Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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ConnectionsSession 06 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Connections
  Introduction | The Tangram Puzzle | Making Connections | Reflection Questions | Your Journal


Reflect on each of the following questions about the tangram problems you've just explored. Select "Show Answer" to see our comments, or if you need help thinking about the questions.

Question: What mathematical concepts are developed in each of the tangram activities?

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Our Answer:
As you make a square, the relationships among the shapes are explored. Also, angles, sides, and other properties among adjoining shapes are considered. Spatial visualization skills and transformations (flips, slides, turns) are needed to move the pieces around and get them to fit into the square.

In "How Big Is Each Piece?", the concepts of fractional parts and area are developed. The relationship among the pieces is also explored. For example, if the large triangle is one-fourth of the square, the medium triangle must be one-eighth, since the medium triangle is half of the large triangle. It will take eight medium triangles to make the whole square.

Similarly, in part (b) of "How Big Is Each Piece?", the small square becomes the unit whole, and the size of the pieces are determined based on that unit. Some of the pieces are smaller than the square, which would be fractional parts; others are larger than the square, so their "value" will be greater than 1; and others are equivalent to the whole, even though they look different.

"The Dartboard" connects basic probability concepts to an area model. It also extends the previous work with fractions to expressing the values as percents.

The "Exploring Shapes" activity examines the relationship among the shapes in the tangram puzzle. By moving around and exploring with the individual pieces, important discoveries are made (for example, two small triangles can make a square, a parallelogram, or a medium triangle).

In "Exploring Angles," using a right angle with a measure of 90° as a benchmark, the measure of the angles in other pieces can be determined. An extension of this activity could include exploration of the angles in a triangle or a quadrilateral.


Question: How do the tangram activities connect to the other Process Standards?

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Our Answer:
Each activity provided a context for the development of a mathematical concept. We explored the concepts in the problem-solving context of a puzzle, communicating our ideas to others as we worked. In each activity, it was necessary to use reasoning to determine the part-whole relationship of the pieces and to justify that reasoning by modeling or explaining our thinking. Finally, the physical model of the tangram presented a concrete representation that could be physically moved, combined, and compared.

As you think about the mathematics tasks you plan for your students, it is important to consider how the tasks connect to other mathematical topics, how they relate to other areas of study in the early grades, and how they apply to contexts outside the classroom. These connections provide opportunities for students to experience mathematics as a coherent whole.

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