Aim:

1. To identify fractional parts of whole.

2. To recognize simple fractions as instructions to divide.

3. To use drawing, and models to show what the numerator and denominator of a fraction mean.

Standards:

1. Formulates problems, implements problem solving strategies, and draws conclusions.

2. Describes and compares quantities by using concrete and real world models of simple fractions.

Materials:

tangram pieces, graph paper, pencil, computer, printer, drawing application such as AppleWorks.

Vocabulary:

Dictionary.com may be used to define these words:

 fraction equivalent numerator denominator

Motivation:

1. Trace one large triangle and one small triangle on a piece of graph paper. Cut out the small triangle. Trace 7 of the small triangles and cut them out. Students explore, using these triangles, to answer these questions:

• How many small triangles fit exactly on one large triangle?
• What shape is made if we put two large triangles together?
• Predict how many small triangles fit on this large square.
• What fraction of the large square is each small triangle.

Draw a picture on the AppleWorks drawing application to show what fraction each small triangle is in relation to the large triangle. Explain in words what the relationship is and how you determined this.

Development:

1. Trace one small square on a piece of graph paper. Use small triangles to explore and answer these problems:

• How many small squares fit exactly on one small square?
• What fraction of the small square is one small triangle.
• What fraction of the large square is one small square?

Draw a picture on the AppleWorks drawing application to show what fraction each small triangle is in relation to the small square and what fraction of the large square is one small square. Explain in words what the relationship is and how you determined this.

2. Trace one parallelogram on a piece of graph paper. use small triangles to explore and as were these questions:

• How many small triangle fit exactly on one parallelogram?
• What fraction of the parallelogram is one small triangle?
• What fraction of the large triangle is one parallelogram?
• What fraction of the large square is the parallelogram?
• How many parallelograms would be needed to equal one half of the large square? one fourth?

Draw a picture on the AppleWorks drawing application to show what fraction each small triangle is in relation to the parallelogram.. Explain in words what the relationship is and how you determined this. Draw a picture to show what fraction of the large triangle is in relation to the large triangle and the large square.

3. Trace two large triangles together so that they form a large square.

• How many medium squares fit exactly on the large square?
• What fraction of the large square is each medium square?
• How many medium squares would equal one half of the large square? one fourth? one eighth?

Draw a picture to show what fraction of the medium triangle is in relation to the large square.

Summary:

Students, in cooperative groups formed in Lesson 2, use the tangram characters they created to find fractional relationships among their tangram pieces. Students trace their characters on graph paper, draw on AppleWorks drawing application, and explain in words the fractional relationships they found. Students print and share their findings.

Evaluation:

Students complete the following chart. The first entry is done as a sample.

 Tangram Tangram Unit Fraction Diagram large square small square 1/4 large square small triangle large square medium triangle large square large triangle large square parallelogram parallelogram small triangle large triangle small triangle large triangle medium triangle medium triangle small triangle small square small triangle

Related Web Sites:

1. This site, by Joanne Caniglia, entitled Tangrams and Fractions, provides a lesson plan for grades 5-6 in which students identify the fractional part of each tangram piece add fractions with unlike denominators and create equations using their tangram pieces.

http://mathforum.org/paths/fractions/frac.tangram.html

Related Information:

Julie Kanazawa, Teaching Mathematics with the Internet, Classroom Connect, (El Segunda, CA, 1998) pages 86-89. This tangram unit provides activities and links to tangram construction, tangrams and fractions, and area of tangram pieces.