See PDF version: Measuring Experiences for Young Children» [PDF, 345KB]

Problem introduction
Four-year-olds in a prekindergarten class decided to decorate their classroom with a beautiful multi-colored quilt. The teacher cut construction paper “scrap” pieces into the following sizes:  3" X 3" squares, 3" X 6" rectangles, 6" X 6" squares, 3" X 9" rectangles, and 6" X 9" rectangles. The teacher gave each child a 12" X 18" piece of white paper and told the children to completely cover their white paper with colored paper. Just as in a quilt, the pieces could not overlap. Each child had to order his or her construction paper pieces from the “paper store.” The children had to use words to tell what color and size they needed as well as the specific number of each piece.

Observed investigations
The children’s words and actions were especially interesting. Only a few children ordered multiple pieces of paper. Most ordered one or two pieces of paper, went back to their seats to place the pieces on their paper, and returned to the “store.” Often, they ordered their favorite color, discovered that using only one color was boring, and returned their pieces to get other colors. The words and behaviors that the children used to order also were interesting. “Long ones,” “fat squares,” “tall pieces,” “little rectangles,” “big like my hand,” and “the same as” were all phrases that children used to describe the piece they wanted. They frequently used their hands to show the size of the piece they  were requesting. When the teacher “store clerk” expressed uncertainty about the order, children changed their minds, clarified their responses with phrases such as “more bigger” or “not fat like that one,” or moved their hands to indicate longer or shorter lengths.
 
Problem conversations
As children worked to cover their paper, many of their conversations were between peers as well as with the teacher. Peer interactions were generally commands such as “Move that fat one,” “Take that one off,” or “Go get a tall one.” The teacher-child interactions, however, involved questions and responses such as “I wonder how they could all fit,” “What pieces would fit here?” and “How many more do you think you will need to cover the whole piece?”

Follow-up activities
Children placed all their 12" X 18" rectangles on a large piece of butcher paper so that they could be displayed as one large rectangular quilt made by the class. Initially, they placed the eighteen rectangles as five rectangles in each row; they made three full rows and left three rectangles in an incomplete row. The class agreed with one child who said, “Good thing we didn’t glue it!” After discussion and several variations, the children placed the eighteen rectangles in three rows with six rectangles per row. Later, the children did a similar activity using triangles of equal size.

Connections to the Standards
The four-year-olds in this activity used language to communicate the lengths of paper that they wanted to order from the store. When children were required to “order” their quilt pieces from the store- keeper, they were encouraged to use words to compare and “recognize the attributes of length”(NCTM  2000,  p.  102). After they selected the pieces, they had to fit them together and completely cover the area of their quilt pieces. That task required children to relate the lengths of the individual pieces to the area of the quilt piece and “recognize the attributes of area” (NCTM 2000, p. 102).