SEVEN CIRCLES In here there are activities for years 7 to 9. Each year develops a different aspect.

SEVEN CIRCLESIn here there are activities for years 7 to 9. Each year develops a different aspect.

Year 7Constructing the 7 circles

Finding shapesProperties of shapes

Using notation

SEVEN CIRCLESObjective: 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

A CONVERSATION on POLYGONSBefore 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.

Angles: Sum of the exterior angles 3 equal angles each ___degrees

No equal angles Opposite angles are equal 4 equal angles each ___degreesRight Angle One pair of equal angles 5 equal angles each___degreesAll angles add to 1 pair of opposite angles are equal 6 equal angles each___degrees

Sides:One pair of parallel sidesTwo pairs of parallel sidesOne pair of adjacent sides are equalTwo pairs of adjacent sides are equalNo sides are equal2 sides are equalAll sides are equalTwo pairs of opposite sides are equal

Total number of sides

Diagonals:Diagonals cross at right anglesDiagonals are of equal lengthDiagonals bisect each other

Names of Shapes:Triangles KiteIsosceles RhombusRight Angled Triangle HexagonsScalene Equilateral Triangle PentagonsQuadrilaterals RegularSquare ParallelogramRectangle Trapeziums

Conventions:

Use arrows to show lines are parallel

Use marks to show lines of equal length

Use arcs to show angles are equal

Use this to show a right angle

Symmetry:Lines of SymmetryOrder of Rotational Symmetry


Finding shapesProving the properties of shapes

Using notation

SEVEN CIRCLESObjective: To be to construct the 7 circles and to be

able to discover polygons from circles and to prove why that property is true.


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).


Hexagon

Isosceles Triangle

Rectangle


Trapezium

Kite


Pentagon

Any other shapes?

A CONVERSATION on POLYGONSBefore 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.

Angles: Sum of the exterior angles 3 equal angles each ___degrees

No equal angles Opposite angles are equal 4 equal angles each ___degreesRight Angle One pair of equal angles 5 equal angles each___degreesAll angles add to 1 pair of opposite angles are equal 6 equal angles each___degrees

Sides:One pair of parallel sidesTwo pairs of parallel sidesOne pair of adjacent sides are equalTwo pairs of adjacent sides are equalNo sides are equal2 sides are equalAll sides are equalTwo pairs of opposite sides are equal

Total number of sides

Diagonals:Diagonals cross at right anglesDiagonals are of equal lengthDiagonals bisect each other

Names of Shapes:Triangles KiteIsosceles RhombusRight Angled Triangle HexagonsScalene Equilateral Triangle PentagonsQuadrilaterals RegularSquare ParallelogramRectangle Trapeziums

Conventions:

Use arrows to show lines are parallel

Use marks to show lines of equal length

Use arcs to show angles are equal

Use this to show a right angle

Symmetry:Lines of SymmetryOrder of Rotational Symmetry


Finding shapesFinding Perimeters & Areas

Using notation

SEVEN CIRCLESObjective: To be to construct the 7 circles and find

the area and perimeter of the polygons listed below.


What is the area and circumference of on circle. (Show all working).

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 -


Hexagon

Isosceles Triangle

Rectangle


Trapezium

Kite


Pentagon

Any other shapes?

Extension

Find the above in terms of .

Find the perimeter & area of A, B, C & D.

A CONVERSATION on POLYGONSBefore 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.

A

B

CD


Finding shapesFinding Equations of lines

Using notation

SEVEN CIRCLESObjective: 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.


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 polygon-


Hexagon

Isosceles Triangle

Rectangle


Trapezium

Kite


Pentagon

Any other shapes?

Extension

Place the origin not at the centre.

A CONVERSATION on POLYGONSBefore 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.


Finding areas and perimeters of shapes made from curves

Using notation

SEVEN CIRCLESObjective: To be to construct the 7 circles, draw in a

set of axes and find the equation of each circle.


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.

A CONVERSATION on POLYGONSBefore 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.

OTHER IDEAS

PROBABILITY

A

B

CD

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) =

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

VECTORS

c

O

A

B

C

D

E

F

G

H I J

K

LM

N a

b

Findi) The following vectorsii) Their length

OK = OB = IJ =

BD = HA = OE =

FM = JB = AB =

BF = A vector parallel to GM

Find the angle between these pair if vectors –

OI & OJ KB & BA

ON & OF ML & MI

SEVEN CIRCLES In here there are activities for years 7 to 9. Each year develops a different aspect.

Documents

equal use

equal4 equal angles

right angles diagonals

exterior angles3 equal

equal length diagonals

degrees sides

lines of equal length

circles objective