Pacing Guide

Pacing Guide

 

South Carolina College-and Career-Ready

Geometry

Mathematical Process Standards

 

Standards

Explanations   and Examples

1. Make sense of problems and persevere in   solving them.

 

 

a. Relate a problem to prior knowledge.

b. Recognize there may be multiple entry points to a problem and   more than one path to a solution.

c. Analyze what is given, what is not given, what is being   asked, and what strategies are needed, and make an initial attempt to solve a   problem.

d. Evaluate the success of an approach to solve a problem and   refine it if necessary.

 

2. Reason both contextually and abstractly.

 

 

a. Make sense of quantities and their relationships in   mathematical and real-world situations.

b. Describe a given situation using multiple mathematical representations.  

c. Translate among multiple mathematical representations and   compare the meanings each representation conveys about the situation.

d. Connect the meaning of mathematical operations to the context   of a given situation.

 

3. Use critical thinking skills to justify   mathematical reasoning and critique the reasoning of others.

 

 

a. Construct and justify a solution to a problem.

b. Compare and discuss the validity of various reasoning   strategies.

c. Make conjectures and explore their validity.

d. Reflect on and provide thoughtful responses to the reasoning   of others.

 

 

 

Standards

Explanations   and Examples

4. Connect mathematical ideas and real-world   situations through modeling.

 

 

a. Identify relevant quantities and develop a model to describe   their relationships.

b. Interpret mathematical models in the context of the   situation.

c. Make assumptions and estimates to simplify complicated   situations.

d. Evaluate the reasonableness of a model and refine if   necessary.

 

5. Use a variety of mathematical tools   effectively and strategically.

 

 

a. Select and use appropriate tools when solving a mathematical   problem.

b. Use technological tools and other external mathematical   resources to explore and deepen understanding of concepts.

 

6. Communicate mathematically and approach   mathematical situations with precision.

 

 

a. Express numerical answers with the degree of precision   appropriate for the context of a situation.

b. Represent numbers in an appropriate form according to the   context of the situation.

c. Use appropriate and precise mathematical language.

d. Use appropriate units, scales, and labels.

 

7. Identify and utilize structure and   patterns.

 

 

a. Recognize complex mathematical objects as being composed of   more than one simple object.

b. Recognize mathematical repetition in order to make   generalizations.

c. Look for structures to interpret meaning and develop solution   strategies.

 

 

 

 

 

 

 

 

 

 

WCSD   Pacing Guide

Geometry-CP

SCCCRS

1st   Quarter

South   Carolina College-and Career-Ready (SCCR) Geometry

Unit 1: Points, Lines, Planes, Angles and   Proofs

                           
   

G.GCO.1*    

   
   

Define     angle, perpendicular line, parallel line, line segment, ray, circle, and     skew in terms of the undefined notions of point, line, and plane. Use     geometric figures to represent and describe real-world objects.

   
   

G.GCO.8*    

   

 

   

 

   

 

   

 

   
   

Prove,     and apply in mathematical and real-world contexts, theorems about lines and     angles, including the following:

   

a.     vertical angles are congruent;

   

b.     when a transversal crosses parallel lines, alternate interior angles are     congruent, alternate exterior angles are congruent, and consecutive     interior angles are supplementary;

   

d.     perpendicular lines form four right angles.

   

 

             
   

G.GCO.11*    

   
   

Construct     geometric figures using a variety of tools, including a compass, a     straightedge, dynamic geometry software, and paper folding, and use these     constructions to make conjectures about geometric relationships.

   

 

                                                       
   

G.GGPE.4*    

   
   

Use     coordinates to prove simple geometric theorems algebraically.

   
   

G.GGPE.5*    

   
   

Analyze     slopes of lines to determine whether lines are parallel, perpendicular, or     neither. Write the equation of a line passing through a given point that is     parallel or perpendicular to a given line. Solve geometric and real-world     problems involving lines and slope.

   
   

G.GGPE.6    

   
   

Given     two points, find the point on the line segment between the two points that     divides the segment into a given ratio.

   
   

G.GGPE.7*    

   
   

Use     the distance and midpoint formulas to determine distance and midpoint in a     coordinate plane, as well as areas of triangles and rectangles, when given     coordinates.

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

Unit 2: Triangles

             
   

G.GCI.3    

   
   

Construct     the inscribed and circumscribed circles of a triangle using a variety of     tools, including a compass, a straightedge, and dynamic geometry software,     and prove properties of angles for a quadrilateral inscribed in a circle.

   

 

                                                                                                 
   

G.GCO.2*    

   
   

Represent     translations, reflections, rotations, and dilations of objects in the plane     by using paper folding, sketches, coordinates, function notation, and     dynamic geometry software, and use various representations to help     understand the effects of simple transformations and their compositions.

   
   

G.GCO.3*    

   
   

Describe     rotations and reflections that carry a regular polygon onto itself and     identify types of symmetry of polygons, including line, point, rotational,     and self-congruence, and use symmetry to analyze mathematical situations.

   
   

G.GCO.4*    

   
   

Develop     definitions of rotations, reflections, and translations in terms of angles,     circles, perpendicular lines, parallel lines, and line segments.

   
   

G.GCO.5*    

   
   

Predict     and describe the results of transformations on a given figure using     geometric terminology from the definitions of the transformations, and     describe a sequence of transformations that maps a figure onto its image.

   
   

G.GCO.6*    

   
   

Demonstrate     that triangles and quadrilaterals are congruent by identifying a     combination of translations, rotations, and reflections in various     representations that move one figure onto the other.

   
   

G.GCO.7*    

   
   

Prove     two triangles are congruent by applying the Side-Angle-Side,     Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence     conditions.

   
   

G.GCO.8*    

   

G.GCO.9*

   

 

   

 

   

 

   

 

   

 

   

 

   

G.GCO.11*

   
   

Prove,     and apply in mathematical and real-world contexts, theorems about lines and     angles, including the following:

   

c. any     point on a perpendicular bisector of a line segment is equidistant from the     endpoints of the segment;

                             
     

 

     
     

Prove,       and apply in mathematical and real-world contexts, theorems about the       relationships within and among triangles, including the following:

     

a.       measures of interior angles of a triangle sum to 180°;

     

b.       base angles of isosceles triangles are congruent;

     

c.       the segment joining midpoints of two sides of a triangle is parallel to       the third side and half the length;

     

d.       the medians of a triangle meet at a point.

                                         
       

 

       
       

Construct geometric figures using a variety of         tools, including a compass, a straightedge, dynamic geometry software,         and paper folding, and use these constructions to make conjectures         about geometric relationships.

       
     

 

     
   

 

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

             
   

G.GSRT.5*    

   
   

Use     congruence and similarity criteria for triangles to solve problems and to     prove relationships in geometric figures.

   

 

Unit3: Quadrilaterals

                                                                                   
   

G.GCO.10*    

   
   

Prove,     and apply in mathematical and real-world contexts, theorems about     parallelograms, including the following:

   

a.     opposite sides of a parallelogram are congruent;

   

b.     opposite angles of a parallelogram are congruent;

   

c.     diagonals of a parallelogram bisect each other;

   

d.     rectangles are parallelograms with congruent diagonals;

   

e. a     parallelograms is a rhombus if and only if the diagonals are perpendicular.    

   

 

   
   

G.GCO.11*    

   
   

Construct     geometric figures using a variety of tools, including a compass, a     straightedge, dynamic geometry software, and paper folding, and use these     constructions to make conjectures about geometric relationships.

   
   

G.GGPE.4*    

   
   

Use     coordinates to prove simple geometric theorems algebraically.

   
   

G.GGPE.5*    

   
   

Analyze     slopes of lines to determine whether lines are parallel, perpendicular, or     neither. Write the equation of a line passing through a given point that is     parallel or perpendicular to a given line. Solve geometric and real-world     problems involving lines and slope.

   
   

 

   
   

 

   
   

G.GGPE.7*    

   
   

Use     the distance and midpoint formulas to determine distance and midpoint in a     coordinate plane, as well as areas of triangles and rectangles, when given     coordinates.

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

             
   

G.GSRT.5*    

   
   

Use     congruence and similarity criteria for triangles to solve problems and to     prove relationships in geometric figures.

   

 

Unit 4:Similarity

                                         
   

G.GCO.2*    

   
   

Represent     translations, reflections, rotations, and dilations of objects in the plane     by using paper folding, sketches, coordinates, function notation, and     dynamic geometry software, and use various representations to help     understand the effects of simple transformations and their compositions.

   
   

G.GCO.5*    

   
   

Predict     and describe the results of transformations on a given figure using     geometric terminology from the definitions of the transformations, and     describe a sequence of transformations that maps a figure onto its image.

   
   

G.GCO.9*

   

 

   

 

   

G.GCO.11*

   
   

Prove,     and apply in mathematical and real-world contexts, theorems about the     relationships within and among triangles, including the following:

   
        
  1. the segment joining midpoints of two sides of a triangle is          parallel to the third side and half the length;
  2.    
                             
     

 

     
     

Construct       geometric figures using a variety of tools, including a compass, a       straightedge, dynamic geometry software, and paper folding, and use these       constructions to make conjectures about geometric relationships.

     
   

 

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

                                                                     
   

G.GSRT.1    

   
   

Understand     a 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.     Verify experimentally the properties of dilations given by a center and a     scale factor. Understand the dilation of a line segment is longer or     shorter in the ratio given by the scale factor.

   
   

G.GSRT.2*    

   
   

Use     the definition of similarity to decide if figures are similar and justify     decision. Demonstrate that two figures are similar by identifying a     combination of translations, rotations, reflections, and dilations in     various representations that move one figure onto the other.

   
   

G.GSRT.3*    

   
   

Prove     that two triangles are similar using the Angle-Angle criterion and apply     the proportionality of corresponding sides to solve problems and justify     results.

   
   

G.GSRT.4*    

   
   

Prove,     and apply in mathematical and real-world contexts, theorems involving     similarity about triangles, including the following:

   

a. A     line drawn parallel to one side of a triangle divides the other two sides     into parts of equal proportion.

   

b. If     a line divides two sides of a triangle proportionally, then it is parallel     to the third side.

   
   

G.GSRT.5*    

   
   

Use     congruence and similarity criteria for triangles to solve problems and to     prove relationships in geometric figures.

   

 

 

 

 

WCSD   Pacing Guide

Geometry-CP

SCCCRS

2nd   Quarter

Unit 5: Right Triangles and Trigonometry

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

                                                                     
   

G.GSRT.4*    

   
   

Prove,     and apply in mathematical and real-world contexts, theorems involving     similarity about triangles, including the following:

   

c. The     square of the hypotenuse of a right triangle is equal to the sum of squares     of the other two sides.

   

 

   
   

 

   
   

 

   
   

G.GSRT.6*    

   
   

Understand     how the properties of similar right triangles allow the trigonometric     ratios to be defined and determine the sine, cosine, and tangent of an     acute angle in a right triangle.

   
   

G.GSRT.7    

   
   

Explain     and use the relationship between the sine and cosine of complementary     angles.

   
   

G.GSRT.8*    

   
   

Solve     right triangles in applied problems using trigonometric ratios and the     Pythagorean Theorem.

   

 

Unit 6: Area and Volume

             
   

G.GCI.5*    

   
   

Derive     the formulas for the length of an arc and the area of a sector in a circle     and apply these formulas to solve mathematical and real-world problems.

   

 

             
   

G.GCO.1*    

   
   

Define     angle, perpendicular line, parallel line, line segment, ray, circle, and     skew in terms of the undefined notions of point, line, and plane. Use     geometric figures to represent and describe real-world objects.

   

 

             
   

G.GCO.11*    

   
   

Construct     geometric figures using a variety of tools, including a compass, a     straightedge, dynamic geometry software, and paper folding, and use these     constructions to make conjectures about geometric relationships.

   

 

             
   

G.GGPE.7*    

   
   

Use     the distance and midpoint formulas to determine distance and midpoint in a     coordinate plane, as well as areas of triangles and rectangles, when given     coordinates.

   

 

                                                                                                               
   

G.GGMD.1*    

   
   

Explain     the derivations of the formulas for the circumference of a circle, area of     a circle, and volume of a cylinder, pyramid, and cone. Apply these formulas     to solve mathematical and real-world problems.

   
   

G.GGMD.2    

   
   

Explain     the derivation of the formulas for the volume of a sphere and other solid     figures using Cavalieri’s principle.

   
   

G.GGMD.3*    

   
   

Apply     surface area and volume formulas for prisms, cylinders, pyramids, cones,     and spheres to solve problems and justify results. Include problems that     involve algebraic expressions, composite figures, geometric probability,     and real-world applications.

   
   

G.GGMD.4     *

   
   

Describe     the shapes of two-dimensional cross-sections of three-dimensional objects     and use those cross-sections to solve mathematical and real-world problems.    

   
   

 

   
   

 

   
   

 

   
   

 

   
   

 

   
   

 

   
   

 

   
   

 

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use geometry     concepts and methods to model real-world situations and solve problems     using a model.

   

 

Unit 7: Circles

                                                       
   

G.GCI.1    

   
   

Prove     that all circles are similar.

   
   

G.GCI.2*    

   
   

Identify     and describe relationships among inscribed angles, radii, and chords; among     inscribed angles, central angles, and circumscribed angles; and between     radii and tangents to circles. Use those relationships to solve     mathematical and real-world problems.

   
   

G.GCI.3    

   
   

Construct     the inscribed and circumscribed circles of a triangle using a variety of     tools, including a compass, a straightedge, and dynamic geometry software,     and prove properties of angles for a quadrilateral inscribed in a circle.

   
   

G.GCI.4    

   
   

Construct     a tangent line to a circle through a point on the circle, and construct a     tangent line from a point outside a given circle to the circle; justify the     process used for each construction.

   

 

             
   

G.GGPE.1*    

   
   

Understand     that the standard equation of a circle is derived from the definition of a     circle and the distance formula.

   

 

                           
   

G.GM.1*    

   
   

Use     geometric shapes, their measures, and their properties to describe     real-world objects.

   
   

G.GM.2    

   
   

Use     geometry concepts and methods to model real-world situations and solve     problems using a model.

   

 

Unit 8: Statistics

                                         
   

G.SPID.1*    

   
   

Select     and create an appropriate display, including dot plots, histograms, and box     plots, for data that includes only real numbers.

   
   

G.SPID.2*    

   
   

Use     statistics appropriate to the shape of the data distribution to compare     center and spread of two or more different data sets that include all real     numbers.

   
   

G.SPID.3*    

   
   

Summarize     and represent data from a single data set. Interpret differences in shape,     center, and spread in the context of the data set, accounting for possible     effects of extreme data points (outliers).

   

 

 

Vocabulary:

 

 

 

 

 

 

Resources:

 

 

 

 

 

 

 

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