Geometry

BACK TO Core Content Connectors

(K-4) Elementary School Learning Targets	(5-8) Middle School Learning Targets	(9-12) High School Learning Targets
E.GM-1 Recognize that two-and three-dimensional shapes have particular attributes: Describe and compare objects and figures based on reasoning and the properties and attributes of the shapes; Compose, decompose, and draw figures based on spatial reasoning and the properties and attributes of the shapes; Apply concepts of symmetry.	GM-1 Apply reasoning using properties of two- and three-dimensional shapes to analyze, represent, and model geometric relationships: Classify objects based on attributes and properties and solve problems using geometric relationships and properties; Decompose figures into new figures and construct figures with given conditions; Apply concepts of parallel and perpendicular.	H.GM-1 Explain solutions using geometric attributes and relationships in diverse contexts: Extend understanding of congruence and similarity working with complex figures and situations; Solve problems involving quadrilaterals and triangles; Perform geometric constructions and use informal proofs to describe relationships and transformations

Grade Differentiation

Elementary School Progress Indicators

Progress Indicator: E.GM.1a recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment
Core Content Connectors: K	CCSS Domain/Cluster	Common Core State Standard
K.GM.1a1 Recognize two-dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation or size	Geometry K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)	K.G.A.2 Correctly name shapes regardless of their orientations or overall size.
K.GM.1a2 Recognize two-dimensional shapes in environment regardless of orientation or size	Geometry K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)	K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to.
K.GM.1a3 Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes	Geometry K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)	K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to.
Progress Indicator: E.GM.1c composing two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter circles)
Core Content Connectors: K	CCSS Domain/Cluster	Common Core State Standard
K.GM.1c 1 Compose a larger shape from smaller shapes	Geometry K G Analyze, compare, create, and compose shapes.	K.G.B.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?"
Explanations and clarifications: CCSS not addressed: K.G.B.4 Analyze and compare two and three dimensional shapes in different sizes and orientations, using information language to describe their similarities, differences, parts, and other attributes K.G.B.5 Model shapes in the world by building shapes from components and drawing shapes

Progress Indicator: E.GM.1b analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length)
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.GM.1b1 Identify shapes as two-dimensional (lying flat) or three dimensional (solid)	Geometry K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)	K.G.A.3 Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
1.GM.1b2 Distinguish two-dimensional shapes based upon their defining attributes (i.e., size, corners, and points)	Geometry 1 G Reason with shapes and their attributes.	1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
Progress Indicator: E.GM.1c composing two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles)
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.GM.1c 2 Compose two- and three-dimensional shapes	Geometry 1 G Reason with shapes and their attributes.	1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Progress Indicator: E.GM.1f partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds)
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.GM.1f1 Partition circles and rectangles into two equal parts	Geometry 1 G Reason with shapes and their attributes.	1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares
Explanations and clarifications:

Progress Indicator: E.GM.1a recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.GM.1a4 Identify two-dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles	Geometry 2 G Reason with shapes and their attributes.	2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Progress Indicator: E.GM.1b analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length)
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
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)	Geometry 2 G Reason with shapes and their attributes.	2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Progress Indicator: E.GM.1d composing three-dimensional shapes, using concrete models/materials (cubes, prisms, cones, and cylinders)
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.GM.1d1 Compose three- dimensional shapes	Geometry 1 G Reason with shapes and their attributes.	1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half circles, and quarter circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Progress Indicator: E.GM.1e drawing and identifying shapes with specific attributes (e.g., number of sides or equal angles) not determined by direct measuring
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.GM.1e1 Draw two- dimensional shapes with specific attributes	Geometry 2 G Reason with shapes and their attributes.	2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Progress Indicator: E.GM.1f partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds)
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.GM.1f2 Partition circles and rectangles into 2 and 4 equal parts	Geometry 2 G Reason with shapes and their attributes.	2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
2.GM.1f3 Label a partitioned shape (e.g., one whole rectangle was separated into 2 halves, one whole circle was separated into three thirds)	Geometry 2 G Reason with shapes and their attributes.	2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Explanations and clarifications: The following Progress Indicator was not included due to complexity, no CCSS are linked to this Progress Indicator: E.GM.1g using spatial language to describe and name more complex or atypical shapes based on their defining characteristics.

Progress Indicator: E.GM.1h describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.GM.1h1 Identify shared attributes of shapes	Geometry 3 G Reason with shapes and their attributes.	3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having 4 sides) and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals that do not belong to any of these subcategories.
Progress Indicator: E.GM.1i partitioning shapes into equal parts with equal areas and recognizing that each part is a unit fraction of the whole
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.GM.1i1 Partition rectangles into equal parts with equal area	Geometry 3 G Reason with shapes and their attributes.	3.G.A.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape.
Explanations and clarifications: CCSS not addressed

Progress Indicator: E.GM.1h describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.GM.1h2 Classify two-dimensional shapes based on attributes (# of angles)	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.2 Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right angles as a category, and identify right angles.
Progress Indicator: E.GM.1j recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
4.GM.1j3 Recognize an angle in two-dimensional figures	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
4.GM.1j4 Categorize angles as right, acute, or obtuse	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.2 Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right angles as a category, and identify right triangles.
Progress Indicator: E.GM.1k recognizing and drawing lines of symmetry in a variety of figures
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.GM.1k1 Recognize a line of symmetry in a figure	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts, identify line-symmetric figures and draw lines of symmetry.
Explanations and clarifications:

Progress Indicator: E.GM.1j recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures	Geometry 4 G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.	4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
Progress Indicator: M.GM.1a describing and classifying plane figures based on their properties
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.GM.1a1 Recognize properties of simple plane figures	Geometry 5 G 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.
Progress Indicator: M.GM.1b recognizing and using properties belonging to categories and subcategories of plane figures (e.g., all rectangles have four right angles, so all squares are rectangles and have four right angles)
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.GM.1b1 Distinguish plane figures by their properties	Geometry 5 G Classify two-dimensional figures into categories based on their properties.	5.G.B.4 Classify two dimensional figures in a hierarchy based on properties.
Progress Indicator: M.GM.1c demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.GM.1c1 Locate the x and y axis on a graph	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.GM.1c2 Locate points on a graph	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.GM.1c3 Use order pairs to graph given points	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
Explanations and Clarifications: CCSS not addressed

Middle School Progress Indicators

Progress Indicator: M.GM.1c demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.GM.1c4 Locate points on a graph	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
6.GM.1c5 Use order pairs to graph given points	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
6.GM.1c6 Find coordinate values of points in the context of a situation	Geometry 5 G Graph points on the coordinate plane to solve real-world and mathematical problems.	5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
6.GM.1c7 Use coordinate points to draw polygons	Geometry 6 G Solve real-world and mathematical problems involving area, surface area, and volume.	6.G.A.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 in the context of solving real-world and mathematical problems.
6.GM.1c8 Use coordinate points to find the side lengths of polygons that are horizontal or vertical	Geometry 6 G Solve real-world and mathematical problems involving area, surface area, and volume.	6.G.A.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 in the context of solving real-world and mathematical problems.
Progress Indicator: M.GM.1d solving area, surface area, and volume problems by composing and decomposing figures
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.GM.1d1 Find area of quadrilaterals	Geometry 6 G Solve real-world and mathematical problems involving area, surface area, and volumes.	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.GM.1d2 Find area of triangles	Geometry 6 G Solve real-world and mathematical problems involving area, surface area, and volumes.	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
Explanations and clarifications:

Progress Indicator: M.GM.1e constructing or drawing geometric shapes from given conditions (e.g., draw triangles given three angle or side measures; change scale)
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.GM.1e1 Construct or draw plane figures using properties	Geometry 7 G Draw, construct, and describe geometrical figures and describe the relationships between them.	7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Progress Indicator: M.GM.1h solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures)
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.GM.1h1 Add the area of each face of a prism to find surface area of three-dimensional objects	Geometry 7 G 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.
7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles	Geometry 7 G 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.
7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals)	Geometry 7 G 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.
7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle	Geometry 7 G 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.
7.GM.1h5 Describe the two dimensional figures that result from a decomposed three dimensional figure.	Geometry 7 G Draw, construct, and describe geometrical figures and describe the relationships between them.	7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Explanations and clarifications:

Progress Indicator: M.GM.1f recognizing and demonstrating rotations, reflections, and translations using multiple contexts (e.g., using coordinates, models, drawings, technology)
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.GM.1f1 Recognize a rotation, reflection, or translation of a figure	Geometry 8 G Understand congruence and similarity using physical models, transparencies, or geometry software.	8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: a) Lines are taken to lines, and line segments to line segments of the same length. b) Angles are taken to angles of the same measure. c) Parallel lines are taken to parallel lines.
8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates	Geometry 8 G Understand congruence and similarity using physical models, transparencies, or geometry software.	8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Progress Indicator: M.GM.1g demonstrating congruence and similarity using a variety of two-dimensional figures
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.GM.1g1 Recognize congruent and similar figures	Geometry 8 G Understand congruence and similarity using physical models, transparencies, or geometry software.	8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Progress Indicator: M.GM.1i exploring and explaining angle relationships (e.g., pairs of parallel lines cut by a transversal, including perpendicular lines)
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.GM.1i1 Identify supplementary angles	Geometry 7 G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.	7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
8.GM.1i2 Identify complimentary angles	Geometry 7 G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.	7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
8.GM.1i3 Identify adjacent angles	Geometry 7 G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.	7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
8.GM.1i4 Use angle relationships to find the value of a missing angle	Geometry 7 G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 8 G Understand congruence and similarity using physical models, transparencies, or geometry software.	7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle for triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and given an argument in terms of transversals why this is so.
Progress Indicator: M.GM.1j applying the Pythagorean Theorem
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.GM.1j1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)	Geometry 8 G Understand and apply the Pythagorean Theorem.	8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.GM.1j2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)	Geometry 8 G Understand and apply the Pythagorean Theorem.	8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Explanations and clarifications:

High School Progress Indicators

Progress Indicator: H.GM.1a applying the Pythagorean Theorem
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.GM.1a1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)	Geometry 8 G Understand and apply the Pythagorean Theorem.	8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
H.GM.1a2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)	Geometry 8 G Understand and apply the Pythagorean Theorem.	8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
H.GM.1a3 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.	Geometry 8 G Understand and apply the Pythagorean Theorem.	8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Progress Indicator: H.GM.1b using congruence and similarity relationships to solve problems, including triangle congruence relationships
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures	Congruence G CO Understand congruence in terms of rigid motions. Similarity, Right Triangles, and Trigonometry G.SRT Understand similarity in terms of similarity transformations.	HSG.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Progress Indicator: H.GM.1c applying understanding of rotations, reflections, and translations to construct figures (e.g., using coordinates, models, drawings, transparencies, dynamic geometry software)
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.GM.1c1 Construct, draw or recognize a figure after its rotation, reflection, or translation	Congruence G CO Experiment with transformations in the plane.	HSG.CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformation that will carry a given figure onto another. HSG.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry onto itself.
Progress Indicator: H.GM.1d applying scale factors in solving multiple similarity problems, including transformations in the coordinate plane and similarity relationships with right triangles
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.GM.1d1 Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles	Geometry 8 G Understand congruence and similarity using physical models, transparencies, or geometry software. Similarity, Right Triangles, and Trigonometry G SRT Understand similarity in terms of similarity transformations.	8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations a) Lines are taken to lines, and line segments to line segments of the same length. b) Angles are taken to angles of the same measure. c) Parallel lines are taken to parallel lines. HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformation the meaning of similarity for triangles and the equality of all corresponding pairs and angles and the proportionality of all corresponding pairs of sides.
Progress Indicator: H.GM.1e making various geometric constructions, including use of dynamic geometry software, and creating informal proofs of relationships (lines and angles, circles, polygons)
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.GM.1e1 Make formal geometric constructions with a variety of tools and methods	Congruence G CO Make Geometric constructions.	HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straight edge, string, reflective devices, paper folding dynamic geometric software, etc.) Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Explanations and clarifications: High school standards not addressed; will be in a separate document