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.
