Illuminations: Paper Quilts

Paper Quilts

Parts of a Square

Students investigate the ways shapes can be divided into equal pieces with one or two cuts. It provides a review of the following vocabulary terms: square, triangle, and rectangle; congruent, one-half, and one-fourth. The other lessons in this unit build on this introductory lesson.

Learning Objectives
 
Students will:
  • explore ways to divide a square into two equal parts with a single cut
  • explore ways to divide a square into four equal parts
  • use geometric and fractional terms to name the parts

Materials
 
Paper Quilts Bibliography
Three-Inch Squares Template
Scissors
3-inch by 3-inch paper squares (white paper)
Glue
Large sheets of paper

Instructional Plan

To set the stage for learning, you may wish to read one of the books listed in the Paper Quilts Bibliography, such as Tar Beach or The Patchwork Quilt. After reading the stories, ask students to name squares, rectangles and triangles as you display model figures on the chalkboard, overhead or on a surface all can see. Sample shapes are shown below:

Give each student a 3" square of paper. You may want to print out and cut for students from the following template.

Three-Inch Squares Template></A> </TD> <TD valign=bottom><a href=Three-Inch Squares Template

Encourage students to find as many ways as they can of folding the square into 2 and 4 equal parts. Then distribute scissors and several 3" paper squares, and ask the students to explore how many ways they can cut a square into two or four equal parts. They should use a different square for each example. Demonstrate how they can place one half on the other to show the parts are the same size and shape, or congruent. You may ask the students to record the ways they found by gluing them on a large sheet of paper. Encourage them to label the pieces with a fractional symbol.

When the children are ready, call them together to share what they have found. As you discuss with the students how the square can be divided, model the vocabulary you wish them to use. Ask them to explain how they cut their squares and to defend their claim that the parts are equal. Then have students reflect on how they can tell two figures are halves (or quarters) of the whole. You may ask students to provide you with written reflections.

Questions for Students
 

What type of cuts did you use?

[Student responses may vary.]

How can we tell the parts are equal?

[The shapes are congruent.]

Can you cut a square into 4 squares? 4 rectangles? 4 triangles?

[Students should be able to perform the cuts.]

What did you do to check that the parts were the same size and shape?

[Student responses may vary, but they may say they tried to overlay the shapes to see if they fit perfectly.]

Did all the cuts produce rectangles? Which ones? Triangles? Did you get any other shapes?

[Student results may vary.]

Assessment Options
 
  1. At this stage of the unit, it is important for students to know:
    • the names of the shapes
    • how to determine when shapes are equal parts of a whole
    • how to use the fractional names one-half and one-fourth correctly
  2. The guiding questions help students focus on the mathematics and aid you in understanding the students’ level of knowledge and skill with the mathematical concepts of this lesson. Documenting information about student understanding and skills throughout the unit helps you focus on individual needs and strengths and helps you provide appropriate learning opportunities.

Teacher Reflection
 
  • Which students met all the objectives of this lesson? What extension activities would be appropriate for those students? What evidence did you collect to document that learning targets were met?
  • Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification? What evidence did you collect to document that learning targets were not met?
  • What adjustments would you make the next time you teach this lesson?

NCTM Standards and Expectations
 
Geometry 3-5
  1. Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
Number & Operations 3-5
  1. Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
  2. Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

References
 
  • Cohen, Luanne Seymour. Quilt Design Masters. Palo Alto, CA: Dale Seymour, 1996.
  
1 period   

NCTM Resources

Navigating through Geometry in Grades 3‑5

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