IXL Skill Plan | Next Generation Learning Standards: Geometry

Next Generation Learning Standards: Geometry

Skills available for New York Geometry standards

Domain

Geometry

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GEO-G	Geometry
GEO-G.CO Congruence
Experiment with transformations in the plane.
Experiment with transformations in the plane.

GEO-G.CO.1: Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.		1. Angle vocabulary
GEO-G.CO.1: Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.
1. Angle vocabulary
GEO-G.CO.2: Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.		Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Congruence transformations 8. Classify congruence transformations 9. Reflections and rotations: write the rule Dilations 10. Dilations: graph the image 11. Dilations: find the coordinates 12. Dilations: find the scale factor
GEO-G.CO.2: Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.
Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Congruence transformations 8. Classify congruence transformations 9. Reflections and rotations: write the rule Dilations 10. Dilations: graph the image 11. Dilations: find the coordinates 12. Dilations: find the scale factor
GEO-G.CO.3: Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.		1. Transformations that carry a polygon onto itself
GEO-G.CO.3: Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.
1. Transformations that carry a polygon onto itself
GEO-G.CO.4: Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.		1. Rotate polygons about a point
GEO-G.CO.4: Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.
1. Rotate polygons about a point
GEO-G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.		Graph an image 1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image Sequences of transformations 4. Sequences of congruence transformations: graph the image 5. Sequences of congruence transformations: choose the sequence 6. Sequences of congruence transformations: find the rules
GEO-G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.
Graph an image 1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image Sequences of transformations 4. Sequences of congruence transformations: graph the image 5. Sequences of congruence transformations: choose the sequence 6. Sequences of congruence transformations: find the rules
Checkpoint opportunity		1. Checkpoint: Definitions of geometric objects 2. Checkpoint: Congruence transformations 3. Checkpoint: Transformations in the plane
Checkpoint opportunity
1. Checkpoint: Definitions of geometric objects 2. Checkpoint: Congruence transformations 3. Checkpoint: Transformations in the plane

Understand congruence in terms of rigid motions.
Understand congruence in terms of rigid motions.

GEO-G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.		1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: choose the sequence 3. Transformations that carry a polygon onto itself 4. Congruence transformations: mixed review 5. Determine if two figures are congruent: justify your answer
GEO-G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: choose the sequence 3. Transformations that carry a polygon onto itself 4. Congruence transformations: mixed review 5. Determine if two figures are congruent: justify your answer
GEO-G.CO.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.		1. Prove triangles are congruent using rigid motions
GEO-G.CO.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.
1. Prove triangles are congruent using rigid motions
GEO-G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.
GEO-G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.

Checkpoint opportunity		1. Checkpoint: Rigid motion and congruence
Checkpoint opportunity
1. Checkpoint: Rigid motion and congruence

Prove geometric theorems
Prove geometric theorems

GEO-G.CO.9: Prove and apply theorems about lines and angles.		Angles 1. Angle bisectors 2. Proofs involving angles Parallel lines 3. Transversals of parallel lines: solve for x 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II Perpendicular bisectors 6. Perpendicular Bisector Theorem
GEO-G.CO.9: Prove and apply theorems about lines and angles.
Angles 1. Angle bisectors 2. Proofs involving angles Parallel lines 3. Transversals of parallel lines: solve for x 4. Proofs involving parallel lines I 5. Proofs involving parallel lines II Perpendicular bisectors 6. Perpendicular Bisector Theorem
GEO-G.CO.10: Prove and apply theorems about triangles.		Isosceles triangles 1. Proofs involving isosceles triangles Angles in triangles 2. Proofs involving triangles I Segments in triangles 3. Proofs involving triangles II Centroids or orthocenters of triangles 4. Construct the centroid or orthocenter of a triangle 5. Find the centroid of a triangle
GEO-G.CO.10: Prove and apply theorems about triangles.
Isosceles triangles 1. Proofs involving isosceles triangles Angles in triangles 2. Proofs involving triangles I Segments in triangles 3. Proofs involving triangles II Centroids or orthocenters of triangles 4. Construct the centroid or orthocenter of a triangle 5. Find the centroid of a triangle
GEO-G.CO.11: Prove and apply theorems about parallelograms.		1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of rhombuses 4. Properties of squares and rectangles
GEO-G.CO.11: Prove and apply theorems about parallelograms.
1. Properties of parallelograms 2. Proving a quadrilateral is a parallelogram 3. Properties of rhombuses 4. Properties of squares and rectangles
Checkpoint opportunity		1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle theorems 3. Checkpoint: Parallelogram theorems
Checkpoint opportunity
1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle theorems 3. Checkpoint: Parallelogram theorems

Make geometric constructions.
Make geometric constructions.

GEO-G.CO.12: Make, justify, and apply formal geometric constructions.		Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct the inscribed or circumscribed circle of a triangle
GEO-G.CO.12: Make, justify, and apply formal geometric constructions.
Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct the inscribed or circumscribed circle of a triangle
GEO-G.CO.13: Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.		1. Construct an equilateral triangle inscribed in a circle 2. Construct a square inscribed in a circle 3. Construct a regular hexagon inscribed in a circle
GEO-G.CO.13: Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.
1. Construct an equilateral triangle inscribed in a circle 2. Construct a square inscribed in a circle 3. Construct a regular hexagon inscribed in a circle
Checkpoint opportunity		1. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Geometric constructions
GEO-G.SRT Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
Understand similarity in terms of similarity transformations.

GEO-G.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.
GEO-G.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.

GEO-G.SRT.1a: Verify experimentally that dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.		1. Dilations: graph the image 2. Dilations and parallel lines
GEO-G.SRT.1a: Verify experimentally that dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
1. Dilations: graph the image 2. Dilations and parallel lines
GEO-G.SRT.1b: Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.		1. Dilations: find length, perimeter, and area 2. Dilations: find the scale factor 3. Dilations: find the scale factor and center of the dilation
GEO-G.SRT.1b: Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
1. Dilations: find length, perimeter, and area 2. Dilations: find the scale factor 3. Dilations: find the scale factor and center of the dilation
GEO-G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.		1. Identify similar figures 2. Side lengths and angle measures in similar figures 3. Similar triangles and similarity transformations 4. Determine if two figures are similar: justify your answer
GEO-G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
1. Identify similar figures 2. Side lengths and angle measures in similar figures 3. Similar triangles and similarity transformations 4. Determine if two figures are similar: justify your answer
GEO-G.SRT.3: Use the properties of similarity transformations to establish the AA~, SSS~, and SAS~ criterion for two triangles to be similar.		1. Similarity rules for triangles
GEO-G.SRT.3: Use the properties of similarity transformations to establish the AA~, SSS~, and SAS~ criterion for two triangles to be similar.
1. Similarity rules for triangles
Checkpoint opportunity		1. Checkpoint: Dilations 2. Checkpoint: Similarity transformations
Checkpoint opportunity
1. Checkpoint: Dilations 2. Checkpoint: Similarity transformations

Prove theorems involving similarity.
Prove theorems involving similarity.

GEO-G.SRT.4: Prove and apply similarity theorems about triangles.		1. Proofs involving similarity in right triangles 2. Proofs involving triangles II 3. Prove the Pythagorean theorem
GEO-G.SRT.4: Prove and apply similarity theorems about triangles.
1. Proofs involving similarity in right triangles 2. Proofs involving triangles II 3. Prove the Pythagorean theorem
GEO-G.SRT.5: Use congruence and similarity criteria for triangles to:
GEO-G.SRT.5: Use congruence and similarity criteria for triangles to:

GEO-G.SRT.5a: Solve problems algebraically and geometrically.		Congruent triangles 1. Congruency in isosceles and equilateral triangles 2. Hypotenuse-Leg Theorem Similar triangles 3. Similar triangles and indirect measurement 4. Angle-angle criterion for similar triangles 5. Similarity rules for triangles 6. Triangle Proportionality Theorem 7. Similarity and altitudes in right triangles Area and perimeter of similar figures 8. Perimeters of similar figures 9. Areas of similar figures
GEO-G.SRT.5a: Solve problems algebraically and geometrically.
Congruent triangles 1. Congruency in isosceles and equilateral triangles 2. Hypotenuse-Leg Theorem Similar triangles 3. Similar triangles and indirect measurement 4. Angle-angle criterion for similar triangles 5. Similarity rules for triangles 6. Triangle Proportionality Theorem 7. Similarity and altitudes in right triangles Area and perimeter of similar figures 8. Perimeters of similar figures 9. Areas of similar figures
GEO-G.SRT.5b: Prove relationships in geometric figures.		Congruence theorems 1. SSS and SAS Theorems 2. ASA and AAS Theorems 3. SSS, SAS, ASA, and AAS Theorems 4. SSS Theorem in the coordinate plane Proofs involving congruent triangles 5. Proving triangles congruent by SSS and SAS 6. Proving triangles congruent by ASA and AAS 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving corresponding parts of congruent triangles Proofs involving similar triangles 9. Prove similarity statements 10. Prove proportions or angle congruences using similarity
GEO-G.SRT.5b: Prove relationships in geometric figures.
Congruence theorems 1. SSS and SAS Theorems 2. ASA and AAS Theorems 3. SSS, SAS, ASA, and AAS Theorems 4. SSS Theorem in the coordinate plane Proofs involving congruent triangles 5. Proving triangles congruent by SSS and SAS 6. Proving triangles congruent by ASA and AAS 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving corresponding parts of congruent triangles Proofs involving similar triangles 9. Prove similarity statements 10. Prove proportions or angle congruences using similarity
Checkpoint opportunity		1. Checkpoint: Triangle similarity and congruence
Checkpoint opportunity
1. Checkpoint: Triangle similarity and congruence

Define trigonometric ratios and solve problems involving right triangles.
Define trigonometric ratios and solve problems involving right triangles.

GEO-G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles
GEO-G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles
GEO-G.SRT.7: Explain and use the relationship between the sine and cosine of complementary angles.		1. Sine and cosine of complementary angles
GEO-G.SRT.7: Explain and use the relationship between the sine and cosine of complementary angles.
1. Sine and cosine of complementary angles
GEO-G.SRT.8: Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.		Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Solve a right triangle 6. Solve a right triangle
GEO-G.SRT.8: Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.
Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Solve a right triangle 6. Solve a right triangle
Checkpoint opportunity		1. Checkpoint: Right triangle trigonometry
Checkpoint opportunity
1. Checkpoint: Right triangle trigonometry

Apply Trigonometry to general triangles.
Apply Trigonometry to general triangles.

GEO-G.SRT.9: Justify and apply the formula A = 1/2 ab sin(C) to find the area of any triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.		1. Area of a triangle: sine formula
GEO-G.SRT.9: Justify and apply the formula A = 1/2 ab sin(C) to find the area of any triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
1. Area of a triangle: sine formula
GEO-G.C Circles
Understand and apply theorems about circles.
Understand and apply theorems about circles.

GEO-G.C.1: Prove that all circles are similar.		1. Similarity of circles
GEO-G.C.1: Prove that all circles are similar.
1. Similarity of circles
GEO-G.C.2a: Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.		1. Central angles and arc measures 2. Arcs and chords 3. Inscribed angles 4. Angles in inscribed right triangles 5. Angles in inscribed quadrilaterals II
GEO-G.C.2a: Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.
1. Central angles and arc measures 2. Arcs and chords 3. Inscribed angles 4. Angles in inscribed right triangles 5. Angles in inscribed quadrilaterals II
GEO-G.C.2b: Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.		1. Arcs and chords 2. Tangent lines 3. Perimeter of polygons with an inscribed circle 4. Angles formed by chords, secants, and tangents 5. Segments formed by chords, secants, and tangents
GEO-G.C.2b: Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.
1. Arcs and chords 2. Tangent lines 3. Perimeter of polygons with an inscribed circle 4. Angles formed by chords, secants, and tangents 5. Segments formed by chords, secants, and tangents
Checkpoint opportunity		1. Checkpoint: Prove circles are similar 2. Checkpoint: Angles and lines in circles 3. Checkpoint: Inscribed and circumscribed circles
Checkpoint opportunity
1. Checkpoint: Prove circles are similar 2. Checkpoint: Angles and lines in circles 3. Checkpoint: Inscribed and circumscribed circles

Find arc lengths and area of sectors of circles.
Find arc lengths and area of sectors of circles.

GEO-G.C.5: Using proportionality, find one of the following given two others: the central angle, arc length, radius or area of sector.		1. Understand arc length and sector area of a circle 2. Arc length 3. Convert between radians and degrees 4. Radians and arc length 5. Area of sectors
GEO-G.C.5: Using proportionality, find one of the following given two others: the central angle, arc length, radius or area of sector.
1. Understand arc length and sector area of a circle 2. Arc length 3. Convert between radians and degrees 4. Radians and arc length 5. Area of sectors
Checkpoint opportunity		1. Checkpoint: Arc length and area of sectors
Checkpoint opportunity
1. Checkpoint: Arc length and area of sectors
GEO-G.GPE Expressing Geometric Properties with Equations
Translate between the geometric description and the equation of a conic section.
Translate between the geometric description and the equation of a conic section.

GEO-G.GPE.1a: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.		1. Write equations of circles in standard form from graphs 2. Write equations of circles in standard form using properties 3. Convert equations of circles from general to standard form 4. Find properties of circles from equations in general form
GEO-G.GPE.1a: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.
1. Write equations of circles in standard form from graphs 2. Write equations of circles in standard form using properties 3. Convert equations of circles from general to standard form 4. Find properties of circles from equations in general form
GEO-G.GPE.1b: Graph circles given their equations.		1. Graph circles from equations in standard form 2. Graph circles from equations in general form
GEO-G.GPE.1b: Graph circles given their equations.
1. Graph circles from equations in standard form 2. Graph circles from equations in general form
Checkpoint opportunity		1. Checkpoint: Equations of circles
Checkpoint opportunity
1. Checkpoint: Equations of circles

Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically.

GEO-G.GPE.4: On the coordinate plane, algebraically prove geometric theorems and properties.		1. Classify shapes on the coordinate plane: justify your answer 2. Determine if a point lies on a circle
GEO-G.GPE.4: On the coordinate plane, algebraically prove geometric theorems and properties.
1. Classify shapes on the coordinate plane: justify your answer 2. Determine if a point lies on a circle
GEO-G.GPE.5: On the coordinate plane:
GEO-G.GPE.5: On the coordinate plane:

GEO-G.GPE.5a: Explore the proof for the relationship between slopes of parallel and perpendicular lines;
GEO-G.GPE.5a: Explore the proof for the relationship between slopes of parallel and perpendicular lines;

GEO-G.GPE.5b: Determine if lines are parallel, perpendicular, or neither, based on their slopes; and		1. Slopes of parallel and perpendicular lines
GEO-G.GPE.5b: Determine if lines are parallel, perpendicular, or neither, based on their slopes; and
1. Slopes of parallel and perpendicular lines
GEO-G.GPE.5c: Apply properties of parallel and perpendicular lines to solve geometric problems.		1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between a point and a line 4. Find the distance between two parallel lines
GEO-G.GPE.5c: Apply properties of parallel and perpendicular lines to solve geometric problems.
1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between a point and a line 4. Find the distance between two parallel lines
GEO-G.GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.		1. Midpoints 2. Midpoint formula: find the midpoint 3. Partition a line segment in a given ratio 4. Midpoint formula: find the endpoint
GEO-G.GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
1. Midpoints 2. Midpoint formula: find the midpoint 3. Partition a line segment in a given ratio 4. Midpoint formula: find the endpoint
GEO-G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.		1. Distance formula 2. Area and perimeter in the coordinate plane I 3. Area and perimeter in the coordinate plane II
GEO-G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
1. Distance formula 2. Area and perimeter in the coordinate plane I 3. Area and perimeter in the coordinate plane II
Checkpoint opportunity		1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines 4. Checkpoint: Area and perimeter in the coordinate plane
Checkpoint opportunity
1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines 4. Checkpoint: Area and perimeter in the coordinate plane
GEO-G.GMD Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems.
Explain volume formulas and use them to solve problems.

GEO-G.GMD.1: Provide informal arguments for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
GEO-G.GMD.1: Provide informal arguments for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

GEO-G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.		1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
GEO-G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
Checkpoint opportunity		1. Checkpoint: Volume
Checkpoint opportunity
1. Checkpoint: Volume

Visualize relationships between two-dimensional and three-dimensional objects.
Visualize relationships between two-dimensional and three-dimensional objects.

GEO-G.GMD.4: Identify the shapes of plane sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.		1. Cross sections of three-dimensional figures 2. Solids of revolution
GEO-G.GMD.4: Identify the shapes of plane sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
1. Cross sections of three-dimensional figures 2. Solids of revolution
Checkpoint opportunity		1. Checkpoint: Cross sections and solids of revolution
Checkpoint opportunity
1. Checkpoint: Cross sections and solids of revolution
GEO-G.MG Modeling with Geometry
Apply geometric concepts in modeling situations.
Apply geometric concepts in modeling situations.

GEO-G.MG.1: Use geometric shapes, their measures, and their properties to describe objects.		1. Pythagorean theorem
GEO-G.MG.1: Use geometric shapes, their measures, and their properties to describe objects.
1. Pythagorean theorem
GEO-G.MG.2: Apply concepts of density based on area and volume of geometric figures in modeling situations.		1. Calculate density, mass, and volume
GEO-G.MG.2: Apply concepts of density based on area and volume of geometric figures in modeling situations.
1. Calculate density, mass, and volume
GEO-G.MG.3: Apply geometric methods to solve design problems.
GEO-G.MG.3: Apply geometric methods to solve design problems.

Checkpoint opportunity		1. Checkpoint: Geometric modeling and design 2. Checkpoint: Density
Checkpoint opportunity
1. Checkpoint: Geometric modeling and design 2. Checkpoint: Density