Middle Measurement Unit Standards Overview
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:::'''[http://www.corestandards.org/Math/Content/5/MD/C/3/a| 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. | :::'''[http://www.corestandards.org/Math/Content/5/MD/C/3/a| 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. | ||
− | '''[http://www.corestandards.org/Math/Content/5/MD/C/3/b| 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. | + | :::'''[http://www.corestandards.org/Math/Content/5/MD/C/3/b| 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. |
− | '''[http://www.corestandards.org/Math/Content/5/MD/C/4| 5.MD.C.4]''' Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | + | ::'''[http://www.corestandards.org/Math/Content/5/MD/C/4| 5.MD.C.4]''' Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. |
− | '''[ | + | ::'''[http://www.corestandards.org/Math/Content/5/MD/C/5| 5.MD.C.5]''' Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. |
− | '''[ | + | |
− | '''[ | + | :::'''[http://www.corestandards.org/Math/Content/5/MD/C/5/a| 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. |
+ | |||
+ | :::'''[http://www.corestandards.org/Math/Content/5/MD/C/5/b| 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. | ||
+ | |||
+ | :::'''[http://www.corestandards.org/Math/Content/5/MD/C/5/c| 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 '''Geometry | ||
− | '''5.G.B '''Classify two-dimensional figures into categories based on their properties. | + | |
− | '''[ | + | :'''5.G.B''' Classify two-dimensional figures into categories based on their properties. |
+ | |||
+ | ::'''[http://www.corestandards.org/Math/Content/5/G/B/3| 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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− | |width = "2500" style="background-color:#FFFFFF;"|''' CCSS.Math.Practice.MP1 '''Make sense of problems and persevere in solving them. | + | |width = "2500" style="background-color:#FFFFFF;"|'''CCSS.Math.Practice.MP1''' Make sense of problems and persevere in solving them. |
− | ''' CCSS.Math.Practice.MP2 '''Reason abstractly and quantitatively. | + | '''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. | ''' CCSS.Math.Practice.MP8 '''Look for and express regularity in repeated reasoning. | ||
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− | |width = "2500" style="background-color:#FFFFFF;"|'''M.ME.1a | + | |width = "2500" style="background-color:#FFFFFF;"|'''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 | + | |
− | '''M.ME.2a | + | '''M.ME.1c''' recognizing how the formulas for area and volume for a variety of shapes and solids are related |
− | '''M.ME.2b | + | |
− | '''M.ME.2c | + | '''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.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.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.GM.1h '''solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures) | + | |
+ | '''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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|width = "2500" style="background-color:#FFFFFF;"|CCCs addressed: | |width = "2500" style="background-color:#FFFFFF;"|CCCs addressed: | ||
− | * '''5.GM.1a1 '''Recognize properties of simple plane figures | + | * '''5.GM.1a1''' Recognize properties of simple plane figures |
− | * 4.GM.1h2 | + | * '''4.GM.1h2''' Classify two--dimensional shapes based on attributes (\# of angles) |
− | * 2.GM.1b3 | + | * '''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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|width = "2500" style="background-color:#FFFFFF;"|CCCs addressed: | |width = "2500" style="background-color:#FFFFFF;"|CCCs addressed: | ||
− | * '''7.ME.2c1 '''Solve one step real world measurement problems involving area, volume, or surface area of two- and three-dimensional objects | + | * '''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.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.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 | * '''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.2b1''' Use filling and multiplication to determine volume | ||
− | * | + | * '''5.ME.2b2''' Apply formula to solve one step problems involving volume |
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Revision as of 09:31, 14 August 2013
Unit Standards Overview
Common Core State Standard: |
7.G Geometry
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6.G Geometry
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5.MDMeasurement & Data
5.G Geometry
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Common Core State Standard: Standards for Mathematical Practice |
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP2Reason 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. |
Learning Progressions Frameworks Progress Indicator |
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) |
Instructional Family: Geometric Problems |
CCCs addressed:
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Instructional Family: Recognizing, Describing, Naming and Classifying |
CCCs addressed:
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Instructional Family: Perimeter, Area, Volume |
CCCs addressed:
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