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Mathematics and Patchwork Quilting
Developed by an ATM working group
supported by a grant from the Clothworkers Guild
We would like to thank Pat Doyle from Carlisle for allowing us to reproduce her quilt. Pat is a member of a quilting group who meet and construct quilts together at Quilt Essentials at Orton Grange near Carlisle.
Quilting
Quilts come in many guises. They may be created to illustrate or celebrate a particular event and contain individual panels relating to that event or they may be constructed from ‘blocks’ using colour, position and shapes to produce an overall design.
The quilts suggested in this ATM site arise from making a design for a basic building ‘block’, reproducing several of these ‘blocks’ sometimes varying the colours, or textures, and placing the blocks together to form larger and larger patchworks. The ‘blocks’ can either be placed edge to edge or separated by a border. In the world of quilting, quilts are made by sewing material together to form the larger patchworks. This patchwork is then made into a quilt by backing the patchwork with batting or insulating material, backing material and sewing the three layers together.
Our ‘quilting’ activities are based on gluing paper shapes together rather than sewing material. We made this choice because of curriculum and time pressures on teachers and children. A school ‘quilt’ can be made from discarded wallpaper book pages, coloured paper, Christmas wrapping paper, or material glued on to large sheets of heavy duty paper or hardboard.
What we have produced, in these web pages, are a number of ways of working with patchwork designs. One of our starting points was an article Quilted Math which gives many starting points for working with quilting projects in school.
This article states, amongst much else, that “Quilts can be thought of as pictures painted in fabric pieces. Quilt designs often honour a birth or a marriage, or mark the occasion of a special community or state event, like a centennial.”
A school may find it useful to take the idea of ‘marking a special community event’ as a way of involving the whole school and community in producing a quilt perhaps in a series of curriculum days based around a common theme. Designing and making a Quilt will incorporate, as a minimum, aspects from the following curriculum areas: Mathematics, History, language, CDT and use of IT. Using a basic block, as we suggest, gives many opportunities to work with the mathematical processes of visualising, reasoning and communicating.
Connections with mathematics and the KS2 curriculum
If you look at the picture of a quilt at the top, you may not initially notice that the basic ‘block’ is reproduced twelve times. The skill of the quilter is in the way she has disguised the block by:
- interchanging the colours,
- rotating the original block,
- reflecting the block in a horizontal, or vertical axis...
- ...and so on
A good way of starting to notice these subtle changes is to look at any pair of the blocks and ask yourself, or a small group of pupils, ‘What is the same, and what is different, between these two blocks?’, ‘Are there any that are the same?’
Another thing to notice is that the basic ‘block’ is comparatively simple. In this quilt the square is divided into just six areas. Simplicity of the basic ’block’ is an important attribute of quality quilts.
The mathematical task then is to design a ‘block’ by setting rules that keep the design clear and simple such as limiting the number of lines in the basic ‘block’. The children need to make several copies of this ‘block’ and explore what happens when they place ‘blocks’ together to make a larger ‘patchwork’ design.
Introducing rules like:
- always rotate clockwise
- reflect first horizontally, then vertically, etc.
makes the children work systematically and start to notice and work with some of the structure that connects reflections, rotation and translation. In no way are we suggesting that this content should be made overt at the start of any project. Rather by working with clean simple designs the relations between the various symmetries will become embedded in a child’s understanding. With some designs in progress, it is worth asking is ‘Are there any other ways of placing 2, 3, 4 ‘blocks’ together?’ and ‘Are you sure you have found them all?’. The really hard question, and it gets to the basis of proof in mathematics is ’How do you know that there are no more?’.
Quilting and Patchwork
These two activities are often confused. People talk of patchwork when they mean quilting and vice versa.
From Wikipedia the following definitions should clear your thinking:
Quilting is a sewing method done either by hand, sewing machine or Longarm quilting system. The process uses a needle and thread to join two or more layers of material together to make a quilt. Typical quilting is done with three layers, the top fabric or quilt top, batting or insulating material and backing material.
Patchwork or "pieced work" is a form of needlework that involves sewing together pieces of fabric into a larger design. The larger design is usually based on repeat patterns built up with different colored shapes. These shapes are carefully measured and cut, straight-sided, basic geometric shapes making them easy to piece together. Precise joining makes for patchwork that lies flat without puckers.
Quilting activities in detail
- Working with ATM square mats
- Design your own quilting block
- Say what you see
- Working with a quilt block made up of four by four squares
- Extending the four by four to n by n and analysing and creating your own designs
- Making patterns (tessellations) using square tiles each quartered into four colours
- Easy start quilting
Technical help in detail
- Working with year 6 • Faux, Hepburn, Tinniswood article in Mathematics Teaching 210
- Working with ATM tiles in word
- Image of Cumbrian Quilt
- Whiteboard images for Activities 4 and 5 (PDF)
- Whiteboard images for Activities 4 and 5 (PowerPoint)
- Printable set of cards for Activity 6
- Using Word to design your own block
- Using Geogebra to design your own block
Other quilting websites
A typical search might include the words ‘quilt school mathematics’. This will show several sites listed for schools in North America linking quilts and the Mathematics curriculum. This information can be easily adapted to fit other countries curricula.
The history of quilting can also, make fascinating reading and can link to work on codes and story telling.
- Making Quilts, NRICH, A page compiled by Jenny Murray
- Quilting Assistant: templates and examples of designs
- How NCTM suggests quilts can be used to develop maths skills
- An American site about quilt blocks
- An example of a quilt made in a classroom
- Different types of quilt and how they are made
- Exploring Mathematics through quilts written for school use
- Illustrations of quilts made from different shapes
- Quilting and transformations written for children
