MAT-04.GM Domain 

(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.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (G) Geometry Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.

Proficiency Scale

Progressions

Two-Dimensional Shapes

• MAT-00.GM.G.01 Name shapes and identify them as two-dimensional (squares, circles, triangles, rectangles)regardless of their orientations or overall size.
• MAT-00.GM.G.03 Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).
• MAT-01.GM.G.01 Name shapes and identify them as two-dimensional (trapezoids, rhombuses, pentagons, hexagons, octagons).
• MAT-01.GM.G.03 Determine geometric attributes of two-dimensional and three-dimensional shapes.
• MAT-02.GM.G.01 Identify two-dimensional shapes (parallelograms and quadrilaterals).
• 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-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-03.GM.G.02 Sort quadrilaterals into categories based on attributes.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.
• MAT-05.GM.G.01 Classify two-dimensional figures in a hierarchy based on properties.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.11 Prove and apply theorems about parallelograms.
• MAT-10.GM.34 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

Angles/Triangles

• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.
• MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.
• MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.
• MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
• MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.
• MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).
• MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
• MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.
• MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.
• MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (G) Geometry Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.

Proficiency Scale

Progressions

Two-Dimensional Shapes

• MAT-00.GM.G.01 Name shapes and identify them as two-dimensional (squares, circles, triangles, rectangles)regardless of their orientations or overall size.
• MAT-00.GM.G.03 Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).
• MAT-01.GM.G.01 Name shapes and identify them as two-dimensional (trapezoids, rhombuses, pentagons, hexagons, octagons).
• MAT-01.GM.G.03 Determine geometric attributes of two-dimensional and three-dimensional shapes.
• MAT-02.GM.G.01 Identify two-dimensional shapes (parallelograms and quadrilaterals).
• 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-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-03.GM.G.02 Sort quadrilaterals into categories based on attributes.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.
• MAT-05.GM.G.01 Classify two-dimensional figures in a hierarchy based on properties.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.11 Prove and apply theorems about parallelograms.
• MAT-10.GM.34 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (G) Geometry Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.

Proficiency Scale

Progressions

Symmetry

• MAT-03.GM.G.03 Identify lines of symmetry in quadrilaterals.
• MAT-04.GM.G.03 Draw lines of symmetry in two-dimensional figures

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Units of Measurement

• MAT-03.GM.M.02 Measure and estimate liquid volumes and masses of objects using standard units. Solve one step authentic word problems involving masses or volumes given in the same units.
• MAT-04.GM.M.01 Know the relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Record measurement equivalents in a two-column table.
• MAT-04.GM.M.03 Identify and use the appropriate tools, operations, and units of measurement, both customary and metric to solve problems involving time, length, weight, mass, and capacity.
• MAT-04.GM.M.02 Generate simple conversions from a larger unit to a smaller unit to solve authentic problems within a single system of measurement, both customary and metric systems.
• MAT-05.GM.M.01 Generate conversions among different-sized standard measurement units within a given measurement system, both customary and metric systems. Use these conversions in solving multi-step, authentic word problems.
• MAT-06.AR.RP.05 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
• MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Money

• MAT-01.GM.M.04 Identify and tell the value of a dollar bill, quarter, dime, nickel, and penny.
• MAT-01.GM.M.05 Count collections of coins (pennies, nickels, and dimes) relating to patterns of counting by 1s, 5s, and 10s up to one dollar.
• MAT-02.GM.M.04 Count collections of money (quarters, dimes, nickels, and pennies) relating to patterns of counting by 1s, 5s, and 10s up to one dollar.
• MAT-03.GM.M.05 Solve authentic word problems involving dollar bills, quarters, dimes, nickels, and pennies using the $ and ¢ symbols appropriately.
• MAT-04.GM.M.04 Solve word authentic problems involving dollar bills, quarters, dimes, nickels, and pennies using the $ and ¢ symbols and decimal notation appropriately.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Perimeter

• MAT-03.GM.M.06 Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).
• 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-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply given formulas to calculate the area and circumference of a circle, including in authentic problems.
• MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.

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.

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Angles/Triangles

• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.
• MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.
• MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.
• MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
• MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.
• MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).
• MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
• MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.
• MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.
• MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context

4th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (M) Measurement Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.

Proficiency Scale

Progressions

Angles/Triangles

• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.
• MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.
• MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.
• MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.
• MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.
• MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
• MAT-10.GM.09 Prove and apply theorems about lines and angles.
• MAT-10.GM.10 Prove and apply theorems about triangles.
• MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
• MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.
• MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).
• MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
• MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
• MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.
• MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.
• MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context