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 Quilting Techniques : Middle School Math Lesson Plan

Quilting With Middle School Students: Using Proportionality to Develop Quilt designs

Why?

It may seem strange to think about something like quilting with middle school students because some of the math is so obvious: sizes of squares, numbers of squares, amount of fabric, number of pieces per yard. All of these are great review topics through quilting. We tend to forget that perhaps the most important concept in pre-algebra is that of proportionality, and quilting gives you a simple yet unique way to look at this concept.

You can do this activity with paper (probably the easiest) or with fabric. Rather than having students cut and work with cloth, chances are one of your students has a parent or grandparent that does traditional quilting and could provide some quilts for a lesson. This activity will look at fractions, decimals, percents and ratio within the designs of quilts and will have students make their own paper quilt squares utilizing these concepts.

Middle school students work to develop flexible understanding of strategies for making comparisons, ways of comparing different amounts. Students can use ratios, fractions decimals, percents, or differences, with each one more useful in a particular situation than another. Helping students realize which works best is a middle school challenge. Giving students concrete experiences with visual representations of ratio is essential. While middle school students have probably had experience with fractions and decimals, their ability to recognize similarities and appropriate representations depending on a situation is still weak. Making the conceptual jump to ratio needs good concrete models, and quilting can provide this.

NCTM Standards

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:

  • work flexibly with fractions, decimals, and percents to solve problems;
  • compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
  • develop meaning for percents greater than 100 and less than 1;
  • understand and use ratios and proportions to represent quantitative relationships;
  • develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios;
  • solve problems involving scale factors, using ratio and proportion.

    The Basic Activity

    You will have students analyze amounts of shapes or colors in quilt blocks and represent them as fractions, decimals, percents, and differences. Students will then develop ratios that will also represent the colors or shapes. Start with squares that have fourths, eighths or sixteenths, as these are basic, familiar fractions for students to work with.

    Diagram 1

    Add thirds, sixths, and twelfths later in the activity.

    Diagram 4

    You can start with actual fabric quilts chosen for good representations of fractions, websites (see below) that show traditional quilts, or you can plunge right in and have students design their own squares and then do comparisons. Do what will work best for your students. The key will be the questions you ask, student responses, and follow-up work by students.

    Supplies

    Construction paper for mounting finished designs or for using as borders for a larger "group quilt".

    Template or graph paper or other design to use (suggested size for graph paper of 4 squares to the inch or centimeter graph paper) so students can draw their own.

    Colored pencils or crayons. Overheads of graph paper or centimeter paper for modeling.

    Activity - Part 1

    1) Start by reviewing fractions, decimals, and percents. Use a simple quilt block, as in Diagram 1, and ask how many squares would be colored for one-eighth, one-fourth, three-sixteenths, and so forth. Ask how those fractions would be represented as decimals.

    Diagram 2

    2) Give students sample blocks. Have them color specific fraction or decimal amounts. Mix amounts within one block; for example, color one-fourth of the block blue and one-eighth of the block red.

    3) Give students another sample block. Ask them to color specific percents. Decide ahead of time what percents you will use, so that initially the percents are easily converted from fractions and decimals.

    4) A variation if you need it is to give a sample block of one hundred squares and work with percent amounts.

    5) With a new sample block, ask students to color one-fourth blue, one-eighth yellow, one-sixteenth green, one-half red, and another one-sixteenth black.

    Diagram 3

    6) Choose other combinations, making sure the amount adds to one whole. At this point, you can ask for decimal or percent amounts, especially if your class is working well with converting fractions, decimals, and percents, not just through algorithms, but through genuine understanding.

    7) When you feel your students are ready, then add thirds, sixths, and twelfths into the set of blocks. You can work with a different block, or move to a 100-block.

    Diagram 4

    7) When students are ready, ask them to design a block with any fractional colors they want. They will need to write on the back of their block the fraction sentence, the decimal sentence, and the percent sentence that represents their block.

    8) Collect these and mount them into a "finished" quilt, either mounting on colored paper so there is a border around each square, or using strips of colored paper to separate the squares.

    9) Have students search for particular blocks that represent correct fraction /decimal/percent sentences that you give them.

    This would be a great place to look at specific traditional quilts that have been brought in, or use websites that show quilts. Use the same questions from Part 1 of the activity.

    These sites are all active at the time this article was written. You will want to check before actually using these sites in a lesson to be sure they are still active. You will also want to be selective with these images to be sure they meet your objectives in the lesson.

    http://www.equilters.com/library/logcabin/easy_log_cabin_part4.html

    This site shows a traditional Log Cabin quilt pattern and suggestions for color choices. Potential questions would be: what percent of the quilt design is blue? what percent is red? what percent is yellow, and so forth.

    http://www.portup.com/%7Ehjbe/quilt/9patch.html

    This site, while it has links to actual designing patterns, shows some basic nine-patch blocks that could lead to easy conversions of fractions, decimals, and percent. The pictures would need to be larger, but these give good simple examples of other quilt designs you could use. These are very traditional blocks, and many can be found in printed resources for teachers (see below).

    http://quiltart.com/gallery.html

    This is a portal to contemporary quilts, in case you are interested in showing your students how traditional quilting is breaking new paths.

    http://www.unl.edu/mjames_quilts/quilt_images/archive/index.htm

    Michael James is one of the foremost males in quilting. This might help bring your boys around more favorably to the idea of quilting!

    http://www.nancycrow.com/HTML/imagesofquilts.html

    Nancy Crow has revolutionized the use of color and design in quilting. These are great images for looking at fractions and percents.

    http://bryerpatch.com/gallery/gallery.htm

    Carol Bryer Fallert designs and prints her own fabric. You can pick and choose which modern designs would fit with this activity.

    This is only a minuscule sampling of sites available on line concerning quilting. The PowerPoint that accompanies these lessons gives more information about the history of quilting and traditional patterns.

    Activity - Part 2

    Now that you have students looking at color and making comparisons using fractions, decimals, and percents, let's introduce the concept of ratio. Ratio is a "part to part" comparison, whereas a fraction is a part-to-whole comparison. This is a difficult distinction for students, and it is the basis of proportionality.

    1) Take one of the original 16-square block designs. Instead of comparing the fraction of red to the whole block, now you will be comparing the amount of one color to the amount of another color - a "part-to-part" comparison. Ask a question like "what is the ratio of red to blue in this block?" Continue with simpler questions, comparing one color to another until students are comfortable with this.

    2) Now give students some sample blocks for them to complete. Students can use a variety of colors, but two colors will be used for the ratio. If you are using a sixteen-square block, make sure the ratios you give your students will work. Squares that don't fit a particular ratio can utilize another color.

    3) Sample direction: Create a block where the ratio of blue to red is 3 to 1. Students can have the following blocks: 3 blue 1 red, 6 blue 2 red, 9 blue 3 red, 12 blue 4 red. All of these ratios simplify to 3 to 1. In this example, all the blocks could be in two colors.

    4) Give students plenty of practice with this type of simple ratio. When students are ready, then increase the difficulty of the ratio combinations. Have students revisit the completed paper quilts and create ratios based on the designs.

    In Conclusion

    This activity can be as simple or as complex as you would like, depending on the skills of your students. Too often the whole idea of ratio is not explored in middle grades beyond teaching cross-multiplication to solve a proportion. Yet a ratio is the key to so many more mathematical skills. Understanding of ratio is critical to understanding why cross-multiplication works in so many situations. We must do all we can to ensure that students develop proportionality before they head into algebra.

    Resource

    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 and perfect for this activity. The companion poster provides nine quilt blocks that could be used with this lesson.

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