| Common Core State Standard:
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7.G Geometry
- 7.G.B Solve real-life and mathematical problems involving angle measure, area, surface, area, and volume.
- 7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
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6.G Geometry
- 6.G.A Solve real-world and mathematical problems involving area, surface, area, and volume.
- 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l x w x h and V = b x h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- 6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems
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5.MD Measurement & Data
- 5.MD.C Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- 5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- 5.MD.C.3a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
- 5.MD.C.3b A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
- 5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
- 5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- 5.MD.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
- 5.MD.C.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
- 5.MD.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems
5.G Geometry
- 5.G.B Classify two-dimensional figures into categories based on their properties.
- 5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
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| Common Core State Standard: Standards for Mathematical Practice
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| CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
CCSS.Math.Practice.MP6 Attend to precision.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
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| Learning Progressions Frameworks Progress Indicator
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| M.ME.1a identifying and describing measurable attributes (including area, surface area, volume, fractional units, absolute value with temperature), and selecting appropriate customary or metric units of measure when solving problems
M.ME.1c recognizing how the formulas for area and volume for a variety of shapes and solids are related
M.ME.2a selecting and applying appropriate standard units, tools, and level of precision in real-world measurement problems (e.g., area, surface area, volume, rate)
M.ME.2b using a variety of strategies (decomposing complex shapes, using formulas and models) to measure area (triangles, quadrilaterals, polygons) and volume (rectangular prisms)
M.ME.2c selecting and applying appropriate standard units and tools to measure to an appropriate level of precision
M.GM.1a describing and classifying plane figures based on their properties
M.GM.1d solving area, surface area, and volume problems by composing and decomposing figures
M.GM.1h solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures)
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| Instructional Family: Geometric Problems
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CCCs addressed:
- 7.GM.1h1 Add the area of each face of a prism to find surface area of three dimensional objects
- 7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles
- 7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals)
- 7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle
- 6.GM.1d1 Find area of quadrilaterals
- 6.GM.1d2 Find area of triangles
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| Instructional Family: Recognizing, Describing, Naming and Classifying
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CCCs addressed:
- 5.GM.1a1 Recognize properties of simple plane figures
- 4.GM.1h2 Classify two--dimensional shapes based on attributes (\# of angles)
- 2.GM.1b3 Distinguish two- or three- dimensional shapes based upon their attributes (i.e., \#of sides, equal or different lengths of sides, \# of faces, \# of corners)
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| Instructional Family: Perimeter, Area, Volume
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CCCs addressed:
- 7.ME.2c1 Solve one step real world measurement problems involving area, volume, or surface area of two- and three-dimensional objects
- 6.ME.2a3 Apply the formula to find the area of triangles
- 6.ME.2b2 Decompose complex shapes (polygon, trapezoid, pentagon) into simple shapes (rectangles, squares, triangles) to measure area
- 6.ME.1c1 Find the area of a 2-dimensional figure and the volume of a 3-dimensional figure 6.ME.1a2 Identify the appropriate formula (i.e., perimeter, area, volume) to use when measuring for different purposes in a real life context
- 5.ME.2b1 Use filling and multiplication to determine volume
- 5.ME.2b2 Apply formula to solve one step problems involving volume
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