Instructional Families: Geometry

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Additional References

To view the Common Core State Standards visit: Common Core State Standards Initiative

For ideas about how to teach Geometry curriculum see the Curriculum Resource Guide Measurement and Geometry.

For a broader understanding of content related to Geometry see the Perimeter, Area and Volume Content Module and the Coordinate Plane Content Module.

To view the Learning Progressions Frameworks document, please visit Learning Progressions Frameworks Designed for Use with the Common Core State Standards in Mathematics K-12.

Download this document as a PDF Instructional Families Geometry pdf

Labeling Reference Key

Reference Format	Reference Source
ME-1	This is the reference format for the learning targets found in Karin Hess's Learning Progressions Frameworks (LPF), the Measurement (ME) strand.
K.ME.1a1	This is a Core Content Connector reference. The Core Content Connector (CCC) references are directly related to the LPF Progress Indicator references. The first five characters and included periods in this example, K.ME.1a, are the reference for the LPF Progress Indicator, the final digit, 1, indicates the number of the CCC that has been developed in relation to the indicator.
3.MD.A.1	This is a Common Core State Standard reference. In this reference, the 3 indicates the grade level, the MD indicates the domain, Measurement and Data,the A indicates the cluster, "Solve problems involving measurement and estimation",and the 1 indicates the number of the standard.

View of Learning Progressions Frameworks (LPF) Targets and Instructional Families across Grades

Distribution of Instructional Families: LPF Strand - Geometry

(K-4) Elementary School Learning Progressions Frameworks Targets	(5-8) Middle School Learning Progressions Frameworks Targets	(9-12) High School Learning Progressions Frameworks 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.	M.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.
INSTRUCTIONAL FAMILIES:

Recognizing, Describing, Naming and Classifying

Constructing/Building

Constructing/Establishing A Figure

Geometric Problems

Transforming and Graphing

K	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	HS

View of Grade Band Core Content Connectors (CCCs) by Learning Progressions Frameworks Targets and Instructional Families

Overview of CCCs: LPF Strand- Geometry (K-4)

(K-4) Elementary School Learning Progressions Frameworks 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.
Recognizing, Describing, Naming and Classifying	Constructing/Building	Geometric Problems	Transforming and Graphing

K	Grade 1	Grade 2	Grade 3	Grade 4
K.GM.1a1 Recognize two- dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation of size K.G.A.2	1.GM.1b1 Identify shapes as two-dimensional (lying flat) or three dimensional (solid) K.G.A.3	2.GM.1a4 Identify two- dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles 2.G.A.1	3.GM.1h1 Identify shared attributes of shapes 3.G.A.1	4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures 4.G.A.1
K.GM.1a2 Recognize two-dimensional shapes in environment regardless of orientation of size K.G.A.1	1.GM.1b2 Distinguish two-dimensional shapes based upon their defining attributes (i.e., size, corners, and points) 1.G.A.1	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) 2.G.A.1	3.GM.1i Partition rectangles into equal parts with equal area 3.G.A.2	4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures 4.G.A.1
K.GM.1a3 Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes K.G.A.1	1.GM.1c 2 Compose two- and three-- dimensional shapes 1.G.A.3	2.GM.1d1 Compose three- dimensional shapes 1.G.A.2		4.GM.1j3 Recognize an angle in two-dimensional figures 4.G.A.1
K.GM.1c1 Compose a larger shape from smaller shapes K.G.B.6	1.GM.1f1 Partition circles and rectangles into two equal parts 1.G.A.3	2.GM.1e1 Draw two- dimensional shapes with specific attributes 2.G.A.1		4.GM.1h2 Classify two--dimensional shapes based on attributes (# of angles) 4.G.A.2
		2.GM.1f2 Partition circles and rectangles into 2 and 4 equal parts 2.G.A.3		4.GM.1j4 Categorize angles as right, acute, or obtuse 4.G.A.2
		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) 2.G.A.3		4.GM.1k1 Recognize a line of symmetry in a figure 4.G.A.3

Overview of CCCs: LPF Strand- Geometry (5-8)

(5-8) Middle School Learning Targets
M.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.
Recognizing, Describing, Naming and Classifying	Constructing/Establishing A Figure	Geometric Problems	Transforming and Graphing
Grade 5	Grade 6	Grade 7	Grade 8
5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures 4.G.A.1	6.GM.1d1 Find area of quadrilaterals 6.G.A.1	7.GM.1h1 Add the area of each face of a prism to find surface area of three dimensional objects 7.G.B.6	8.GM.1g1 Recognize congruent and similar figures 8.G.A.4
5.GM.1a1 Recognize properties of simple plane figures 5.G.B.3	6.GM.1d2 Find area of triangles 6.G.A.1	7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles 6.G.A.4	8.GM.1i1 Identify supplementary angles 7.G.B.5
5.GM.1b1 Distinguish plane figures by their properties 5.G.B.4	6.GM.1c4 Locate points on a graph 5.G.A.1	7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals) 7.G.B.6	8.GM.1i2 Identify complimentary angles 7.G.B.5
5.GM.1c1 Locate the x and y axis on a graph 5.G.A.1	6.GM.1c5 Use order pairs to graph given points 5.G.A.1	7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle 7.G.B.6	8.GM.1i3 Identify adjacent angles 7.G.B.5
5.GM.1c2 Locate points on a graph 5.G.A.1	6.GM.1c6 Find coordinate values of points in the context of a situation 5.G.A.2		8.GM.1i4 Use angle relationships to find the value of a missing angle 7.G.B.5 8.G.A.5
5.GM.1c3 Use order pairs to graph given points 5.G.A.1	6.GM.1c7 Use coordinate points to draw polygons 6.G.A.3		8.GM.1j1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7
	6.GM.1c8 Use coordinate points to find the side lengths of polygons that are horizontal or vertical 6.G.A.3		8.GM.1j2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7
			8.GM.1f1 Recognize a rotation, reflection, or translation of a figure 8.G.A.1
			8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates 8.G.A.3

Overview of CCCs: LPF Strand- Geometry (9-12)

(9-12) High School Learning Targets
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.
Recognizing, Describing, Naming and Classifying	Constructing/Building	Transforming and Graphing
High School
H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures G.CO.B.7 G.SRT.A.2 8.G.A.2
H.ME.2b2 Determine if 2 figures are similar G.SRT.A.2
H.ME.2b3 Describe or select why two figures are or are not similar G.SRT.A.2
H.GM.1e1 Make formal geometric constructions with a variety of tools and methods G.CO.D.12
H.GM.1a1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7
H.GM.1a2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem) N.Q.A.1
H.GM.1c1 Construct, draw or recognize a figure after its rotation, reflection, or translation G.CO.A.3
H.GM.1d1 Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles 8.G.A.1

View of Core Content Connectors (CCCs) by Instructional Families and Common Core State Standards (CCSS) Domains

Instructional Families: LPF Strand- Geometry

CCSS Domain Name: Geometry
Recognizing, Describing, Naming and Classifying	Constructing - Building	Constructing - Establishing a Figure	Geometric Problems	Transforming and Graphing
K.GM.1a1 Recognize two- dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation of size K.G.A.2	K.GM.1c1 Compose a larger shape from smaller shapes K.G.B.6	8.GM.1i4 Use angle relationships to find the value of a missing angle 7.G.B.5 8.G.A.5	1.GM.1f1 Partition circles and rectangles into two equal parts 1.G.A.3	4.GM.1k1 Recognize a line of symmetry in a figure 4.G.A.3
K.GM.1a2 Recognize two-dimensional shapes in environment regardless of orientation of size K.G.A.1	1.GM.1c2 Compose two and three-dimensional shapes	8.GM.1j1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7	2.GM.1f2 Partition circles and rectangles into 2 and 4 equal parts 2.G.A.3	5.GM.1c1 Locate the x and y axis on a graph 5.G.A.1
K.GM.1a3 Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes K.G.A.1	2.GM.1d1 Compose three- dimensional shapes 1.G.2	8.GM.1j2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7	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) 2.G.A.3	5.GM.1c2 Locate points on a graph
	2.GM.1e1 Draw two- dimensional shapes with specific attributes 2.G.A.1			5.GM.1c3 Use order pairs to graph given points 5.G.A.1
1.GM.1b1 Identify shapes as two-dimensional (lying flat) or three dimensional (solid) K.G.A.3		H.GM.1e1 Make formal geometric constructions with a variety of tools and methods G.CO.D.12	3.GM.1i1 Partition rectangles into equal parts with equal area 3.G.A.2	6.GM.1c4 Locate points on a graph 5.G.A.1
				6.GM.1c5 Use order pairs to graph given points 5.G.A.1
1.GM.1b2 Distinguish two-dimensional shapes based upon their defining attributes (i.e., size, corners, and points) 1.G.A.1		H.GM.1a1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem) 8.G.B.7	6.GM.1d1 Find area of quadrilaterals 6.G.A.1	6.GM.1c6 Find coordinate values of points in the context of a situation 5.G.A.2
			6.GM.1d2 Find area of triangles 6.G.A.1	6.GM.1c7 Use coordinate points to draw polygons 6.G.A.3
2.GM.1a4 Identify two- dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles 2.G.A.1		H.GM.1a2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem) N.Q.A.1	7.GM.1h1 Add the area of each face of a prism to find surface area of three dimensional objects 7.G.B.6	6.GM.1c8 Use coordinate points to find the side lengths of polygons that are horizontal or vertical 6.G.A.3
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) 2.G.A.1			7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles 6.G.A.4	8.GM.1f1 Recognize a rotation, reflection, or translation of a figure 8.G.A.1
3.GM.1h1 Identify shared attributes of shapes 3.G.A.1			7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals) 7.G.B.6	8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates 8.G.A.3
4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures 4.G.A.1			7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle 7.G.B.6	H.GM.1c1 Construct, draw or recognize a figure after its rotation, reflection, or translation G.CO.A.3
4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures 4.G.A.1				H.GM.1d1 Use the reflections, rotations, or translations in the coordinate plane to solve problems with right angles 8.G.A.1
4.GM.1j3 Recognize an angle in two-dimensional figures 4.G.A.1
4.GM.1h2 Classify two--dimensional shapes based on attributes (# of angles) 4.G.A.2
4.GM.1j4 Categorize angles as right, acute, or obtuse 4.G.A.2
5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures 4.G.A.1
5.GM.1a1 Recognize properties of simple plane figures 5.G.B.3
5.GM.1b1 Distinguish plane figures by their properties 5.G.B.4
8.GM.1g1 Recognize congruent and similar figures 8.G.A.4
8.GM.1i1 Identify supplementary angles 7.G.B.5
8.GM.1i2 Identify complimentary angles 7.G.B.5
8.GM.1i3 Identify adjacent angles 7.G.B.5
H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures G.CO.B.7 G.SRT.A.2 8.G.A.2
H.ME.2b2 Determine if 2 figures are similar G.SRT.A.2
H.ME.2b3 Describe or select why two figures are or are not similar G.SRT.A.2

• Note: To access the Common Core State Standards (CCSSs), visit http://www.corestandards.org/Math/Content