Overview of Lessons
The unit begins with a review of plane figures (triangle, quadrilateral, pentagon, hexagon, and octagon), lines (intersecting, parallel, perpendicular), kinds of triangles (equilateral, isosceles, scalene), and angles (right, acute, obtuse). Diane uses material from her textbook and examples from everyday objects in the classroom to conduct this lesson. To expand the review and to add concepts of similar and congruent figures, as well as lines of symmetry, and to introduce the quilt project, Diane copies examples of quilts from the Internet (e.g., The Decorative Arts Center of Ohio at http://www decartsohio.org).
Diane: Students, when I say “geometry,” what do you think of? Give me some examples of what
that word brings to mind.
Hands shoot into the air, and as Diane calls on her students for their ideas, she writes each example on the board under a heading, “Geometry Words.”
Keri: I think of figures like rectangles, squares, triangles.
Brian: Don’t forget lines. You wouldn’t have those figures without ’em.
Keith: I remember how we studied some weird shapes that had more than four sides, but I don’t
remember what we called them.
Diane: Would you draw one of these figures on the board for us? Then perhaps someone else in
the class can give it a name.
Keith draws a five-sided figure on the board, and eventually Josh remembers that the figure is a pentagon.
Ashley: I guess we should put “circle” on our list even though it isn’t made up of straight lines. Mike: Angles are made of lines. Do we put them on our list?
Diane: Of course, and while we’re talking about angles, can anyone give us some examples of
kinds of angles?
The class has to stop and think about this for a while, so Diane draws examples of acute, right, obtuse, and straight angles on the board. Eventually, the names of each are recalled, and each name goes on the growing list. Diane makes sure that each geometric term on the list of required features for the quilt block is reviewed. (See Figure 10.1 for guidelines.) Next she hands out a copy of the Ohio Star pattern quilt block to each student (see Quilt 1 in Figure 10.2).
Diane: Take a close look at this quilt pattern. Since we’ve been talking about triangles, let’s see if
we can find any triangles in this pattern. See if you can find an easy way to count all of the triangles in the pattern.
Chris: Well, I notice that there are repeating parts in this pattern. The corners each have the same
shapes, and only the middle seems to be different from the rest of the block.
Diane: Good point. Does anyone notice anything else about the triangles in the pattern?
Morgan: I noticed lots of squares in the pattern. Does that mean we’ll have to think of each square as two triangles?
Kim: I think we should only count the actual triangles and not count the squares unless the
square has a definite line in it cutting it into two parts.
Before proceeding to another example of a quilt block pattern, Diane asks her students to trace the lines of symmetry in the Ohio Star pattern. Continuing with the discussion of triangles, Diane shows her students a large copy of the Pine Burr pattern (see Quilt 2 in Figure 10.2).
Diane: This pattern is interesting in that it contains examples of all four types of angles we just
reviewed. Let’s see if we can spot them, and let’s keep a count of the number of each.
The students again notice that this block has repeated patterns in it, and Diane reinforces the idea that large quilts are made by sewing together many blocks so that the finished quilt is really a
FIGURE 10.2 Quilts from the Decorative Arts Center of Ohio
Source: From www.decartsohio.org, with permission.
big example of repeated patterns. Diane has one more sample block for her students to study. It’s the ShooFly pattern (see Quilt 3 Figure 10.2). This time she has a more challenging task for them.
Diane: I’m going to give you a piece of graph paper along with the ShooFly block. This block
contains four smaller blocks. I want you to draw a line around one of these small blocks and then copy the quilt one block at a time onto the graph paper. You should use two different colored pencils as you copy the block. That way, you’ll have an attractive design, and the color will make it easier for you to copy the design.
In this task, Diane’s students will apply the concept of symmetries and any terms that didn’t make the list of “Geometry Words.” Throughout these math lessons, Diane emphasizes the connection of the activities to the quilt block each of her students will make.
Diane asks her students in their social studies lessons to find out from their parents and/or grandparents what countries their ancestors left to come to America. She encourages them to find out what they can about the immigration of their family members (e.g., when they came to America, where they settled, what work they did).
To get her students thinking about using color and symbols to communicate information about the country that they will portray in their quilt block, she asks the students to review what they know about Ohio by naming a fact about the state.
Diane: We’ve been studying Ohio history and geography. I want you to think of things that
represent Ohio. If you drew these symbols, what color would you use for each symbol? Mike: Well, I know that people think of Ohio as the Buckeye state, so I’d draw a buckeye, and
I’d color it brown because that’s the color of the buckeye.
Keri: I think the state bird is the cardinal, and he’s red.
Chris: There’s the Ohio flag, and it’s red, white, and blue, just like America’s flag.
Josh: Can we use blue again? I’m thinking of the Ohio River, and it has to be blue because it’s
water, and water is blue.
This exercise gets the students thinking about how color and symbols communicate information about a place. When Diane polls the class to find out about her students’ ancestors, she finds that 13 different countries are represented. Many students have ancestors from two or more countries. She tells the students to choose one of these countries. She tells the students to choose one of these countries and, with an adult’s help, to search the Internet and books for information about the country that they picked.
Diane has six computers hooked up to a printer in her classroom, but most of her students will use their families’ computers or will be able to complete their research in the school’s library during their study time. She gives the students a list of seven required topics to include in their reports. These topics will help the students focus their research and organize their written and oral reports. (See Figure 10.3 for the rubric and guidelines.)
When the students get the guidelines for making their quilt blocks, they realize that thought, care, and planning will be needed to incorporate both elements of geometry and information about their country into the project. This combination challenges doesn’t overwhelm the students, who eagerly get to work each day. They know that Diane will encourage, advise, and assist, but in the end, the product will be born of their creativity and their personal connection to their family. Each student has personal ownership and a responsibility to the class, too.
For the next three or four days, students busily draw, measure, research, write, color, share ideas, and move around the room to observe each other’s work. Two or three students make several
FIGURE 10.3 (Continued)
rough drafts. The thought of filling up the whole sheet of graph paper with a repeated pattern overwhelms some students, so Diane tells them to think of the graph paper in smaller pieces. She later explained her intervention: “I suggested that they fold the paper in four sections and think of the project in smaller pieces because they were having a hard time making the pattern and putting in the geometric shapes in the one big piece.”
Not every student finds this project easy to complete. Diane helps two students get started by actually assisting them in making the first row, because one of them is having a hard time figuring out what he needs to do. Some of the students got off track in coloring their patterns and “mess up,” and several started over more than once.
Once the quilt blocks are finished, both Diane and the students review the checklist to assess their inclusion of the required geometric shapes, transformations, and patterns (see Figure 10.4). Diane holds her students to high standards: They would have to redo the project if the requirements were not met.
Diane uses construction paper to make a border around each block, fastens all the blocks together, and hangs the finished quilt from the ceiling of the classroom. As an incentive, she tells them, “On Grandparents’ Day, you will give your oral reports to the class and to our visitors.”
Excitement fills the classroom as Grandparents’ Day approaches, and students prepare to give their oral reports. Diane opens a discussion of etiquette, “What are your expectations of your grandparents’ behavior as an audience during your presentations?” One student offers, “They’ll be good listeners.” Diane follows, “How can you tell they’ll be listening?” Students’ hands fly into the air, “They’ll be looking at the speaker.” “They won’t be talking.” “They’ll ask questions about the speech at the end.” Next, Diane asks, “What will be your grandparents’ expectations of the presenters?” Students enumerate, “The presenter speaks loudly and clearly; the speaker shows expression; the speaker talks slowly enough to be understood.” Instead of dictating a list of behaviors, Diane helps her students, with some guidance, to determine procedures and establish classroom rules.
FIGURE 10.4 Sample Student Quilts
Grandparents of more than half of Diane’s students come to hear their grandchildren’s presentations. Diane welcomes the grandparents and gives a brief explanation of the project just completed by her students. The students not only report about the country of their ancestor; they also point out the geometric shapes and patterns in their quilt blocks (see Figure 10.5).
Midway through the time for the reports, the students are dismissed to the cafeteria for lunch. Grandparents have brought dishes of their own ethnic food for their lunch and for the children to sample when they return to class. Diane’s room mother has set a festive table for the platters of galuska, paprikash, kolache, cakes, sweets, and cups of Italian ice. The grandparents delight in tasting, comparing recipes, and recounting how they helped their grandchildren on the project.
Rachael’s grandmother: I had to dig out the family tree to check for names and dates. I
found the family crest and other items in the attic.
Sarah’s grandmother: I had to call my sister and my aunt—they have a better memory
for this information than I have.
Brandon’s grandparents : We had fun sharing the past with Brandon. We still make our
own spaghetti sauce, Italian ice, and dandelion soup.
Jeff’s grandparents speak for many: This was a wonderful project. It got us talking about the past and
combined two important school subjects—math and social studies. We wish we could have had such fun when we were in the fourth grade!
Lunchtime passes quickly. When the children return, they are given small portions of the ethnic foods, and then the reports continue. At the conclusion, applause and hugs fill the classroom. It’s been a wonderful celebration!
The next day, Diane asks the students to tell what they learned from this project. Students report that they found out something they didn’t know about another country connected to their family Some say they were glad they heard stories about their families’ past history from their elders. Most students express an interest in learning more about their origin and want to travel to the country they studied. Several students comment on how much they learned about other countries by listening to other students’ reports. One student sums up the realization of many, “Our quilt is like the United States. The United States is made up of many different people from many countries, just like our quilt is made up of many different blocks. Each block makes the whole quilt beautiful just like each person makes the country beautiful.”
Diane closes the unit with a quick review of the math concepts her students applied in the unit. As she asks students to point to examples in the blocks of transformations, angles, shapes, and lines, her students almost jump out of their seats to identify what she’s highlighting. All agree that this project was a great way to use geometry and was a lot of fun.
Overall, Diane is satisfied with the efforts of her students and with their application of geometry, and she plans to teach the unit again. She comments:
I had no problems keeping my students on task. This was a very engaging project. I’m convinced they were able to apply the geometry ideas we rushed through earlier in the year. What was really interesting is the fact that many students started making patterns in rows as they drew their block. When the block was finished, they were delighted to see more patterns in the block than they had intended. Some patterns ran diagonally as well as up or down, left or right.