Shapes at Work In Quilts (Activity # 3) Goals/Rationale



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Shapes at Work In Quilts (Activity # 3)

Goals/Rationale: To investigate the ways in which shapes can be used in quilts. 
Focus Content Area: Geometry
Target Grade Level: 2

NCTM Standards:



Setting/Context/Problem: In this lesson, students will explore various shapes and record findings in their math journals. They will record shapes that they observe in quilt examples in class, in books, or on the Internet. Students will especially identify those geometric shapes found in historic/cultural quilts. It would be helpful to display class findings on a bulletin board entitled “Shapes We Have Used (or Made)”.

Materials:

  • Blocks, tangrams, or other traceable shapes

  • Book with quilting examples (present day quilts, historic, and cultural)

  • Internet access with web-links to quilting sites

  • Example of actual quilts with unique patterns and shapes.

Instructional Plan:

Opening Motivation:

Read The Keeping Quilt by Patricia Polacco and distribute a classroom block, tangram, or other traceable shape pattern to each student.  This book is another personalized example of quilting that exhibits the use of a mathematical element.

Have students:



  1. Trace a shape from the story quilt in their journal. 

  2. Draw and label three examples of places where they saw this shape (which in-class quilt?).

  3. Create a sketch of an original patch that includes this shape. 

  4. Share and post their sketches. 

Development

Take students on a guided shape hunt.  To make sure students explore the absolute context of shapes with quilts, explore appropriate examples in a class discussion.

Ask students preliminary questions:



  • What shapes do you expect to see?

  • How do you expect to find them?

  • Which shapes do you think you will find most often? Why?

  • Why did people make quilts?

Note: You may wish to adapt this activity by assigning small groups of students to look for examples of one specific shape.  Or, you might distribute a worksheet with pictures of several shapes for students to find, with a blank space for drawing and/or writing.  Have students record the shapes they see using words and pictures. 
Here are some possible resources for this shape hunt—

Literature Resources:

  • The Log Cabin Quilt by Ellen Howard

  • Sweet Clara and the Freedom Quilt by Deborah Hopkinson

  • The Patchwork Quilt by Valerie Flournoy

  • Sam Johnson and the Blue Ribbon Quilt by Lisa Campbell Ernst

  • Tar Beach by Faith Ringgold

  • The Bedspread by Sylvia Fair

  • The Keeping Quilt by Patricia Polacco

  • The Quilt Story by Tony Johnson

  • The Josephina Story Quilt by Eleanor Coerr

  • Quilts in the Attic by Robin Fleisher

  • Kate's Quilt by John Burningham

  • The Quiltmaker’s Gift by Jeff Brumbeau

  • Selena and the Bear Paw Quilt by Barbara Smucker

  • The Quilt-Block History of Pioneer Days by Mary Cobb, Jan Davey Ellis

  • Quilting Now and Then by Karen B. Willing

  • The Canada Geese Quilt by Natalie Kinsey

  • Eight Hands Round: A Patchwork Alphabet by Ann Whitford Paul

Web Resources:

    • American Patchwork Quilt Design

    • African American Quilting Traditions - History of quilting in African American history and traditions. Actual photos of quilts illustrated.

    • A thumbnail sketch of the quilt type. - Reference for making a quilt square.

    • Archive of American Quilt Designs - Examples and illustrations of many, many quilt patterns and designs.

    • Click and drag the colored triangles to the grid to make your quilt. - A fun, interactive site to help design a quilt block.

    • History and glossary of quilting terms - Useful resource for background information.

    • A fun, printable coloring page of quilt designs - Ideas for quilt blocks and a fun, printable coloring page of quilt designs.

    • How to sew, for children - Step-by-step instructions on how to sew.

    • How to design a quilt block

    • Native American Quilts

    • Seminole Patchwork Designs

    • Abolition Quilts and the Underground Railroad

    • Amish Quilts: Beauty in Simplicity

    • EUROPEAN AMERICAN QUILTING TRADITIONS

Have students answer the following questions in their journal:

  • Which shapes did you find? 

  • Which of these shapes are found in the quilts?

  • Were there any shapes that you expected to see and did not?  Why might that be?

Assessment: Have students revisit their original sketch from the Motivation activity.  Using what they've learned about the uses of shapes, have them add to the sketch so that the object in the drawing can be potentially used in their own quilt. 

Have students write responses to the following questions in their math journal:



  • Why did you pick those shapes, describe why you picked them?

  • Describe elements of the shapes you used?

  • What role does each of these shapes play in your design?

Kim’s Lesson (Activity #??????)
Goals/Rationale: Students will access a website. Students will solve at least 2 tangram puzzles using visualization and spatial reasoning. Students will select tangram for final assessment; students will provide justification for selection.
Focus Content Area: Geometry (Tangrams)
Target Grade Levels: 2-3
NCTM Standards:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:



  • Investigate the results of putting together and taking apart two- and three-dimensional shapes.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems:

  • Interpret relative positions in space and apply ideas about relative position.

Apply transformations and use symmetry to analyze mathematical situations:

  • Recognize and apply slides, flips, and turns.

Use visualization, spatial reasoning, and geometric modeling to solve problems:

  • Recognize and represent shapes from different perspectives.


Setting/Context/Problem: Students will manipulate tangram square pieces to create new figures.
Materials/Resources: Computers, Internet access, overhead projector for demonstration computer, tangram square pieces, journal, pencil
Instructional Plan:

  1. Students will visit the computer lab and log on to http://www.tangram.i-p.com/.

  2. Explicit instruction will be given to help students get accustomed to site:

    1. “This is how you find a puzzle.”

    2. “This is how you select the red triangle.”

    3. “This is how you flip the red triangle.”

    4. “This is how you move the red triangle around.”

    5. “This is how you put the red triangle where you want it to go.”

  3. Teacher will demonstrate 2 tangram puzzles, one easy and one challenging.

  4. Students will complete at least 2 tangram puzzles.

    1. One of the 2 puzzles must be selected from the following: puzzle #8, 14, 93

Hints will be provided as needed. (i.e. “The large red triangle goes in this spot. Now try to figure out where the other pieces go.”)

    1. Students select additional puzzles.

    2. Students might utilize paper tangram pieces to help them think through puzzles. For students having difficulty manipulating pieces on the computer, tangram pieces may be used instead.

  1. Students will select one tangram figure they want to re-create for their assessment. Figure can be from book or from website.

  2. In their journals, students will describe figure they want to re-create. Students will list at least 2 reasons for their selection.


Assessment:

Students will be assessed based on informal observation while they are thinking and solving tangram puzzles. Teacher will take anecdotal notes.

Teacher will review student journals, especially checking that each student has chosen a figure to re-create.


Tessellating Shapes (Activity #11)
Goals/Rationale: Students will define what a polygon is. Students will be able to give examples of where they can find different polygons around the environment. Students will use the information they already know about polygons to explore the concept of tessellations. They will practice creating tessellations using pattern blocks or other shape manipulatives.
Focus Content Area: Geometry (Tessellations)
Target Grade Levels: 2-3
NCTM Standards:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:



  • Investigate the results of putting together and taking apart two- and three-dimensional shapes.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems:

  • Interpret relative positions in space and apply ideas about relative position.

Apply transformations and use symmetry to analyze mathematical situations:

  • Recognize and apply slides, flips, and turns.

Use visualization, spatial reasoning, and geometric modeling to solve problems:

  • Recognize and represent shapes from different perspectives.


Setting/Context/Problem: Students will manipulate patter blocks to create tessellating shapes.
Materials/Resources: Chart paper, Markers, Large cut outs of various shapes, Pattern blocks
Instructional Plan:

  1. Introduce lesson by displaying big shapes on the board. Ask the students to remember what they learned the last two weeks. What are they called? Define what a polygon is for vocabulary. Remind them that it is a closed shape that has straight lines.

  2. Ask the first question: where in the environment can we find examples of different polygons or shapes, and what are they used for? Allow the students to talk to a neighbor and discuss it. Write some examples on the chart paper.

  3. Form a big circle on the floor with the whole class. Take pattern blocks and introduce the students to the idea of tessellations or tiling. Explain that these shapes put together can be used to tile a surface without any gaps or overlaps showing. Show them an example using the square pattern blocks in the circle.

  4. Then ask the second question: How do polygons fit together to create tessellations? Ask the students to think about all the shapes they know of and then have them predict which ones will tessellate and which ones will not. This will take many examples to show them what tessellate means. Explain that a circle or oval won’t tessellate because it does not have straight lines.

  5. Write some examples of what they come up with on chart paper.

  6. Have the students return to their seats and pass out pattern blocks. Practice tessellating shapes. Then review what they learned today before switching subjects.


Assessment:

Students will be assessed based on informal observation while they are seated at their desks creating their own tessellating shapes. Also, based on answering questions about where they can find polygons in the environment.









Problem Solving and Quilts (Activity #17)
Goals/Rationale: Students will solve problems involving real life geometry applications.
Focus Content Area: Geometry
Target Grade Levels: 2-3
NCTM Standards:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.



  • Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

  • Create mental images of geometric shapes using spatial memory and spatial visualization.

  • Recognize and represent shapes from different perspectives.

  • Relate ideas in geometry to ideas in number and measurement.

  • Recognize geometric shapes and structures in the environment and specify their location.

Apply and adapt a variety of appropriate strategies to solve problems.
Setting/Context/Problem: 1. We want to make a quilt that has 36 squares, and is a square. In numbers of squares, what would the length and width of this quilt have to be? 2. The length and width of the quilt are both 60”. What are the dimensions of each of the small squares?
Materials/Resources: paper, pencil, 36 small square tiles for each student
Instructional Plan:

  1. Read the problem to the students and write it on the board.

  2. Ask the students if they understand the problem. Define the terms length, width, and dimension.

  3. Divide the students into groups of three. Give each group 36 small square tiles to visually represent the quilt.

  4. Tell the students that each group needs to turn in a picture of the quilt, with 36 squares in it. They should label the length and width of the quilt, in terms of how many squares each side has. They should also draw a small square, and label the length and width of the small square in inches.

  5. As the students are working, walk around the room monitoring them. If they are stuck on the problem, provide suggestions in the form if questions such as, “What type of math do you think needs to be done? Addition? Multiplication?”

  6. Have the students turn in their work when they finish.


Assessment:

Observe students while they are working to see that each student is participating.



Use the following rubric.
15 pts. possible




5 pts.

3 pts.

0 pts.

Drawings

Drawings include the quilt with 36 squares, and a separate drawing of a small square.

Drawings are missing the quilt with 36 squares, or the small square.

Drawings are absent.

Quilt measurements

Length and width are given in terms of the number of squares.

Length or width is missing.

Length and width are missing.

Square measurements

Length and width are given in inches.

Length or width is missing, or units of measurement are missing.

Length and width are missing.


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