Unit Number of Days Dates. 1 Angles, Lines and Shapes 14 8/2 8/ Reasoning and Proof with Lines and Angles 14 8/22 9/9

Size: px
Start display at page:

Download "Unit Number of Days Dates. 1 Angles, Lines and Shapes 14 8/2 8/ Reasoning and Proof with Lines and Angles 14 8/22 9/9"

Transcription

1

2 8 th Grade Geometry Curriculum Map Overview Unit Number of Days Dates 1 Angles, Lines and Shapes 14 8/2 8/ Reasoning and Proof with Lines and Angles 14 8/22 9/9 3 - Congruence Transformations and Triangles 18 9/12 10/6 4 - Relationships in Triangles 15 10/17 11/4 5 - Quadrilaterals 26 11/7 12/ Transformations and Similarity 14 1/4 1/ Right Triangles and Trigonometry 20 1/25 2/ Area and Volume with Modeling 19 2/23 3/24 TN Ready Part 1 Testing Window 9 - Circles 15 4/3 4/21 TN Ready Part 2 Testing Window

3 Unit 1 Angles, Lines and Shapes Standards G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Make Geometric Constructions G.CO.A.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, 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. Expressing Geometric Properties with Equations G.GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Essential Understandings 1. A point is a location that has neither shape nor size. 2. A line is made up of points and has no thickness or width. There is exactly one line through two any points. 3. An angle is formed by two noncollinear rays with a common endpoint. 4. A circle is the locus or the set of all points in a plane equidistant from a given point called the center of the circle. 5. Perpendicular lines form rights angles 6. Parallel lines are coplanar lines that do not intersect 7. A line segment is a measurable part of a line that consists of two pints, called endpoints, and all of the points between them. 8. The distance formula is derived from the Pythagorean Theorem and is and can be used to compute perimeters and areas of triangles and rectangles using coordinates. 9. The midpoint formula is used to find the point on a line a segment that divides the segment into two congruent segments and is

4 Unit 2 Reasoning and Proof with Lines and Angles Standards Prove Geometric Theorems G.CO.C.1 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints Make Geometric Constructions G.CO.A.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, 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. Expressing Geometric Properties with Equations G.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines Essential Understandings 1. Complementary angles have a sum of Supplementary angles have a sum of If the noncommon sides of two adjacent angles form a right angle, then they are complementary angles. 4. If two angles form a linear pair, then they are supplementary angles. 5. Vertical angles are two nonadjacent angles formed by two intersecting lines and are congruent. 6. When a transversal intersects two parallel lines, pairs of congruent angles are formed. These include alternate interior angles, corresponding angles, alternate exterior angles 7. The perpendicular bisector in a triangle, a line, segment or ray is the segment that passes through the midpoint of that side and is perpendicular to that side. 8. Slopes of parallel lines are congruent. 9. Slopes of perpendicular lines are opposite reciprocals of each other. 10. The equation of a line is y = mx + b where m is the slope and b is the y-intercept. and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

5 Unit 3 - Congruence Transformations and Triangles Standards Prove Geometric Theorems G.CO.C.9 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Experiment with Transformations in the Plane G.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand Congruence in Terms of Rigid Motions G.CO.B.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. Essential Understandings 1. The sum of the measures of the angles of a triangle is The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 3. The acute angles of a right triangle are complementary. 4. There can be at most one right or one obtuse angle in a triangle. 5. The two congruent sides of an isosceles triangle are called legs and the angle whose sides are the legs is called the vertex angle. 6. The side of the isosceles triangle opposite the vertex angle is called the base. 7. The two angles formed by the base and the congruent sides are called the base angles and they are congruent. 8. In two congruent polygons, all the parts of one polygon are congruent to corresponding parts of the other polygon. These corresponding parts include corresponding angles and corresponding sides. 9. A transformation is an operation that maps an original geometric figure, the preimage, onto a new figure, the image. 10. A congruence transformation, also called a rigid transformation or an isometry, is one in which the position of the image may differ from the preimage, but the two figures remain congruent. 11. A reflection is a transformation over a given line called the line of reflection. Each point of the preimage and image are the same distance from the line of reflection. 12. A translation is a transformation that moves all points of the preimage the same distance and direction. 13. A rotation is transformation around a fixed point called

6 G.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. G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. the center of rotation, through a specific angle, and in a specific direction. Each point of the original figure and its image are the same distance from the center. 14. If three sides of a triangle are congruent to three sides of another triangle then they are congruent by Side-Side- Side postulate (SSS). 15. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then they are congruent by Side-Angle-Side (SAS). 16. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then they are congruent by Angle-Side-Angle (ASA). 17. If two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle, then they are congruent by Angle- Angle-Side (AAS).

7 Unit 4 Relationships in Triangles Standards Prove Geometric Theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Essential Understandings 1. If a point is on the perpendicular bisector of a segment, then it is equidistant to the endpoints of the segment. 2. When three or more lines intersect at a common point, they are called concurrent lines and the point of intersection point is called the point of concurrency. 3. The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter of the triangle and is equidistant from the vertices of the triangle. 4. If a point is on the bisector of an angle, then it is equidistant to the sides of the angle. 5. The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle. 6. A median of a triangle is a segment with endpoints being a vertex and the midpoint of the opposite side. 7. The medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from each vertex to the midpoint of the opposite side. The centroid is always inside the triangle. 8. The altitude of a triangle is a segment from the vertex to the line containing the opposite side and perpendicular to the line containing that side. The altitude can be in the interior, exterior, or on the side of the triangle. 9. The lines containing the altitudes of a triangle are concurrent, meeting at a point called the orthocenter. 10. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. 11. If one side of a triangle is longer than another side, then the angle opposite the longer side than the angle opposite the shorter side. 12. The sum of the lengths of any two sides of a triangle must be greater than the lengths of the third side.

8 13. The Hinge Theorem that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

9 Unit 5 Quadrilaterals Standards Prove Geometric Theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints G.CO.C.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Use Coordinates to Prove Simple Geometric Relationships G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). Essential Understandings 1. The sum of the interior angles of a polygon is (n-2) * 180 where n is the number of sides of the polygon. 2. A parallelogram is a quadrilateral that has both pairs of opposite sides congruent and parallel, both pairs of opposite angles congruent, and its consecutive angles are supplementary. 3. The diagonals of a parallelogram bisect each other. 4. A rectangle is a parallelogram with four right angles and congruent diagonals. 5. A rhombus is a parallelogram with all four sides congruent 6. A trapezoid is a quadrilateral with at least one pair of parallel sides. 7. The midsegment of a trapezoid is a segment that connects the midpoints of the legs of a trapezoid. The midsegment is parallel to each base and is ½ the sum of the lengths of the bases. 8. A kite is a quadrilateral with exactly two pairs of consecutive congruent sides. A kite is not a parallelogram. 9. A quadrilateral can be proven to be a parallelogram if one of the following conditions are met: both pairs of opposite sides are congruent and parallel, both pairs of opposite angles are congruent, one pair of opposite sides are both congruent and parallel, or if the diagonals bisect each other. 10. A parallelogram can be proven to be a rectangle if its diagonals are congruent or if it has right angles. 11. A parallelogram can be proven to be a rhombus if it has four congruent sides. 12. A parallelogram can be proven to be a square if it is both a rhombus and a rectangle.

10 Unit 6 Transformations and Similarity Standards Use Coordinates to Prove Simple Geometric Theorems Algebraically G.GPE.B6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Understand Similarity in Terms of Similarity Transformations G.SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. 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. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G.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. G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Essential Understandings 1. A ratio is a comparison of two quantities using division. 2. Similar polygons have the same shape but not necessarily the same size. 3. The ratio of the lengths of the corresponding sides of similar polygons is called the scale factor. 4. The corresponding angles of similar polygons are congruent. 5. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar by Angle-Angle (AA). 6. If the corresponding side lengths of two triangles are proportional, then the triangles are similar by Side- Side-Side Similarity (SSS ) 7. If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar by Side- Angle-Side Similarity (SAS ) 8. A dilation is a similarity transformation that enlarges or reduces a figure proportionally with respect to a center point and a scale factor. If the scale factor is greater than one then it is called an enlargement. A scale factor between 0 and 1 is called a reduction. 9. If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the

11 Prove Theorems Involving Similarity G.SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Prove Geometric Theorems sides into segments of proportional lengths. 10. If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides. 11. If two triangles are similar, the lengths of corresponding angle bisectors are proportional to the lengths of corresponding sides. 12. If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides. G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

12 Unit 7 Right Triangles and Trigonometry Standards Prove Geometric Theorems G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Define Trigonometric Ratios and Solve Problems Involving Right Triangles G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Apply Trigonometry to General Triangles G.SRT.D.9 (+) Derive the formula A = 1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. G.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Essential Understandings 1. The geometric mean of two numbers is the positive square root of their product. 2. If an altitude is drawn to the hypotenuse of a right triangle, then the triangles formed are similar to the original triangle and each other. 3. The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of the altitude is the geometric mean between the lengths of these two segments. 4. The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of a leg of the triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg. 5. In a right triangle, the sum of the squares of the legs is equal to the square of the length of the hypotenuse. This relationship can be represented by a 2 + b 2 = c 2 where a and b are the legs and c is the hypotenuse and is known as the Pythagorean Theorem. 6. A Pythagorean triple is a set of three non-zero whole numbers that satisfy the Pythagorean Theorem. (3, 4, 5; 5, 12, 13; 8, 15, 17, etc.) 7. In a triangle, the legs are congruent and the hypotenuse is 2 times the length of a leg. 8. In a degree triangle, the length of the hypotenuse is 2 times the length of the shorter leg and the longer leg is 3 times the length of the shorter leg. 9. A trigonometric ratio is the ratio of two sides of a right triangle. 10. The sine of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle and the length of the hypotenuse. 11. The cosine of an acute angle in a right triangle is the ratio

13 of the length of the leg adjacent to the angle and the length of the hypotenuse. 12. The tangent of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle and the leg adjacent to the angle. 13. The sine of one acute angle in a right triangle is the same as the cosine of its complement. 14. The area of a triangle can be found by using the formula A = 1/2 ab sin(c). 15. The Law of Sines and Law of Cosines can be used to find unknown measurements in both right and non-right triangles. 16. The Law of Sines can be represented by 17. The Law of Cosines can be represented by a 2 = b 2 + c 2 2bc cos A b 2 = a 2 + c 2 2ac cos B c 2 = a 2 + b 2 2ab cos C 18. A vector describes both the magnitude and direction of a real number.

14 Unit 8 Area and Volume with Modeling Standards Explain Area and Volume Formulas and Use Them to Solve Problems G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. G.GMD.A.2 (+) Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures. G.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Visualize Relationships between Two-Dimensional and Three-dimensional Objects G.GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Translate Between the Geometric Description and the Equation for a Conic Section Essential Understandings 1. The area of a circle is equal to times the square of the radius (r) or * r 2 2. The volume of a cylinder is r 2 h where r is the radius and h is the height of the cylinder 3. The volume of a pyramid is 1/3 B*h where B is the area of the base and h is the height of the pyramid. 4. The volume of a cone is 1/3 B*h or 1/3 r 2 h where B is the area of the base, h is the height of the cone and r is the radius of the base. 5. The volume of a sphere is 4/3 r 3 where r is the radius of the sphere. 6. Cavalieri's Principle states that if two solids have equal altitudes, and if sections made by planes parallel to the bases and at equal distances from them are always in a given ratio, then the volumes of the solids are also in this ratio. The formula is B*h where B is the area of a cross section and h is the height of the solid. 7. A cross section is the intersection of a body in threedimensional space with a plane. G.GPE.A.2 Derive the equation of a parabola given a focus and directrix. G.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 8. The equation of a parabola is ax 2 + bx + c in standard form and a(x-h) 2 + k in vertex form

15 Apply Geometric Concepts in Modeling Situations 9. The equation of an ellipse is G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). G.MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). G.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). where: x,y are the coordinates of any point on the ellipse, a, b are the radius on the x and y axes respectively 10. The equation of a hyperbola is where x 0 and y 0 are the center points and a and b are the major and minor axes.

16 Unit 9 Circles Standards Understand and Apply Theorems about circles G.C.A.1 Prove that all circles are similar. G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G.C.A.4 (+) Construct a tangent line from a point outside a given circle to the circle. Explain Area and Volume Formulas and Use Them to Solve Problems G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. Make Geometric Constructions G.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Find Arc Lengths and Areas of Sectors of Circles G.C.B.5 Derive using similarity the fact that the length of the arc Essential Understandings 1. A circle is the locus or the set of all points in a plane equidistant from a given point called the center of the circle. 2. A radius of a circle is a segment with endpoints at the center and on the circle. 3. A chord is a segment with endpoints on the circle. 4. A diameter of a circle is a chord that passes through the center of the circle. 5. If two circle have congruent radii, then they are congruent circles. 6. All circles are similar. 7. Concentric circles are coplanar and have the same center. 8. The circumference of a circle is the distance around the circle. The ratio of the circumference to the diameter is represented by the symbol. 9. A central angle of a circle is an angle with a vertex in the center of the circle and sides as radii. 10. An arc is a portion of a circle defined by two endpoints. 11. A minor arc is the shortest arc connecting two endpoints on the circle. Its measure is less than 180 and equal to the measure of its related central angle. 12. A major arc is the longest arc connecting two endpoints on the circle. Its measure is greater than 180 and equal to 360 minus the measure of the minor arc with the same endpoints. 13. A semicircle has endpoints that lie on the diameter and has a measure of Arc length is the distance between the endpoints along an

17 intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Translate Between the Geometric Description and the Equation for a Conic Section G.GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation arc measured in linear units. 15. The ratio of the length of an arc to the circumference of the circle is equal to the ratio of the degree measure of the arc to A sector of a circle is a region of a circle bounded by a central angle and its intercepted arc. 17. The ratio of the area of a sector to the area of the whole circle is equal to the ratio of the degree measure of the intercepted arc to Radian measure is a way to measure angles. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. 19. In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. 20. If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc. 21. The perpendicular bisector of a chord is a diameter (or radius) of the circle. 22. In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant to the center. 23. An inscribed angle has a vertex on the circle and sides that contain chords of the circle. 24. An inscribed angle on a diameter is a right angle. 25. An intercepted arc has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle. 26. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

18 27. A tangent is a line in the same plane as a circle that intersects the circle in exactly one point called the point of tangency. 28. In a plane, a radius is perpendicular to the tangent line when drawn to the point of tangency. 29. If two segments from the same exterior point are tangent to a circle, then they are congruent. 30. A secant is a line that intersects a circle in exactly two points. 31. If two secants or chords intersect in the interior of the circle, then the measure of the angle formed is ½ the sum of the measure of the arcs intercepted by the angle and its vertical angle. 32. If a secant and a tangent intersect at the point of tangency, then the measure of angle formed is ½ the measure of the intercepted arc. 33. If two secants, a tangent and a secant, or two tangents intersect in the exterior of the circle, then the measure of the angle formed is ½ the difference of the measures of the intercepted arcs. 34. If two chords intersect in a circle, then the products of the lengths of the chords are equal. 35. If two secants intersect in the exterior of a circle, then the product of the measure of one secant segment and its external secant segment is equal to the product of the measures of the other secant and its external secant segment. 36. If a tangent and a secant intersect in the exterior of a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external segment. 37. The equation of a circle is derived from the Pythagorean Theorem and is represented by:

19 (x-h) 2 + (y-k) 2 = r 2 where r is the radius of the circle, and h,k are the coordinates of its center

20

Common Core Specifications for Geometry

Common Core Specifications for Geometry 1 Common Core Specifications for Geometry Examples of how to read the red references: Congruence (G-Co) 2-03 indicates this spec is implemented in Unit 3, Lesson 2. IDT_C indicates that this spec is implemented

More information

Geometry. Cluster: Experiment with transformations in the plane. G.CO.1 G.CO.2. Common Core Institute

Geometry. Cluster: Experiment with transformations in the plane. G.CO.1 G.CO.2. Common Core Institute Geometry Cluster: Experiment with transformations in the plane. G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of

More information

Geometry Common Core State Standard (CCSS) Math

Geometry Common Core State Standard (CCSS) Math = ntroduced R=Reinforced/Reviewed HGH SCHOOL GEOMETRY MATH STANDARDS 1 2 3 4 Congruence Experiment with transformations in the plane G.CO.1 Know precise definitions of angle, circle, perpendicular line,

More information

Standards to Topics. Common Core State Standards 2010 Geometry

Standards to Topics. Common Core State Standards 2010 Geometry Standards to Topics G-CO.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance

More information

Unit 1: Tools of Geometry

Unit 1: Tools of Geometry Unit 1: Tools of Geometry Geometry CP Pacing Guide First Nine Weeks Tennessee State Math Standards Know precise definitions of angle, circle, perpendicular line, parallel G.CO.A.1 line, and line segment,

More information

Geometry. Geometry. Domain Cluster Standard. Congruence (G CO)

Geometry. Geometry. Domain Cluster Standard. Congruence (G CO) Domain Cluster Standard 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance

More information

Common Core Cluster. Experiment with transformations in the plane. Unpacking What does this standard mean that a student will know and be able to do?

Common Core Cluster. Experiment with transformations in the plane. Unpacking What does this standard mean that a student will know and be able to do? Congruence G.CO Experiment with transformations in the plane. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

More information

Pearson Mathematics Geometry Common Core 2015

Pearson Mathematics Geometry Common Core 2015 A Correlation of Pearson Mathematics Geometry Common Core 2015 to the Common Core State Standards for Bid Category 13-040-10 A Correlation of Pearson, Common Core Pearson Geometry Congruence G-CO Experiment

More information

, Geometry, Quarter 1

, Geometry, Quarter 1 2017.18, Geometry, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1.

More information

Mathematics Standards for High School Geometry

Mathematics Standards for High School Geometry Mathematics Standards for High School Geometry Geometry is a course required for graduation and course is aligned with the College and Career Ready Standards for Mathematics in High School. Throughout

More information

Geometry Unit Plan !

Geometry Unit Plan ! Geometry Unit Plan 2016-17 Unit 1: Introduction to Geometry & Constructions 10 Instructional Days (July 27-August 10) G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line,

More information

Honors Geometry Pacing Guide Honors Geometry Pacing First Nine Weeks

Honors Geometry Pacing Guide Honors Geometry Pacing First Nine Weeks Unit Topic To recognize points, lines and planes. To be able to recognize and measure segments and angles. To classify angles and name the parts of a degree To recognize collinearity and betweenness of

More information

Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts

Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of

More information

GEOMETRY Curriculum Overview

GEOMETRY Curriculum Overview GEOMETRY Curriculum Overview Semester 1 Semester 2 Unit 1 ( 5 1/2 Weeks) Unit 2 Unit 3 (2 Weeks) Unit 4 (1 1/2 Weeks) Unit 5 (Semester Break Divides Unit) Unit 6 ( 2 Weeks) Unit 7 (7 Weeks) Lines and Angles,

More information

Test #1: Chapters 1, 2, 3 Test #2: Chapters 4, 7, 9 Test #3: Chapters 5, 6, 8 Test #4: Chapters 10, 11, 12

Test #1: Chapters 1, 2, 3 Test #2: Chapters 4, 7, 9 Test #3: Chapters 5, 6, 8 Test #4: Chapters 10, 11, 12 Progress Assessments When the standards in each grouping are taught completely the students should take the assessment. Each assessment should be given within 3 days of completing the assigned chapters.

More information

Geometry. Standards for Mathematical Practice. Correlated to the Common Core State Standards. CCSS Units Lessons

Geometry. Standards for Mathematical Practice. Correlated to the Common Core State Standards. CCSS Units Lessons Geometry Correlated to the Common Core State Standards CCSS Units Lessons Standards for Mathematical Practice MP1 Make sense of problems and persevere in solving them. Parallel and Perpendicular Angles

More information

Unit Activity Correlations to Common Core State Standards. Geometry. Table of Contents. Geometry 1 Statistics and Probability 8

Unit Activity Correlations to Common Core State Standards. Geometry. Table of Contents. Geometry 1 Statistics and Probability 8 Unit Activity Correlations to Common Core State Standards Geometry Table of Contents Geometry 1 Statistics and Probability 8 Geometry Experiment with transformations in the plane 1. Know precise definitions

More information

Ohio s Learning Standards-Extended. Mathematics. Congruence Standards Complexity a Complexity b Complexity c

Ohio s Learning Standards-Extended. Mathematics. Congruence Standards Complexity a Complexity b Complexity c Ohio s Learning Standards-Extended Mathematics Congruence Standards Complexity a Complexity b Complexity c Most Complex Least Complex Experiment with transformations in the plane G.CO.1 Know precise definitions

More information

Geometry/Pre AP Geometry Common Core Standards

Geometry/Pre AP Geometry Common Core Standards 1st Nine Weeks Transformations Transformations *Rotations *Dilation (of figures and lines) *Translation *Flip G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle,

More information

Mathematics High School Geometry

Mathematics High School Geometry Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of

More information

Appendix. Correlation to the High School Geometry Standards of the Common Core State Standards for Mathematics

Appendix. Correlation to the High School Geometry Standards of the Common Core State Standards for Mathematics Appendix Correlation to the High School Geometry Standards of the Common Core State Standards for Mathematics The correlation shows how the activities in Exploring Geometry with The Geometer s Sketchpad

More information

Correlation of Discovering Geometry 5th Edition to Florida State Standards

Correlation of Discovering Geometry 5th Edition to Florida State Standards Correlation of 5th Edition to Florida State s MAFS content is listed under three headings: Introduced (I), Developed (D), and Applied (A). Developed standards are the focus of the lesson, and are being

More information

Geometry Geometry Grade Grade Grade

Geometry Geometry Grade Grade Grade Grade Grade Grade 6.G.1 Find the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the

More information

Madison County Schools Suggested Geometry Pacing Guide,

Madison County Schools Suggested Geometry Pacing Guide, Madison County Schools Suggested Geometry Pacing Guide, 2016 2017 Domain Abbreviation Congruence G-CO Similarity, Right Triangles, and Trigonometry G-SRT Modeling with Geometry *G-MG Geometric Measurement

More information

The School District of Palm Beach County GEOMETRY HONORS Unit A: Essentials of Geometry

The School District of Palm Beach County GEOMETRY HONORS Unit A: Essentials of Geometry MAFS.912.G-CO.1.1 MAFS.912.G-CO.4.12 MAFS.912.G-GPE.2.7 MAFS.912.G-MG.1.1 Unit A: Essentials of Mathematics Florida Know precise definitions of angle, circle, perpendicular line, parallel line, and line

More information

GEOMETRY CURRICULUM MAP

GEOMETRY CURRICULUM MAP 2017-2018 MATHEMATICS GEOMETRY CURRICULUM MAP Department of Curriculum and Instruction RCCSD Congruence Understand congruence in terms of rigid motions Prove geometric theorems Common Core Major Emphasis

More information

The School District of Palm Beach County GEOMETRY HONORS Unit A: Essentials of Geometry

The School District of Palm Beach County GEOMETRY HONORS Unit A: Essentials of Geometry Unit A: Essentials of G CO Congruence G GPE Expressing Geometric Properties with Equations G MG Modeling G GMD Measurement & Dimension MAFS.912.G CO.1.1 MAFS.912.G CO.4.12 MAFS.912.G GPE.2.7 MAFS.912.G

More information

Russell County Pacing Guide

Russell County Pacing Guide August Experiment with transformations in the plane. 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance

More information

Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry

Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry Standards for Mathematical Practice SMP.1 Make sense of problems and persevere

More information

Make geometric constructions. (Formalize and explain processes)

Make geometric constructions. (Formalize and explain processes) Standard 5: Geometry Pre-Algebra Plus Algebra Geometry Algebra II Fourth Course Benchmark 1 - Benchmark 1 - Benchmark 1 - Part 3 Draw construct, and describe geometrical figures and describe the relationships

More information

PASS. 5.2.b Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

PASS. 5.2.b Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry. Geometry Name Oklahoma cademic tandards for Oklahoma P PRCC odel Content Frameworks Current ajor Curriculum Topics G.CO.01 Experiment with transformations in the plane. Know precise definitions of angle,

More information

3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ).

3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ). Geometry Kindergarten Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1 Describe objects in the environment using names of shapes,

More information

Sequence of Geometry Modules Aligned with the Standards

Sequence of Geometry Modules Aligned with the Standards Sequence of Geometry Modules Aligned with the Standards Module 1: Congruence, Proof, and Constructions Module 2: Similarity, Proof, and Trigonometry Module 3: Extending to Three Dimensions Module 4: Connecting

More information

Common Core State Standards for Mathematics High School

Common Core State Standards for Mathematics High School Using the Program for Success Common Core State Standards for Mathematics High School The following shows the High School Standards for Mathematical Content that are taught in Pearson Common Core Edition

More information

Test Blueprint Dysart Math Geometry #2 Comp. AZ-HS.G-CO CONGRUENCE. 27.9% on Test. # on AP. # on Test. % on Test

Test Blueprint Dysart Math Geometry #2 Comp. AZ-HS.G-CO CONGRUENCE. 27.9% on Test. # on AP. # on Test. % on Test Blueprint AZ-HS.G-CO CONGRUENCE Page 1 27.9 AZ-HS.G-CO.A.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line,

More information

Geometry GEOMETRY. Congruence

Geometry GEOMETRY. Congruence Geometry Geometry builds on Algebra I concepts and increases students knowledge of shapes and their properties through geometry-based applications, many of which are observable in aspects of everyday life.

More information

Grade 9, 10 or 11- Geometry

Grade 9, 10 or 11- Geometry Grade 9, 10 or 11- Geometry Strands 1. Congruence, Proof, and Constructions 2. Similarity, Proof, and Trigonometry 3. Extending to Three Dimensions 4. Connecting Algebra and Geometry through Coordinates

More information

Curriculum Scope & Sequence

Curriculum Scope & Sequence BOE APPROVED 3/27/12 REVISED 9/25/12 Curriculum Scope & Sequence Subject/Grade Level: MATHEMATICS/HIGH SCHOOL Course: GEOMETRY CP/HONORS *The goals and standards addressed are the same for both levels

More information

GEOMETRY CCR MATH STANDARDS

GEOMETRY CCR MATH STANDARDS CONGRUENCE, PROOF, AND CONSTRUCTIONS M.GHS. M.GHS. M.GHS. GEOMETRY CCR MATH STANDARDS Mathematical Habits of Mind. Make sense of problems and persevere in solving them.. Use appropriate tools strategically..

More information

YEAR AT A GLANCE Student Learning Outcomes by Marking Period

YEAR AT A GLANCE Student Learning Outcomes by Marking Period 2014-2015 Term 1 Overarching/general themes: Tools to Build and Analyze Points, Lines and Angles Dates Textual References To Demonstrate Proficiency by the End of the Term Students Will : Marking Period

More information

Geometry. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Geometry. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Common Core State for Mathematics High School Following is a correlation of Pearson s Prentice Hall Common Core Geometry 2012 to Common Core State for High School Mathematics. Geometry Congruence G-CO

More information

Jefferson County High School Course Syllabus

Jefferson County High School Course Syllabus Jefferson County High School Course Syllabus A. Course: Geometry B. Department: Mathematics C. Course Description: This course includes the state-required basic elements of plane and solid geometry, coordinate

More information

Mathematics Geometry

Mathematics Geometry Common Core Correlations Mathematics Geometry Please note the following abbreviations found in this document: A=Activity L=Lesson AP=Activity Practice EA=Embedded Assessment GR=Getting Ready BENCHMARK

More information

Geometry I Can Statements I can describe the undefined terms: point, line, and distance along a line in a plane I can describe the undefined terms:

Geometry I Can Statements I can describe the undefined terms: point, line, and distance along a line in a plane I can describe the undefined terms: Geometry I Can Statements I can describe the undefined terms: point, line, and distance along a line in a plane I can describe the undefined terms: point, line, and distance along a line in a plane I can

More information

Geometry SEMESTER 1 SEMESTER 2

Geometry SEMESTER 1 SEMESTER 2 SEMESTER 1 Geometry 1. Geometry Basics 2. Coordinate Geometry a) Transformations, e.g., T(x + a, y + b) 3. Angles 4. Triangles a) Circumcenter 5. Construction a) Copy a segment, angle b) Bisect a segment,

More information

GEOMETRY. Changes to the original 2010 COS is in red. If it is red and crossed out, it has been moved to another course.

GEOMETRY. Changes to the original 2010 COS is in red. If it is red and crossed out, it has been moved to another course. The Geometry course builds on Algebra I concepts and increases students knowledge of shapes and their properties through geometry-based applications, many of which are observable in aspects of everyday

More information

Pearson Geometry Common Core 2015

Pearson Geometry Common Core 2015 A Correlation of Geometry Common Core to the Common Core State Standards for Mathematics High School , Introduction This document demonstrates how meets the Mathematics High School, PARRC Model Content

More information

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G- CO.1 Identify Definitions Standard 1 Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, or line segment, based on the undefined

More information

Beal City High School Geometry Curriculum and Alignment

Beal City High School Geometry Curriculum and Alignment Beal City High School Geometry Curriculum and Alignment UNIT 1 Geometry Basics (Chapter 1) 1. Points, lines and planes (1-1, 1-2) 2. Axioms (postulates), theorems, definitions (Ch 1) 3. Angles (1-3) 4.

More information

State Standards. State Standards

State Standards. State Standards State s State s Basics of Geometry One MAFS.912.G CO.1.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line,

More information

Carnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations

Carnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations Carnegie Learning High School Math Series: Logic and Proofs G.LP.1 Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates,

More information

2003/2010 ACOS MATHEMATICS CONTENT CORRELATION GEOMETRY 2003 ACOS 2010 ACOS

2003/2010 ACOS MATHEMATICS CONTENT CORRELATION GEOMETRY 2003 ACOS 2010 ACOS CURRENT ALABAMA CONTENT PLACEMENT G.1 Determine the equation of a line parallel or perpendicular to a second line through a given point. G.2 Justify theorems related to pairs of angles, including angles

More information

ACCRS/QUALITY CORE CORRELATION DOCUMENT: GEOMETRY

ACCRS/QUALITY CORE CORRELATION DOCUMENT: GEOMETRY ACCRS/QUALITY CORE CORRELATION DOCUMENT: GEOMETRY 2010 ACOS GEOMETRY QUALITYCORE COURSE STANDARD Experiment with transformations in the plane. 1. [G-CO1] Know precise definitions of angle, circle, perpendicular

More information

NAEP Released Items Aligned to the Iowa Core: Geometry

NAEP Released Items Aligned to the Iowa Core: Geometry NAEP Released Items Aligned to the Iowa Core: Geometry Congruence G-CO Experiment with transformations in the plane 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and

More information

Agile Mind Geometry Scope and Sequence, Common Core State Standards for Mathematics

Agile Mind Geometry Scope and Sequence, Common Core State Standards for Mathematics Students began their study of geometric concepts in middle school mathematics. They studied area, surface area, and volume and informally investigated lines, angles, and triangles. Students in middle school

More information

Agile Mind CCSS Geometry Scope & Sequence

Agile Mind CCSS Geometry Scope & Sequence Geometric structure 1: Using inductive reasoning and conjectures 2: Rigid transformations 3: Transformations and coordinate geometry 8 blocks G-CO.01 (Know precise definitions of angle, circle, perpendicular

More information

Ref: GIS Math G 9 C.D

Ref: GIS Math G 9 C.D Ref: GIS Math G 9 C.D. 2015-2016 2011-2012 SUBJECT : Math TITLE OF COURSE : Geometry GRADE LEVEL : 9 DURATION : ONE YEAR NUMBER OF CREDITS : 1.25 Goals: Congruence G-CO Experiment with transformations

More information

MADISON ACADEMY GEOMETRY PACING GUIDE

MADISON ACADEMY GEOMETRY PACING GUIDE MADISON ACADEMY GEOMETRY PACING GUIDE 2018-2019 Standards (ACT included) ALCOS#1 Know the precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined

More information

YEC Geometry Scope and Sequence Pacing Guide

YEC Geometry Scope and Sequence Pacing Guide YEC Scope and Sequence Pacing Guide Quarter 1st 2nd 3rd 4th Units 1 2 3 4 5 6 7 8 G.CO.1 G.CO.2 G.CO.6 G.CO.9 G.CO.3 G.CO.7 G.CO.10 G.CO.4 G.CO.8 G.CO.11 Congruence G.CO.5 G.CO.12 G.CO.13 Similarity, Right

More information

Guide Assessment Structure Geometry

Guide Assessment Structure Geometry Guide Assessment Structure Geometry The Common Core State Standards for Mathematics are organized into Content Standards which define what students should understand and be able to do. Related standards

More information

Milford Public Schools Curriculum. Department: Mathematics Course Name: Geometry Level 3. UNIT 1 Unit Title: Coordinate Algebra and Geometry

Milford Public Schools Curriculum. Department: Mathematics Course Name: Geometry Level 3. UNIT 1 Unit Title: Coordinate Algebra and Geometry Milford Public Schools Curriculum Department: Mathematics Course Name: Geometry Level 3 UNIT 1 Unit Title: Coordinate Algebra and Geometry The correspondence between numerical coordinates and geometric

More information

Grade 8 PI+ Yearlong Mathematics Map

Grade 8 PI+ Yearlong Mathematics Map Grade 8 PI+ Yearlong Mathematics Map Resources: Approved from Board of Education Assessments: PARCC Assessments, Performance Series, District Benchmark Assessment Common Core State Standards Standards

More information

Ganado Unified School District Geometry

Ganado Unified School District Geometry Ganado Unified School District Geometry PACING Guide SY 2016-2017 Timeline & Resources 1st Quarter Unit 1 AZ & ELA Standards Essential Question Learning Goal Vocabulary CC.9-12.G.CO. Transformations and

More information

HS Geometry Mathematics CC

HS Geometry Mathematics CC Course Description This course involves the integration of logical reasoning and spatial visualization skills. It includes a study of deductive proofs and applications from Algebra, an intense study of

More information

District 200 Geometry (I, A) Common Core Curriculum

District 200 Geometry (I, A) Common Core Curriculum Length: Two Semesters Prerequisite: Algebra 1 or equivalent District 200 Geometry (I, A) Common Core Curriculum How to read this document: CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems.

More information

Geometry Assessment Structure for Mathematics:

Geometry Assessment Structure for Mathematics: Geometry Assessment Structure for 2013-2014 Mathematics: The Common Core State Standards for Mathematics are organized into Content Standards which define what students should understand and be able to

More information

Monroe County Schools Geometry

Monroe County Schools Geometry Overview Content Standard Domains and Clusters Congruence [G-CO] Experiment with transformations in the plane. Understand congruence in terms of rigid motions. Prove geometric theorems. Make geometric

More information

Pre-AP Geometry Year-at-a-Glance Year-at-a-Glance

Pre-AP Geometry Year-at-a-Glance Year-at-a-Glance Pre-AP Geometry Year-at-a-Glance 2018-2019 Year-at-a-Glance FIRST SEMESTER SECOND SEMESTER Unit 1 Foundations of Geometry Unit 2 Equations of Lines, Angle-Pairs, Triangles Unit 3 Right Triangles, Polygons,

More information

Standards to Topics. Louisiana Student Standards for Mathematics Geometry

Standards to Topics. Louisiana Student Standards for Mathematics Geometry Standards to Topics GM.G-CO.A.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and

More information

Geometry Year at a Glance

Geometry Year at a Glance Geometry Year at a Glance Name of Unit Learning Goals Knowledge & Skills Unit 1: Congruence, Proofs, and Constructions (45 days) Unit 2: Similarity, Proof, and Trigonometry Unit 3: Extending to Three Dimensions

More information

Honors Geometry Year at a Glance

Honors Geometry Year at a Glance Honors Geometry Year at a Glance Name of Unit Learning Goals Knowledge & Skills Unit 1: Congruence, Proofs, and Constructions Unit 2: Similarity, Proof, and Trigonometry Unit 3: Extending to Three Dimensions

More information

GEOMETRY Graded Course of Study

GEOMETRY Graded Course of Study GEOMETRY Graded Course of Study Conceptual Category: Domain: Congruence Experiment with transformations in the plane. Understand congruence in terms of rigid motions. Prove geometric theorems both formally

More information

Sequenced Units for Arizona s College and Career Ready Standards MA32 Honors Geometry

Sequenced Units for Arizona s College and Career Ready Standards MA32 Honors Geometry Sequenced Units for Arizona s College and Career Ready Standards MA32 Honors Geometry Year at a Glance Semester 1 Semester 2 Unit 1: Basics of Geometry (12 days) Unit 2: Reasoning and Proofs (13 days)

More information

Postulates, Theorems, and Corollaries. Chapter 1

Postulates, Theorems, and Corollaries. Chapter 1 Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a

More information

West Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12

West Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12 West Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12 Unit 1: Basics of Geometry Content Area: Mathematics Course & Grade Level: Basic Geometry, 9 12 Summary and Rationale This unit

More information

Geometry. Geometry. No Louisiana Connectors written for this standard.

Geometry. Geometry. No Louisiana Connectors written for this standard. GM: G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a

More information

Common Core Standards Curriculum Map - Geometry Quarter One. Unit One - Geometric Foundations, Constructions and Relationships (24 days/12 blocks)

Common Core Standards Curriculum Map - Geometry Quarter One. Unit One - Geometric Foundations, Constructions and Relationships (24 days/12 blocks) Common Core Standards Curriculum Map - Geometry Quarter One Unit One - Geometric Foundations, Constructions and Relationships (24 days/12 blocks) Experiment with transformations in the plane. G.CO.1. Know

More information

Pearson Mathematics Geometry

Pearson Mathematics Geometry A Correlation of Pearson Mathematics Geometry Indiana 2017 To the INDIANA ACADEMIC STANDARDS Mathematics (2014) Geometry The following shows where all of the standards that are part of the Indiana Mathematics

More information

Power Standards Cover Page for the Curriculum Guides. Geometry

Power Standards Cover Page for the Curriculum Guides. Geometry Power Standards Cover Page for the Curriculum Guides Geometry Quarter 1 G.CO.B.6 G.CO.C.9 G.GPE.B.3 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given

More information

KCAS or Common Core Standards

KCAS or Common Core Standards Unit Title Tools of Geometry Length of Unit 4 Essential Questions/Learning Targets/Student Objectives 1-1 Make Nets & Drawings of 3-D Figures 1-2 Understand Basic Terms & Postulates 1-3 Find & Compare

More information

Achieve Recommended Pathway: Geometry

Achieve Recommended Pathway: Geometry Units Unit 1 Congruence, Proof, and Constructions Unit 2 Similarity, Proof, and Trigonometry Unit 3 Extending to Three Dimensions Unit 4 Connecting Algebra and Geometry through Coordinates Unit 5 Circles

More information

Videos, Constructions, Definitions, Postulates, Theorems, and Properties

Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording

More information

Geometry Critical Areas of Focus

Geometry Critical Areas of Focus Ohio s Learning Standards for Mathematics include descriptions of the Conceptual Categories. These descriptions have been used to develop critical areas for each of the courses in both the Traditional

More information

K-12 Geometry Standards

K-12 Geometry Standards Geometry K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1. Describe objects in the environment using names of shapes, and describe

More information

Mathematics Pacing Guide Alignment with Common Core Standards. Essential Questions What is congruence?

Mathematics Pacing Guide Alignment with Common Core Standards. Essential Questions What is congruence? Time Frame: 6 Weeks September/October Unit 1: Congruence Mathematics Pacing Guide Alignment with Standards Experiment with Transformations in the plane. G.CO.1 Know precise definitions of angle, circle,

More information

Geometry Poudre School District Pacing Overview Semester One

Geometry Poudre School District Pacing Overview Semester One Geometry Pacing Overview Semester One Chapter 1: Basics of Geometry and Chapter 2: Reasoning and Proofs 9-10 days HS.G.CO.A.1, H.G.CO.C.9, HS.G.CO.C.10, HS.G.CO.C.11, HS.G.CO.D.12, HS.G.SRT.B.4, HS.G.GPE.B.7,

More information

Geometry. Geometry Higher Mathematics Courses 69

Geometry. Geometry Higher Mathematics Courses 69 Geometry The fundamental purpose of the Geometry course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of

More information

Manhattan Center for Science and Math High School Mathematics Department Curriculum

Manhattan Center for Science and Math High School Mathematics Department Curriculum Content/Discipline Geometry, Term 2 http://mcsmportal.net Marking Period 1 Topic and Essential Question Manhattan Center for Science and Math High School Mathematics Department Curriculum Unit 7 - (1)

More information

Achievement Level Descriptors Geometry

Achievement Level Descriptors Geometry Achievement Level Descriptors Geometry ALD Stard Level 2 Level 3 Level 4 Level 5 Policy MAFS Students at this level demonstrate a below satisfactory level of success with the challenging Students at this

More information

Ohio s Learning Standards Mathematics Scope and Sequence YEC Geometry

Ohio s Learning Standards Mathematics Scope and Sequence YEC Geometry Youngstown City School District English Language Arts Scope and Sequence Grade K Ohio s Learning Standards Mathematics Scope and Sequence YEC Geometry Mathematics Standards Scope and Sequence, YEC Geometry

More information

Mathematics - High School Geometry

Mathematics - High School Geometry Mathematics - High School Geometry All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in this course will explore

More information

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ACCELERATED GEOMETRY (June 2014)

WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ACCELERATED GEOMETRY (June 2014) UNIT: Chapter 1 Essentials of Geometry UNIT : How do we describe and measure geometric figures? Identify Points, Lines, and Planes (1.1) How do you name geometric figures? Undefined Terms Point Line Plane

More information

MATHEMATICS COURSE SYLLABUS

MATHEMATICS COURSE SYLLABUS MATHEMATICS COURSE SYLLABUS Course Title: TAG II: Transition from Algebra to Geometry Department: Mathematics Primary Course Materials: Big Ideas Math Geometry Book Authors: Ron Larson & Laurie Boswell

More information

G.CO.2 G.CO.3 G.CO.4 G.CO.5 G.CO.6

G.CO.2 G.CO.3 G.CO.4 G.CO.5 G.CO.6 Standard G.CO.1 G.CO.2 G.CO.3 G.CO.4 G.CO.5 G.CO.6 Jackson County Core Curriculum Collaborative (JC4) Geometry Learning Targets in Student Friendly Language I can define the following terms precisely in

More information

Other Materials/Projects

Other Materials/Projects GEOMETRY PACING GUIDE: 1st Nine Weeks UNIT 1: Transformations and Congruence Week Module Standards Learning Target WEEK ONE Goals Expectations Pre-Assessment Proportional Relationships Other Materials/Projects

More information

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Geometry

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Geometry Georgia Standards of Excellence Curriculum Map Mathematics GSE Geometry These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Standards

More information

Course: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days

Course: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days Geometry Curriculum Chambersburg Area School District Course Map Timeline 2016 Units *Note: unit numbers are for reference only and do not indicate the order in which concepts need to be taught Suggested

More information

Geometry Curriculum Map

Geometry Curriculum Map Geometry Curriculum Map Unit 1 st Quarter Content/Vocabulary Assessment AZ Standards Addressed Essentials of Geometry 1. What are points, lines, and planes? 1. Identify Points, Lines, and Planes 1. Observation

More information

MANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM

MANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM COORDINATE Geometry Plotting points on the coordinate plane. Using the Distance Formula: Investigate, and apply the Pythagorean Theorem as it relates to the distance formula. (G.GPE.7, 8.G.B.7, 8.G.B.8)

More information

Course: Geometry PAP Prosper ISD Course Map Grade Level: Estimated Time Frame 6-7 Block Days. Unit Title

Course: Geometry PAP Prosper ISD Course Map Grade Level: Estimated Time Frame 6-7 Block Days. Unit Title Unit Title Unit 1: Geometric Structure Estimated Time Frame 6-7 Block 1 st 9 weeks Description of What Students will Focus on on the terms and statements that are the basis for geometry. able to use terms

More information