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
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Teacher Actions
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Develop area formulas for triangles by making conjectures, modeling, and generalizing patterns identified through investigations using grid paper and other methods.
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Develop mathematical reasoning to assess the reasonableness of area calculations for triangles by first estimating the answer for the problem.
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Communicate mathematically when discussing ways to determine the area of a triangle or to determine the height of a given triangle.
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Develop a deep and flexible conceptual understanding of how to choose and label units appropriately when finding the area of triangles.
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Develop mathematical reasoning to make predictions to draw conclusions when describing how changes in the dimensions of a triangle affects area.
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Develop accurate procedural fluency by correctly applying the formula to find area of triangles.
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Use and connect mathematical representations helping students make connections between the models and generalized patterns in order to develop the area formula for triangles.
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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?)
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Facilitate meaningful discourse by engaging students in solving and discussing tasks involving area of triangles that help students develop a sense of reasonableness.
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Use evidence of student thinking to assess progress towards understanding the difference between units and square units.
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Build procedural fluency to apply the area formula for triangles using conceptual understanding.
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Key Understandings
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Misconceptions
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Area is the amount of space inside a two-dimensional figure.
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Square units are used for area because the area of a figure represents the number of unit squares that will cover that figure.
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Triangles with the same area can have different dimensions.
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How to apply the formulas for finding the area of a triangle.
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A triangle is half the area of a rectangle or a parallelogram.
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The height of a triangle can be measured from the vertex opposite the base to the base using a perpendicular line.
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- Forget to “half” the base x height.
- Forget that the units for area are squared.
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OKMath Framework Introduction
6th Grade Introduction
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