In module 5, students use their understanding of the areas of rectangles to develop formulas for the area of a parallelogram and the area of a triangle. Students apply their prior knowledge of area, equivalent numerical expressions, the properties of operations, and coordinate graphing as they find the areas of composite polygons and trapezoids. They identify attributes of the faces of right prisms and pyramids and use the net of a solid to determine its surface area. By packing right rectangular prisms with cubes of fractional edge lengths, students determine that the formulas
V = lwh and V = Bh
can be applied to find the volume of any right rectangular prism with positive, rational number edge lengths. Students apply these formulas to solve real-world and mathematical problems, and they write and solve single-variable equations to determine unknown measurements of a prism.
In topic B, students apply their understanding of the areas of rectangles and triangles to find the areas of composite polygons and trapezoids. First, they solve problems involving figures graphed in the coordinate plane, using their understanding of rational number coordinates to determine side lengths and find the perimeters and areas of figures. Then students transition to working with trapezoids and composite figures not in the coordinate plane. They use known measurements to determine unknown measurements in a figure and explore multiple strategies to find the areas of polygons, including composition, decomposition, and subtraction.
6.NS.10: Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).
6.AF.2: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them.
6.AF.8: Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
6.GM.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate; apply these techniques to solve real-world and other mathematical problems.
6.GM.4: Find the area of complex shapes composed of polygons by composing or decomposing into simple shapes; apply this technique to solve real-world and other mathematical problems.
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Lesson at a Glance
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