The Quilt Project: Cross-curricular Mathematics

This project took nearly a month the last time I taught it, but it was worth every lesson. The depth of the students' geometric explorations, their artistry, and their deep empathy for slaves using freedom quilts on the Underground Railway were all wonderful to watch and valuable learning. (Copyright 2009; please, please use the unit, and please come back and tell me how it went, but all publishing rights are reserved to E. van Hiel.)

Again, the expectations outlined are from the Ontario curriculum, grade five; the project is also an excellent fit for grade six math and art and would not go amiss in grade seven history, so it's got a lot more cross-curricular potential than just math and art.

Grade 5 Mathematics:
Patterning:
– extend and create repeating patterns that
result from translations, through investigation
using a variety of tools (e.g., pattern
blocks, dynamic geometry software, dot
paper).
– create, identify, and extend numeric and
geometric patterns, using a variety of tools
(e.g., concrete materials, paper and pencil,
calculators, spreadsheets);
Geometry and Spatial Sense:
– identify, perform, and describe translations,
using a variety of tools (e.g., geoboard, dot
paper, computer program);
– create and analyse designs by translating
and/or reflecting a shape, or shapes, using
a variety of tools (e.g., geoboard, grid
paper, computer program) (Sample problem:
Identify translations and/or reflections
that map congruent shapes onto
each other in a given design.).

Grade 5 Art:
– identify the three pairs of complementary
colours (red and green, purple and yellow,
blue and orange);
– describe how line may be used to define
shapes and forms and to create movement
and depth;
– identify negative and positive shapes in
works of art and the environment
(e.g., shapes created by both the branches
of a tree and the spaces between the
branches);
– produce two- and three-dimensional
works of art (i.e.,works involving media
and techniques used in drawing, painting,
sculpting, printmaking) that communicate
a range of thoughts, feelings, and ideas for
specific purposes and to specific audiences
– identify, in their plan for a work of art, the
artistic problem and a number of possible
solutions (e.g., identify different types of
subject matter that they could use to
express their concern for the environment);
– describe the connection between an
element of design and a specific artistic
purpose, using appropriate vocabulary

Overview: Students will view, analyze, deconstruct, plan, and create quilt squares, both traditional forms and those of their own design, using a variety of materials. They will explain the elements of geometry and design that went into creating the squares (e.g. Names of shapes, symmetry, transformations, line, colour, and form.) They will explain the effects they were hoping to achieve through the use of those elements in their original work, and indicate other patterns from which they took their inspiration.

Lessons:

1) Introduction: Bring in a vintage quilt or reproduction that has several different quilt squares in it; spread it out and let students identify the patterns and colours. (If you don't have a teacher on staff who has one of these, as I do, I suggest calling your local quilter's guild, or talking to a local museum that documents the Underground Railway. Antique quilt collectors may be able to help you out, but a reproduction is better because it's not as fragile, and you want the kids to be able to move around on it to point things out.) Name some of the quilt blocks for them, and ask them to explain where they think the quilt block got its name. Begin to direct them towards describing the shapes mathematically by pointing out right-angled triangles, and how putting two triangles together in a quilt block almost always makes a square. Discuss the use of colour, particularly in blocks that rely on it for effect, like Log Cabin or Around the World; negative and positive colour values can be introduced here. If possible, point out how the squares look different if they are put together differently, and remind students of the transformations they're familiar with (reflections, translations - rotations are a grade six expectation but there's no reason they can't be mentioned if someone points them out.)

2) Using the book "Sweet Clara and the Freedom Quilt," by Deborah Hopkinson, review the use of patchwork quilts to guide slaves to the North on the Underground Railway. Discuss the quilt blocks used on each page. Challenge the students to use the other quilting resources, including the internet sites listed below, to find other examples of the same quilt blocks. Reflection question: how do quilters use colour to change the way a quilt block looks? How do they use transformations of blocks? (Other reflection questions and activities related to language may be pulled in here as well.)

3) Pick a relatively simple quilt block such as Ohio Star (nine-patch with triangles in the middle squares of the outside strips.) Using geometric software on a SMARTboard or an overhead transparency of the square and some shapes in different colours, model reproducing the square using blocks and/or paper cut-outs. Point out the grid pattern (three by three) and the way each block of the grid is further divided into triangles to form the pattern. Brainstorm ways the pattern could be adjusted just slightly to make a different look with the same pieces; see if you can find any of those variations in the resources we've collected about quilt blocks. (Since the Ohio Star is the starting point for at least a dozen other classic patterns, it's a good one to start with.) This lesson will likely take several days and may need to be done with more than one block as students become familiar with the language used to describe transformations and patterns.

4) First mini-assignment: Using either a website (listed below) or a quilting book provided, find a block that you like. Print it or photocopy it so you can mark up the original as you analyze it. Reproduce it on graph paper, paying attention to the proportions. Most quilts are designed along grids that are made up of two or more similar-sized squares within the block, so to reproduce the design, you have to figure out what grid the quilter used for the proportions. Materials may involve pattern blocks, square counters, symmetry mirrors, rulers, graph paper, and colouring tools. (Note: this is where the connection to area and multiplication comes in, and possibly to fractions and ratios.) Reflection: How could you make this quilt block look different by changing just one thing about it?

5) Using a double-nine-patch quilt block, investigate growing and shrinking patterns in quilts. Problem-solving question: using this double-nine-block pattern, how would you extend the pattern to a quilt-sized square? (i.e. A triple nine-block) Find another quilt block pattern that involves growing or shrinking patterns in our resources, and explain why the pattern is a growing or shrinking one.

6) Culminating Activity: Design a quilt block of your own. Use what you've learned about traditional quilt blocks. You are welcome to take an existing block and change a few elements of it to make it your own. Explain the pattern in your quilt block in terms of geometry, symmetry, and the elements of design such as line, form, and colour. Create your quilt block using the materials provided or ones you bring in yourself. (Provided: construction paper, origami paper, scraps of felt or other fabrics) Bonus: describe the steps to go through to create your quilt block by cutting each piece from a bigger shape (for example, "The triangles in the corners are made by cutting a 5cmx10cm rectangle into two 5cm squares, and then cutting these diagonally to get two right-angled triangles with the sides on either side of the right angle measuring 5cm.")

Quilt block websites:
http://www.blockcrazy.com/index.htm

http://oldsite.mccallsquilting.com/qb/

http://www.quilterscache.com/QuiltBlocksGalore.html

http://www.quilt.com/Blocks/AlphaBlockList.html

If internet access is not stellar in your class, a few quilting magazines will provide lots of examples of patterns, and the quilters of the quilting guild you contacted at the beginning of the unit may be willing to lend some pattern books as well. Many crochet or cross-stitch patterns are also based on quilt blocks.

Book possibilities:
Hopkinson, Deborah. Sweet Clara and the freedom quilt. Illustrated by James Ransome. New York, Knopf, 1993.
ISBN 0679823115 ages 4-8

Howard, Ellen. The log cabin quilt. Illustrated by Ronald Himler. 1st ed. New York, Holiday House, 1996.
1 v. (unpaged) col. ill. 21 x 26 cm. ISBN 0823412474 ages 4-8
When Elvirey and her family move to a log cabin in the Michigan woods, something even more important than Granny's quilt pieces makes the new dwelling a home.

Polacco, Patricia. The keeping quilt. New York, Simon & Schuster Books for Young Readers, c1988.
[32] p. all ill. (chiefly col.) 23 x 28 cm. ISBN 0671649639 ages 4-9
A homemade quilt ties together the lives of four generations of an immigrant Jewish family, remaining a symbol of their enduring love and faith.

Smucker, Barbara Claasen. Selina and the bear paw quilt. Illustrated by Janet Wilson. New York, Crown Publishers, 1996.
ISBN 051770904X ages 4-8
When her Mennonite family moves to Upper Canada to avoid involvement in the Civil War, young Selina is given a special quilt to remember the grandmother she left behind.

Stroud, Bettye. The Patchwork Path: A Quilt Map to Freedom
ISBN - 10:0763624233
ISBN - 13:9780763624231
A young girl and her father escape from slavery and make their way north with the aid of a quilt map.