Kite Maths



Introduction

Explore Geometry With Kites!

Can you make a kite shape from a single A4 size sheet of paper using only three folds? Click Here to find out how.

Will your kite tessellate? Can you put a number of kites together to make a symmetric design? What about 4 lines of symmetry and rotational symmetry of order 8.... is it possible?

Can you write a procedure in Logo to draw a kite .... what designs can you make with your Logo kites?

What is a kite?

Kite

In geometry a kite, sometimes known as a deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides. A kite can also be described as a quadrilateral with an axis of symmetry along one of its diagonals.

A kite, as defined above, may be either convex or concave, but the word "kite" is often restricted to the convex variety. A concave kite is sometimes called a "dart" or "arrowhead".

Instructions

Fold an A4 sheet of paper to make a kite!

Kite folding instructions Kite folding instructions
Step 1 Step 2
Kite folding instructions Kite folding instructions
Step 3 Step 4

Activities

Challenges and investigations with Kites!

Activity 1
Fold a kite from an A4 sheet of paper by following the given instructions. What type of symmetry does your kite have?
Activity 2
Make seven more kites from sheets of A4 paper. Put your eight kites together to make different patterns. Can you work out the interior angles of the kite from the ways they fit together?
Activity 3
Make a kite from an A5 sheet of paper (half an A4 sheet). Will the smaller kite be half the width of the first kite you made? half the area? Will it's angles be the same?
Activity 4
Can you put a number of kites together to make a symmetric design with 4 lines of symmetry and rotational symmetry of order 8? Is it possible?
Activity 5
Use a computer program such as Logo or Geogebra to create patterns with kites.
Activity 6
You can fold an A4 sheet of paper to make a pentagon too. Click here to find out how.

Logo

Use a computer to draw kites!

Logo kite pattern

Here is a Year 8 student's design

to kite :size
lt 22.5
fd :size * 1.85
rt 67.50
fd :size
rt 90
fd :size
rt 67.5
fd :size * 1.85
rt 157.5
pu
fd 10
fill
bk 10
pd
end



to design
setfillcolor 7
kite 55 rt 45
setfillcolor 1
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 1
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 0
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 0
kite 55 rt 45
setfillcolor 10
repeat 8 [kite 35 rt 45]
end

Here are some more designs made with Logo

Logo kite pattern

Logo kite pattern

Display

Colourful kites make great displays!

Kite Display

Click on an image below to see the full size animation.

Area of a kite Properties of a kite
Investigate a kite Kite Pattern

It may take a while for Geogebra animations to load.

Other Shape Activities
More paper folding

Paper Constructions

Paper Constructions

Practical mathematical skills are required to work out how to construct these three dimensional items from paper.

The short web address is:

Transum.org/go/?to=paper

Another investigation

Pin Board

Pin Board

Rows and columns of dots that can be joined using straight lines to create shapes.

The short web address is:

Transum.org/go/?to=pinboard

Know the names

Polygons

Polygons

Name the polygons and show the number of lines and order of rotational symmetry.

The short web address is:

Transum.org/go/?to=polygons

Pattern Creating

Tessellations

Tessellations

Which polygons tessellate? Drag the shapes onto the canvas to create tessellating patterns for investigation.

The short web address is:

Transum.org/go/?to=tesselate

Polygon puzzles

Shapes In The Stars

Shapes In The Stars

Join up the stars to find the hidden regular polygons. An interactive series of challenging puzzles.

The short web address is:

Transum.org/go/?to=shapestars

Say what you see

The Great Dodecahedron

The Great Dodecahedron

Pupils are not allowed to use their hands to point but must describe fully any shapes they can see in this picture.

The short web address is:

Transum.org/go/?to=dodecahedron

All Shape Activities

Apple

©1997-2016 WWW.TRANSUM.ORG