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6-GM-1-2

Page history last edited by Brenda Butz 6 years, 2 months ago

6.GM.1.2 Develop and use formulas to determine the area of triangles.

In a Nutshell

Students may continue exploring area using grid paper and unit squares. Modeling the decomposition (taking apart) of two-dimensional shapes such as rectangles and parallelograms into triangles will help students develop the formula for finding area of a triangle. Two equal right triangles will be produced from a rectangle, while half of a parallelogram is also a triangle. This will further develop the understanding of the formula A = ½(bh). Students will further learn that height of a triangle must be measured with a perpendicular line from one vertex to the opposite base.

Student Actions	Teacher Actions
Develop area formulas for triangles by making conjectures, modeling, and generalizing patterns identified through investigations using grid paper and other methods. Develop mathematical reasoning to assess the reasonableness of area calculations for triangles by first estimating the answer for the problem. Communicate mathematically when discussing ways to determine the area of a triangle or to determine the height of a given triangle. Develop a deep and flexible conceptual understanding of how to choose and label units appropriately when finding the area of triangles. Develop mathematical reasoning to make predictions to draw conclusions when describing how changes in the dimensions of a triangle affects area. Develop accurate procedural fluency by correctly applying the formula to find area of triangles.	Use and connect mathematical representations helping students make connections between the models and generalized patterns in order to develop the area formula for triangles. Pose purposeful questions to assess the students’ understanding of mathematical properties and ability to explain their thinking and justify their results for area problems involving triangles. (Ex: How is the formula for the area of a triangle similar to finding the area of a rectangle?) Facilitate meaningful discourse by engaging students in solving and discussing tasks involving area of triangles that help students develop a sense of reasonableness. Use evidence of student thinking to assess progress towards understanding the difference between units and square units. Build procedural fluency to apply the area formula for triangles using conceptual understanding.
Key Understandings	Misconceptions
Area is the amount of space inside a two-dimensional figure. Square units are used for area because the area of a figure represents the number of unit squares that will cover that figure. Triangles with the same area can have different dimensions. How to apply the formulas for finding the area of a triangle. A triangle is half the area of a rectangle or a parallelogram. The height of a triangle can be measured from the vertex opposite the base to the base using a perpendicular line.	Forget to “half” the base x height. Forget that the units for area are squared. When given an area, students may think there are always unique dimensions that will form a triangle with that area. Confuse a slanted side of a triangle for the measure of the height.