Quilting With Elementary School Students : Using Fractions To Develop Quilt Designs
One of the most important concepts teachers in elementary school must teach is fractions and equivalence. This is more than a two-week or month-long unit in specific grades; fraction sense needs to permeate the elementary classroom. Students need to be immersed in activities that build understanding. Without this conceptual work, students enter middle school unable to use fractions as a tool to develop proportionality, the key middle school concept. Creating fraction quilts is another activity that can do this.
While you might want to think about doing quilts in fabric, basic colored pencil or crayon, construction paper and graph paper are all you need. You can decorate the classroom or the hallways with fraction quilts that will last for a year's worth of fraction activities. You will actually have several examples of working with the idea of "one whole" - a single square representing a particular fraction, and a group of squares representing the same fraction. This is a critical leap students have to make in understanding the concept of "whole".
If you are going to use this activity, you will want to match your district or state standards for proportionality. What follows is a sampling of NCTM Standards that would be appropriate for this activity:
The Basic Activity
Students create paper "quilt blocks" that represent specific fractions. You will have students color squares in halves, fourths, eighths, and sixteenths. These are basic, familiar fractions for students. They can use a set color for the particular fraction they are coloring, and use other colors to "fill in" the rest of the block. Students can investigate the idea that one-half and other related fractions can cover different parts of a quilt block
Add thirds, sixths, and twelfths later in the activity.
You can then take representative blocks and mount them together so that the idea of a "whole" changes from one specific block to a group of blocks.
Construction paper for mounting finished designs or for using as borders for a larger "group quilt".
Activity - Part 1
1) Start with a blank square. Ask students to divide the square into half, using a particular color that you specific - make sure it is a color easily visible from a distance (not yellow!). Encourage students to do more than just divide the block down the middle. Reinforce the idea that half of the block doesn't have to be one side of a straight line. (Refer back to diagram 1 and 2 for other placements.)
2) Collect these squares for students to view. Construct a paper quilt of these squares by taping them together. (Wait to use border strips, since with beginning students you will be distorting the idea of "half.") (Refer back to diagram 3.)
3) See what insights the students have by looking at the whole paper quilt. They should see ultimately that half the whole quilt is colored, and that "half" can look different.
4) Follow the same process with blank squares and fourths. Mount as before and lead a discussion to see what students notice. They should see that each square has less of a particular color. Students should see that it will take two of the "fourth" blocks to have the same amount of color as one of the "half" blocks.
5) Repeat the process with eighths, and then with sixteenths. Do these separately. Do not hurry student understanding of each of these fractions. Spend time letting students observe the paper quilts and analyze what they see for relationships.
You now have a set of paper quilts showing basic fractions. If you want, you can repeat the process using thirds, sixths, and twelfths. This will give you a good selection of basic fractions to use. You may decide to leave these quilts taped together or take them apart later to mix with new squares.
Activity - Part 2, Advanced
This activity can be done with crayons or colored pencils, but with some more preparation on your part, you can create a more effective, hands-on experience in experiencing fractional parts. Cut centimeter squares of different colors (you might want to limit to the same colors you used in the first part of the activity) so that students can create mosaic quilt blocks of smaller squares to see relationships of halves, thirds, fourths, sixths, eighths, twelfths, and sixteenths. An easy way to do this is to make copies of a centimeter square grid on colored paper and then use a paper cutter.
You will give white gridded paper for this activity to act as guidelines for placement of smaller squares. Cut your grid paper so that it has a dimension of a multiple of four: 4 x 4, 8 x 8, 12 x 12, 16 x 16, and so forth. This gives you control over finished sizes and provides ruled lines for fine motor control in students. You will want glue sticks for easy clean-up.
Four by 4, 8 x 8, and 16 x 16 allows easy use of halves, fourths, eighths and sixteenths. Twelve by 12 allows for easy use of halves, thirds, fourths, sixths, and twelfths. Think through what fractional combinations you would like to do. Don't try to incorporate too many at once; you can save that as an enrichment activity.
Have students determine a design that will use different colors to represent specific fractions. For example, one-fourth of the design can be one color. One-half of the design can be another color, and so on. This activity lets student develop fraction number sentences that represent one whole. For example, one quilt block can be one-fourth red, three-eighths blue, three-sixteenths green, and three-sixteenths brown (colors are chosen so they are distinct from a distance). Students will create interesting designs with little duplication, which gives you many possibilities for asking good questions: what designs show one-fourth red, and so on. You also can ask for blocks that represent specific number sentences.
You can put these designs together into larger paper quilts, and then continue with more advanced questions, such as what squares together show half of the quilt in a particular color, and what squares show a number sentence of one-half red and so on.
This activity can be as simple or as complex as you would like, depending on the skills of your students. You want to provide as many concrete experiences as possible to reinforce very abstract concepts. You can set this up as a centers activity, with students selecting fraction number sentences to create a new quilt block. Your task is also complex: asking the questions that will lead students to see the relationships among fractional parts, as well as relationships to different "wholes." Take time to work this through; both you and your students deserve the time spent on these concepts.
Quilt Design Masters by Luanne Seymour Cohen, ISBN 0866519416, Dale Seymour Publications, available through Pearson Learning Group. The book has numerous traditional quilt patterns, all reproducible. There are some simple quilt block designs that would work for basic fractions. For enrichment, you have more complex designs for students who would like a challenge.
Fractions Resources: all available from www.mathsolutions.com
Lessons for Introducing Fractions, Grades 4-5, Marilyn Burns
Lessons for Extending Fractions, Grade 5, Marilyn Burns
Lessons for Multiplying and Dividing Fractions, Grades 5-6, Marilyn Burns
Related : Math And Quilting