is 3
points and D is worth 1 point.
What assumption(s) do you have to make?
Work out the following probabilities –
P(A) =
P(B) =
P(C) =
P(D) =
P(not 12 points) =
C
B
A
D
You have 2 throws of a dart and add
the totals, find these probabilities –
P(12) =
P(square number) =
P(prime) =
P(multiple of 3) =
Extension:
You have 3 throws of the dart, find
these probabilities –
P(36) =
P(21) =
P(minimum points) =
P(12) =
P(10) =
VECTORS
Find
i) The following vectors
ii) Their length
VECTORS
A
I
H
J
b
G
N
F
a
B
K
O
L
E
OB =
IJ =
BD =
HA =
OE =
FM =
JB =
AB =
BF =
A vector parallel to GM
Find the angle between these pair if
vectors –
c
M
OK =
C
D
OI & OJ
KB & BA
ON & OF
ML & MI