## Math on Your Lap Quilt

### Kristy RousseauBay District Schools

#### Description

Student-created quilt blocks are used to investigate and develop procedures for finding the area of squares and rectangles.

#### Objectives

The student uses concrete and graphic models to develop procedures for solving problems related to measurement including length, weight, time, temperature, perimeter, area, volume, and angles.

The student writes for a variety of occasions, audiences, and purposes (for example, journals to reflect upon ideas, reports to describe scientific observations).

#### Materials

-Student-created patchwork samples from previous lesson, -Patchwork Quilting- OR
-Student copies of the Design Template (see Associated File)
-Pencils
-Crayons, colored pencils, or markers
-One-centimeter grid paper
-Student and group copies of the Layout Designs sheet (see Associated File)
-Math journals
-Paper

Books:
-THE PATCHWORK QUILT by Valerie Flournoy, E.P. Dutton, 1985.
-THE KEEPING QUILT by Patricia Polacco, Simon & Schuster, 1998.

#### Preparations

1. Gather student-created patchwork blocks from the lesson -Patchwork Quilting- OR copy the Design Template for students to use.
2. Gather crayons, markers, and colored pencils, if needed.
3. Preview books.
4. Copy the Layout Designs sheet for students and groups.
5. Gather one-centimeter grid paper for small group activity and assessment.
6. Gather math journals and paper.

#### Procedures

BACKGROUND: This lesson may be used in conjunction with the lesson -Patchwork Quilting- or as an independent exploration. Students may use the individual patchwork blocks created in the lesson -Patchwork Quilting,- or they may design one using the Design Template, and crayons, colored pencils, or markers. Encourage students to be creative with their quilt blocks. If desired, a theme can be established for the quilt (i.e., Friendship, Love, Independence) in order to integrate this activity with other topics being studied.

*Note: If your classroom incorporates centers or work stations, you may want to use this time to have students complete their quilt blocks prior to the lesson.

DAY ONE
GAIN ATTENTION
1. Share one of the books on quilts. Discuss the purpose of quilts (warmth), and how they were originally made (by hand from scrap pieces, or patches, of material).
2. Tell students that quilts also contain a lot of math! Review pictures in the book with the students and ask them, -Where's the math on this quilt?- Lead students to identify previously discussed geometric shapes (squares, triangles, rectangles, hexagons, etc.) and concepts (symmetry).

PRESENT OBJECTIVES
3. Explain that they will be using quilt blocks today to explore the different areas that can be covered with their patchwork samples. (In this initial lesson, area will be emphasized as a measure of covering. Mathematical formulas will not be formally introduced. )

RELATE TO PRESENT KNOWLEDGE
4. Ask students about the different types and uses for quilts today (bed covers, wall hangings, lap quilts, pillows, keepsakes and heirlooms, etc.). Explain that quilters often start with a basic shape (such as the square) and build the quilt to cover a specific -area- such as a pillow, a bed, a lap, etc.
5. Ask students where they have heard the word -area- before. Select students to share sentences using this word. Use examples provided to compose a class definition of -area.- Display the word and defintion on the board for reference.

ENGAGE IN LEARNING
6. Select one quilt block and ask, -What area can be covered with this one?- Solicit answers from students (a small pillow, a doll-bed cover, etc.) Select another quilt block and ask, -What area can be covered with two?- Again, solict answers from students (a larger pillow, a baby's lap, etc.) Encourage both useful and creative responses.
7. Select a third block and ask students to describe all possible layout designs. For each design offered, display the blocks on the board and identify the rows and columns covered. Accept all designs offered, but explain that most quilt designs are in the form of squares or rectangles.
8. Pass out copies of the Layout Designs sheet, and model how to record each layout arrangement and the area covered by the rows and columns of the quilt blocks. Discuss possible purposes for a quilt containing three blocks.
9.Continue with four quilt blocks. Encourage students to explore both square and rectangular arrangements, and model how to find and record the area of each new arrangement on the Layout Designs sheet. Discuss possible purposes for a quilt containing four blocks.
10. Have students work in pairs to continue adding blocks (up to 10). Remind students to explore all possible arrangements and to record the area that each new arrangement covers on the Layout Designs sheet.
11. When students are finished, redirect their attention to the definition of -area- placed on the board. Based on the class' observations and experiences today, how does the definition need to be revised? As a class, compose a -new and improved- definition of area. Display the revised definition under the first one for reflection and future reference.
12. Journal Entry: Show all possible layout designs for a quilt of 12 blocks. (You may sketch the designs, or list the rows and columns covered by each design.) For each design, provide at least one purpose for the quilt. Be creative as you think about the areas that can be covered with these blocks!

DAY TWO
PROVIDE OPPORTUNITY FOR PRACTICE AND FEEDBACK

1. Review and discuss the mathematical elements of quilts (shapes, symmetry, area, etc.) Ask students to describe the layout designs and purposes they proposed in their journal entries for a 12 block quilt.
2. Select a student to read the -new and improved- definition of area that was posted yesterday on the board. Tell the students that they will be working in small groups today to develop procedures for finding the areas of squares and rectangles.
3. Divide the class into groups of 2 or 3 students. Provide one sheet of centimeter grid paper for each student, and one copy of the Layout Designs sheet for each group.
a) On the grid paper, sketch all possible arrangements for quilts containing 16, 20, and 24 blocks. (One centimeter square = one quilt block)
b) Use the Layout Designs sheet to record the rows and columns of each layout design and the total area covered by the square units as modeled and practiced on DAY ONE (see procedure steps #8-10 for review).
c) When finished, brainstorm different ways to find the area of square and rectangular designs. List ideas on the back of the Layout Designs sheet.
* After the groups are settled and working, rotate among them to offer additional guidance and teaching as misunderstandings and misconceptions are observed.
5. Recovene as a whole class, and solicit from student groups the various procedures developed to find the area of square and rectangular regions (count individual squares, multiply the rows and columns, etc.). Summarize and categorize their findings as necessary to help the students -make sense- of what they have experienced.
6. Revisit the definition of -area- posted on the classroom board. Rewrite or streamline the definition to reflect additional classroom experiences and observations. Add to the definition a list of procedures for finding the area of square and rectangular regions. (Use student wording and ideas!)
7. Journal Entry: Show all possible layout designs for a quilt of 30 blocks. Describe two different procedures for finding the area covered by these designs.

#### Assessments

Scenario: The librarians have agreed to display a patchwork quilt, but they need it to cover a large area. They want to see all possible layout designs for a quilt using 36 blocks.

a) On a sheet of grid paper, sketch all possible arrangements for a quilt of 36 blocks. Number each design (1, 2, 3, etc.).
b) On a clean sheet of paper, list by number the rows and columns covered by each layout design.
c) Explain at least two different procedures for finding the area of square and rectangular regions. (Use the examples of the 36 quilt blocks to model and support your explanation.)

Review students' work and assess for the following criteria:
a) Five (5) different layout design sketches for 36 quilt squares.
b) A list of the rows and columns covered by each numbered layout design. (i.e., 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6)
c) An explanation that reflects comprehension of the different procedures that can be used to find the area of square and rectangular regions (i.e, count individual squares, multiply the rows and columns, etc.).

Scoring Criteria
a) 8 points for each different layout design (TOTAL points possible= 40 points)
b) 8 points for each row and column listing (TOTAL points possible= 40 points)
c) 10 points for each procedure explained (TOTAL points possible= 20 points)

#### Extensions

Extensions:

1. Place blank copies of the Design Template and scissors at a math center. Allow students to cut apart the 6 x 6 block template and redesign the quilt to show other possible arrangements. Ask students to explain why the area did not change with each new arrangement.

2. The Design Template is based on the unit of one square inch. Have the class explore the area (in square inches) of each quilt block (36 square inches) as well as the area of a quilt containing 36 blocks. Point out where one square foot would occur in the class quilt in order to extend students' understanding of the concept of area and the units that can be used to explain it.