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(GM) Geometry and Measurement

MAT-06.GM

BPSS-MAT-GM logo  MAT-06.GM Domain 
BPSS-MAT-GM logo

(GM) Geometry and Measurement 

Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.

Sub-Categories

  • (G) Geometry 
    Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.
  • (M) Measurement 
    Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.
  • (AV) Area and Volume 
    Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.
  • (GF) Geometric Figures
    Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-06.GM.AV.01

BPSS-MAT-GM logo 6th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
(AV) Area and Volume
Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.
MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals by composing and/or decomposing them into rectangles and triangles, including authentic problems.*

proficiency scale iconProficiency Scale

Progressions

Area/Surface Area

  • MAT-03.GM.M.07 Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • MAT-03.GM.M.08 Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.
  • MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
  • MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
  • MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles and triangles.
  • MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.
  • MAT-07.GM.AV.02 Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.
  • MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.
  • MAT-12.GM.04 Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

MAT-06.GM.AV.02

BPSS-MAT-GM logo 6th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
(AV) Area and Volume
Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.
MAT-06.GM.AV.02 Describe the concept of volume of aright rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.*

proficiency scale iconProficiency Scale

Progressions

Volume

  • MAT-05.GM.M.03 Recognize volume as an attribute of rectangular prisms and measure volume by counting unit cubes.
  • MAT-06.GM.AV.02 Describe the concept of volume of a right rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.
  • MAT-07.GM.AV.03 Solve problems involving the volume of prisms and composite solids, including authentic problems.
  • MAT-08.GM.AV.01 Apply given formulas to solve problems involving the volume of cones, cylinders, and spheres, including authentic problems.
  • MAT-10.GM.32 Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
  • MAT-10.GM.33 Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
  • MAT-10.GM.35 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

MAT-06.GM.GF.01

BPSS-MAT-GM logo 6th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
(GF) Geometric Figures
Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-06.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.*

proficiency scale iconProficiency Scale

Progressions

Coordinate Plane

  • MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
  • MAT-05.GM.G.02 Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.
  • MAT-05.GM.G.03 Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.
  • MAT-06.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.
  • MAT-06.GM.GF.02 Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.
  • MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.
  • MAT-10.GM.28 Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.
  • MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.
  • MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.
  • MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
  • MAT-12.NO.14 Recognize vector quantities as having both magnitude and direction, writing them in polar form.
  • MAT-12.NO.15 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
  • MAT-12.NO.16 Solve problems involving magnitude and direction that can be represented by vectors.
  • MAT-12.NO.17 Add and subtract vectors.
  • MAT-12.NO.18 Multiply a vector by a scalar.
  • MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • MAT-12.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

MAT-06.GM.GF.02

BPSS-MAT-GM logo 6th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
(GF) Geometric Figures
Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-06.GM.GF.02 Draw polygons in the coordinate plane given coordinates for the vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.

proficiency scale iconProficiency Scale

Progressions

Coordinate Plane

  • MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
  • MAT-05.GM.G.02 Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.
  • MAT-05.GM.G.03 Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.
  • MAT-06.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.
  • MAT-06.GM.GF.02 Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.
  • MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.
  • MAT-10.GM.28 Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.
  • MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.
  • MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given complex number represent the same number.
  • MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
  • MAT-12.NO.14 Recognize vector quantities as having both magnitude and direction, writing them in polar form.
  • MAT-12.NO.15 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
  • MAT-12.NO.16 Solve problems involving magnitude and direction that can be represented by vectors.
  • MAT-12.NO.17 Add and subtract vectors.
  • MAT-12.NO.18 Multiply a vector by a scalar.
  • MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • MAT-12.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

MAT-06.GM.GF.03

BPSS-MAT-GM logo 6th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
(GF) Geometric Figures
Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.

proficiency scale iconProficiency Scale

Progressions

Three-Dimensional Shapes

  • MAT-00.GM.G.02 Name shapes and identify them as three-dimensional (cubes and spheres) regardless of their orientations or overall size.
  • MAT-01.GM.G.02 Name and identify solids as three-dimensional (cylinders, cones, triangular prisms, and rectangular prisms).
  • MAT-01.GM.G.03 Determine geometric attributes of two-dimensional and three-dimensional shapes.
  • MAT-02.GM.G.02 Identify two-dimensional shapes found within three-dimensional shapes.
  • MAT-02.GM.G.03 Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.
  • MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.

Area/Surface Area

  • MAT-03.GM.M.07 Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • MAT-03.GM.M.08 Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.
  • MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
  • MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
  • MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles and triangles.
  • MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.
  • MAT-07.GM.AV.02 Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.
  • MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.
  • MAT-12.GM.04 Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.