• understand the formulas for the area of parallelograms and triangles
• apply knowledge of these formulas to compute area

• Varying academic levels: uses mixed-ability groups allow students to learn from one another, small and whole group participation
• Visual learners: incorporates drawings of figures that allow students to see how formulas are calculated
• Auditory learners: uses guided questioning and discussion to help students articulate how they found formulas and computed area
• Kinesthetic learners: engages students in drawing, cutting, and taping geometric figures in order to determine how to compute area

• Interdisciplinary connection: Explain to students that the attempt to find formulas to compute the areas of geometric figures has been going on since the ancient Greeks, Indians, Egyptians, and Babylonians developed formulas to help them survey lands, construct buildings, and study the night sky.
•  Ask the class to draw a rectangle of any size on a piece of grid paper. Have them discuss with a partner ways in which they could find the area of the rectangle.
• Have students find the area of their rectangle.
• Ask students to discuss how they found the area (by counting the squares in the grid, by using a formula, etc.).
• On a white board, or a chalkboard, write the formula for the area of a rectangle, A = w × l.

• Tell students that they can figure out the formula for the area of a triangle and a parallelogram once they know the formula for the area of a rectangle.
•  Ask students to draw and cut out two identical rectangles. Cut one of the rectangles along the diagonal.
• Have students compare the areas of the triangles with the area of the rectangle.
• Invite students to write a formula for the area of a triangle on the board and illustrate the procedure they used to find the formula.
• Explain that the terms base and height are used in place of length and width, so that the formula for a triangle is A = ½ × b × h.
• Have students draw and cut out a parallelogram on the grid paper. Then, use the scissors and tape to create a rectangle from the parallelogram.
• Invite several students to show the class how they formed the rectangle.
•  Use guided questions to arrive at the formula of a parallelogram.
• Explain that the terms base and height are used in place of length and width, so that the formula for a parallelogram is A = b × h.
• Invite students to write a formula for the area of a triangle on the board and illustrate the procedure they used to find the formula.

• Create mixed-ability pairs and ask them to create math problems for each other that involve computing the areas of a series of triangles and rectangles. Pair up stronger academic students with challenged students.

• Invite each pair of students to write one of the problems they created and solved on the board.
•  Ask other students to explain how to find the solutions to the problem.
• If students have difficulty computing the area of a problem, lead them through the steps using grid paper, pencils, scissors and tape to compute the area.

• Remind students that if they ever forget the formula for calculating the area of a triangle or a parallelogram, they can figure it out themselves using pencil, grid paper and scissors.
• Extension:  Ask students to choose from a variety of enrichment activities:

• Present an oral on how geometry was used in the ancient world.
• Write a short biography of Euclid, Pythagoras, Yajnavalkya, or another mathematician who made significant contributions to the field of geometry.
• Create posters for the classroom illustrating how the formulas for triangles and rectangles are calculated.
• Make a craft using the formulas for triangles, rectangles, or parallelograms.