PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22 Days / 10 Days

Unit Topic

(Specify skills/information that will be learned.) / Unit 1
Reasoning and Proof / Unit 2
Spatial Visual /

Unit 3

Triangles

/

Unit 4

2-Dimensional

Enduring Understandings

(Give and/or demonstrate necessary information) / In proofs, deductive reasoning about given information is used to reach mathematical conclusions.
Theorems and properties exist that guarantee two triangles are congruent or similar given certain conditions.
Relationships between lines, angles and figures can be used to establish additional mathematical relationships.
Congruent figures are also similar figures, but similar figures are not always congruent. / Geometric figures and relationships can be represented in the coordinate plane.
Geometric figures can be measured in the coordinate plane.
The slope of a line is the ratio of vertical change (rise) to horizontal change (run).
Slopes, distances and midpoints can be determined when a segment is graphed in the coordinate plane.
A line’s direction and steepness are determined by its slope.
Linear equations can be used to make predictions. / The Pythagorean Theorem is essential to solving problems involving right triangles.
Congruent figures are also similar figures, but similar figures are not always congruent.Congruency and similarity have real life applications in art, architecture, and science.
Parallel and perpendicular lines are used to prove triangles congruent or similar.
30º-60º-90º and 45º-45º-90º triangles are similar triangles. / Polygons are categorized by the number of sides.
Studying patterns can lead to geometric formulas and relationships.
Rectangles, squares, and rhombi are parallelograms and belong to the set of quadrilaterals.Relationships exist between sides, angles and segments in polygons.
By using the area formula of a rectangle, we can derive area formulas for other figures.

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22Days / 10 Days

Enduring Understandings

con’t / Parallel and perpendicular lines are used to prove triangles congruent or similar. / A line’s slope and x- and y-intercepts have real world applications. / Special triangles have real world applications.
Relationships in special right triangles can be determined by the Pythagorean Theorem. / Perimeter and circumference are 1-dimensional measures, while area is a 2-dimenionsal measure.
Measurement of geometric figures is an essential part everyday life.

Essential Questions

(Steps to check for student understanding) / Why write formal proofs?
Why are properties and theorems about parallel and perpendicular lines useful in geometric proofs?
How can reasoning about geometric situations be used to solve real life problems?
If two figures are congruent or similar, what else do you know about their corresponding parts?
What theorems or postulates (properties) guarantee two triangles congruent? / Why is it important to learn about geometric figures and relationships in the coordinate plane?
How do you determine information about a line or segment graphed in the coordinate plane?
How does the Distance Formula relate to the Pythagorean Theorem?
How do you represent geometric figures in the coordinate plane?
How do you measure geometric figures using the coordinate plane? / Why is the intersection point of special segments in triangles important?
What theorems guarantee two triangles congruent?
How do congruent figures differ from similar figures?
Where are parallel and perpendicular lines evident in everyday life?
How are the angles formed by parallel lines used to prove triangles congruent? / How can you use patterns to find the sum of the interior angles of any polygon?
How can you determine the measure of interior and exterior angles in regular polygons?
How do you classify quadrilaterals using special segments and properties?
How do special segments in polygons help solve everyday situations?

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22Days / 10 Days

Essential Questions con’t

/ How do congruent figures differ from similar figures? / How does slope describe a line? How can you use an equation to make a prediction?
What does the slope of the line tell you?
How do you write an equation for a line?
How do you write an equation for a line if you are given two points?
How do you determine the x- and y-intercepts graphically and algebraically? / How are properties of perpendicular lines used to prove congruent and similar triangles?
How is the Pythagorean
Theorem related to the lengths of sides of special right triangles?
How does the concept of similarity apply to special right triangles?How are right triangle relationships used in the real world?
How do you find the lengths of sides of special right triangles? / How can you derive the various area formulas from the area of a rectangle?
How can you find the areas of irregular figures?
How does finding the area of the various figures apply to everyday situations?How are perimeter, circumference, and area different from one another?

Standards

/ G-1.1 Demonstrate an understanding of the axiomatic structure of geometry
using undefined terms, definitions, postulates, theorems, and corollaries. / G-2.4 Use direct measurement to determine the length of a segment, measure
of an angle, and distance from a point to a line.
G-6.1 Use the distance formula to solve problems. / G-3.1 Carry out a procedure to compute the perimeter of a triangle.
G-3.2 Carry out a procedure to compute the area of a triangle.
G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles. / G-2.3 Use the congruence of line segments and angles to solve problems.
G-4.6 Apply congruence and similarity between shapes (including
quadrilaterals and polygons) to solve problems.

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22 Days / 10 Days

Standards con’t

/ G-1.2 Communicate knowledge of geometric relationships using mathematical
terminology appropriately.
G-1.7 Understand the historical development of geometry.
G-1.4 Formulate and test conjectures using a variety of tools such as concrete models, graphing. calculators, spreadsheets, and dynamic geometry
Software
G-1.9 Demonstrate an understanding of how geometry applies to real world contexts (including architecture, construction, farming, astronomy). / G-6.2 Use the midpoint formula to solve problems.
G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut
by a transversal to solve problems.
G-2.5 Carry out a procedure to create geometric constructions (including
midpoint of a line segment, angle bisector,
perpendicular bisector of a line segment, line through a given point that is parallel to a given line,
and line through a given point that is perpendicular to a given line). / G-3.4 Apply properties of isosceles and equilateral triangles to solve problems.
G-3.5 Use interior angles, exterior angles, medians, angle bisectors, altitudes,
and perpendicular bisectors to solve problems.
G-3.6 Apply the Triangle Sum Theorem to solve problems.
G-3.7 Apply the Triangle Inequality Theorem to solve problems.
G-3.8 Apply congruence and similarity between triangles to solve problems.
G-3.9 Apply theorems to prove triangles are similar or congruent.
G-3.10 Use the Pythagorean Theorem and its converse to solve problems. / G-2.5 Carry out a procedure to create geometric constructions (including
midpoint of a line segment, angle bisector, perpendicular bisector of
a line segment, line through a given point that is parallel to a given line,
and line through a given point that is perpendicular to a given line).
G-4.6 Apply congruence and similarity between shapes (including
quadrilaterals and polygons) to solve problems.
G-2.6 Use scale factors to solve problems involving scale drawings and
models.

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22 Days / 10 Days

Standards con’t

/ G-1.10 Understand geometric relationships including constructions through investigations using a variety of tools such as straightedge, compass,
paper folding, dynamic geometry software, and hand-held computing
devices.
G-1.3 Apply basic rules of logic to determine the validity of the converse,
inverse, and contrapositive of a conditional statement
G-1.5 Use inductive reasoning to formulate conjectures.
G-1.6 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement. / G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.
G-3.12 Use trigonometric ratios (including sine, cosine, tangent) to solve
problems involving right triangles. / G-2.7 Use geometric probability to solve problems.
G-4.1 Carry out a procedure to compute the perimeter of quadrilaterals,
regular polygons, and composite figures.
G-4.2 Carry out a procedure to find the
area of quadrilaterals, regular polygons, and composite figures.
G-4.3 Apply procedures to compute measures of interior and exterior angles of polygons. area of quadrilaterals and regular polygons.
G-4.4 Analyze how changes in dimensions affect the perimeter or
area of quadrilaterals and regular polygons

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 14 Days / 14 Days / 22 Days / 10 Days

Standards con’t

/ G-4.5 Apply properties and attributes of quadrilaterals and regular polygons
and their component parts to solve problems.
G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular numbers, rectangular numbers, and number of diagonals in polygons).
G-2.7 Use geometric probability to solve problems.

Integrations

(with other discipline areas)

District Assessments

(culminating assessments) /

Benchmark Exam

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 12 Days / 5Days / 13 Days

Unit Topic

(Specify skills/information that will be learned.) / Unit 5
3-Dimensional / Unit 6
Transformations /

Unit 7

Circles

Enduring Understandings

(Give and/or demonstrate necessary information) / Three-dimensional figures have properties similar to those of two-dimensional figures. / Transformations move or map figures (preimages) onto their images.
Reflections, rotations, and translations are transformations that preserve shape and size (congruency).
Dilation is a transformation that preserves shape only (similarity). / Indirect measurement is based on the properties of geometric figures.
Relationships exist among angles, segments, lengths, circumference, and area of circles.

Essential Questions

(Steps to check for student understanding) / How are two-dimensional relationships connected to the properties of three-dimensional figures? / Why do certain transformations preserve shape and size while others only preserve shape?
How does combining transformations affect the final result?
How are the coordinates affected by transformations in the / How are the areas of polygons and circles related and applied?
How are angles and intercepted arcs of circles related and applied?

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 12 Days / 5 Days / 13 Days

Essential Questions

con’t / coordinate plane?
How are scale factors used in transformations?

Standards

/ G-7.1 Carry out a procedure to compute the surface area of three-dimensional
objects (including cones, cylinders, pyramids, prisms, spheres, and
hemispheres).
G-7.2 Carry out a procedure to compute the volume of three-dimensional
objects (including cones, cylinders, pyramids, prisms, spheres,
hemispheres, and composite objects).
G-7.3 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres). / G-6.3 Apply transformations (translation, reflection, rotation, and dilation) to
figures in the coordinate plane using sketches and coordinates.
G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane using matrices.
G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.
G-6.6 Carry out a procedure to determine the magnitude and direction of the
resultant by direct measurement using a / G-5.1 Carry out a procedure to compute the circumference of circles.
G-5.2 Carry out a procedure to compute the area of circles.
G-5.3 Analyze how a change in radius affects the circumference or area of a circle.
G-5.4 Carry out a procedure to compute arc length or area of a sector of a circle.
G-5.5 Apply properties of component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

PACING GUIDES FOR MATH

Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools

Time Frame: / 12 Days / 5 Days / 13 Days

Standards

/ G-7.4 Apply congruence and similarity between objects to solve problems.
G-7.5 Apply a procedure to draw a top-view, front-view, and side-view of a
three-dimensional object.
G-7.6 Apply a procedure to draw an isometric view of a three-dimensional object / scale drawing.
G-6.7 Carry out a procedure to compute the magnitude of the resultant of two
perpendicular vectors using the Pythagorean Theorem.
G-6.8 Carry out a procedure to determine the direction of the resultant of two
perpendicular vectors using direct measurement. / G-5.6 Apply properties of lines that intersect circles(including two secants, two
tangents, or a secant and a tangent) to solve problems.
G-5.7 Apply properties of central angles, inscribed angles, and arcs of circlesto solve problems.
G-2.7 Use geometric probability to solve problems.

Integrations

(with other discipline areas)

District Assessments

(culminating assessments) /

Final Exam