· Web view1 Unit 1-Basics of Geometry G.CO.1 I can identify the undefined notions used in...

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12

1Unit 1-

Basics of Geometry

G.CO.1 I can identify the undefined notions used in geometry (point, line, plane, distance) and describe their characteristics.

2Unit 1-

Basics of Geometry

G.CO.1 I can identify angles, circles, perpendicular lines, parallel lines, rays, and line segments.

3Unit 1-

Basics of Geometry

G.CO.1 I can identify angles, circles, perpendicular lines, parallel lines, rays, and line segments.

4Unit 1-

Basics of Geometry

G.CO.1 I can define angles, circles, perpendicular lines, parallel lines, rays, and lines segments precisely using the undefined terms and “if-then” and “iff” statements.

5Unit 1-

Basics of Geometry

G.CO.1 I can define angles, circles, perpendicular lines, parallel lines, rays, and lines segments precisely using the undefined terms and “if-then” and “iff” statements.

Quiz6

Unit 1-

Distance and Midpoint

G.GPE.4I can use the distance and midpoint formulas to prove congruence.

7Unit 1-

Distance and Midpoint

G.GPE.4I can use the distance and midpoint formulas to prove congruence.

Quiz

8Unit 1-

Transformations

G.CO.2I can draw transformations of reflections, rotations, translations, and combinations of these using graph paper, transparencies, and/or geometry software.

9Unit 1-

Transformations

G.CO.2I can draw transformations of reflections, rotations, translations, and combinations of these using graph paper, transparencies, and/or geometry software.

10Unit 1-

Transformations

G.CO.2-I can determine the coordinates for the image of a figure when a transformation rule is applied to the preimage.

-I can distinguish between transformations that are rigid and those that are not.

11Unit 1-

Transformations

G.CO.2

12Unit 1-

Transformations

G.CO.3

13Unit 1-

Transformations

G.CO.3

14Unit 1-

Transformations

G.CO.4

15Unit 1-

Transformations

G.CO.4


-I can determine the coordinates for the image of a figure when a transformation rule is applied to the preimage.

-I can distinguish between transformations that are rigid and those that are not.

-I can describe and illustrate how a figure is mapped onto itself using transformations.

-I can calculate the number of lines of reflection symmetry and the degree of rotational symmetry of any regular polygon.

-I can describe and illustrate how a figure is mapped onto itself using transformations.

-I can calculate the number of lines of reflection symmetry and the degree of rotational symmetry of any regular polygon.

Quiz

I can construct the reflection definition by connecting any point on the preimage to its corresponding point on the reflected image and describing the line segment’s relationship to the line of reflection

I can construct the translation definition by connecting any point on the preimage to its corresponding point on the translated image, and connecting a second point on the preimage to its corresponding point on the translated image, and describing how the two segments are equal in length, point the same direction, and are parallel.

16Unit 1-

Transformations

G.CO.4I can construct the rotation definition by connecting the center of rotation to any point on the preimage and to its corresponding point on the rotated image, and describing the measure of the angle formed and the equal measures of the segments that formed the angle as part of the definition.

17Flex day use for remediation and differentiation.

18Mid Term Test

19Unit 1-

Transformations

G.CO.5-I can draw specific transformations.

-I can predict and verify the sequence of transformations that will map a figure onto another.

20Unit 1-

Transformations

G.CO.5-I can draw specific transformations.

-I can predict and verify the sequence of transformations that will map a figure onto another.

21Unit 1-

Transformations

G.CO.6I can define rigid motions as

22Unit 1-

Transformations

G.CO.6I can define congruent

23Unit 1-

Transformations

G.CO.6I can determine if two figures

24Unit 1-

Proofs

G.CO.9I can correctly interpret

25Unit 1-

Proofs

G.CO.9I can order statements based


reflections, rotations, translations, and combinations of these, all preserving distance and angle measure.

figures as figures that have the same size and shape and state that a composition of rigid motions will map one congruent figure onto another.

are congruent by verifying if a series of rigid motions will map one figure onto another

Quiz

geometric diagrams by identifying what can and cannot be assumed.

on the Law of Syllogism when constructing my proof.

26Unit 1-

Proofs

G.CO.9I can identify and use the properties of congruence and equality (reflexive, symmetric, transitive) in my proofs.

27Unit 1-

Proofs

G.CO.9I can use theorems, postulates, or definitions to prove theorems about lines, and angles, including:*Vertical angles are congruent*a transversal with parallel lines creates congruent and supplementary angles.*points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoint.

28Unit 1-

Proofs


29Unit 1-

Proofs


Quiz

30Unit 1-

Constructions

G.CO.12I can identify the tools used in formal constructions.I can use tools and methods to precisely copy a segment, copy an angle, bisect a segment, bisect and angle, construct perpendicular lines and bisectors, and construct a line parallel to a given line through a point not on the line.


31Unit 1-

Constructions

G.CO.12I can identify the tools used in formal constructions.I can use tools and methods to precisely copy a segment, copy an angle, bisect a segment, bisect and angle, construct perpendicular lines and bisectors, and construct a line parallel to a given line through a point not on the line.

32Unit 1-

Constructions

G.CO.12I can informally perform the constructions listed above using string, reflective devices, paper folding, and/or geometric software.



35UNIT TEST


36Unit 2-

Triangles

G.CO.7I can define and classify a triangle.I can identify corresponding sides and corresponding angles of congruent triangles.

37Unit 2-

Triangles

G.CO.7I can define and classify a triangle.I can identify corresponding sides and corresponding angles of congruent triangles.

38Unit 2-

Triangles/Congruence

G.CO.7I can identify corresponding sides and corresponding angles of congruent triangles.

39Unit 2-

Triangles/Congruence

G.CO.7I can demonstrate that when distance is preserved and angle measure is preserved the triangles must also be congruent.

40FLEX DAY USED FOR REMEDIATION AND DIFFERENTIATION

Quiz

41Unit 2-

Triangles

G.CO.8I can define rigid motions as reflections, rotations, translations, and combinations of these, all of which preserve distance and angle measure.

42Unit 2-

Triangles

G.CO.8I can list the sufficient conditions to prove triangles are congruent.

43Unit 2-

Triangles

G.CO.8I can map a triangle with one of the sufficient conditions onto the original triangle and show that corresponding sides and angles are congruent.

44Unit 2-

Triangles

G.CO.8I can map a triangle with one of the sufficient conditions onto the original triangle and show that corresponding sides and corresponding angles are congruent.


Quiz

46Unit 2-

Proofs

47Unit 2-

Proofs

48Unit 2-

Proofs

49Unit 2-

Dilations

50Unit 2-

Dilations

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 G.CO.10I can prove the following theorems about triangles:*Interior angles of a triangle sum to 180*Base angles of isosceles triangles are congruent*Segment joining midpoints of two sides of a triangle is parallel to the third side and ½ its length.*The medians of a triangle meet at one point.

G.CO.10I can prove the following theorems about triangles:*Interior angles of a triangle sum to 180*Base angles of isosceles triangles are congruent*Segment joining midpoints of two sides of a triangle is parallel to the third side and ½ its length.*The medians of a triangle meet at one point.

G.CO.10I can prove the following theorems about triangles:*Interior angles of a triangle sum to 180*Base angles of isosceles triangles are congruent*Segment joining midpoints of two sides of a triangle is parallel to the third side and ½ its length.*The medians of a triangle meet at one point.

Quiz

G.SRT.1I can define dilation.I can perform a dilation with a given center and scale factor on a figure in the coordinate system.

G.SRT.1I can verify that when a side passes through the center of dilation, the side and its image lie on the same line.I can verify that corresponding side of the preimage and images are parallel.

51Unit 2-

Dilations

G.SRT.1I can verify that a side length of the image is equal to the scale factor multiplied by the corresponding side length of the preimage.


Quiz

53Unit 2-

Similarity

G.SRT.2I can define similarity as a composition of rigid motions followed by dilations in which angle measure is preserved and side length is proportional.

54Unit 2-

Similarity

G.SRT.2I can identify corresponding sides and corresponding angles of similar triangles.I can demonstrate that in a pair of similar triangles, corresponding angles are congruent and sides are proportional.

55Unit 2-

Similarity

G.SRT.2I can determine that two figure are similar by verifying that angle measure is preserved and corresponding sides are proportional.

56Unit 2-

Similarity

57Unit 2-

Similarity

58Unit 2-

Similarity

59Unit 2-

Proofs

60Unit 2-

Proofs

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 G.SRT.2I can determine that two figure are similar by verifying that angle measure is preserved and corresponding sides are proportional.

Quiz

G.SRT.3I can show and explain that when two angle measures are known the third angle measure is also known.

G.SRT.3I can conclude and explain that AA similarity is a sufficient condition for two triangles to be similar.

G.SRT.4I can prove the following:

A line parallel to one side of a triangle divides the other two proportionally.

The Pythagorean Theorem proved using triangle similarity.

G.SRT.4I can prove the following:

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

The Pythagorean Theorem proved using triangle similarity.

61Unit 2-

Congruence/Similarity

G.SRT.5I can use triangle congruence and triangle similarity to prove relationships in geometric figures.

62Unit 2-

Congruence/Similarity

G.SRT.5I can use triangle congruence and triangle similarity to prove relationships in geometric figures.

63Mid Term Exam

64Unit 2-

Trigonometry

G.SRT.6I can demonstrate that within a right triangle, line segments parallel to a leg create similar triangles by AA similarity.

65Unit 2-

Trigonometry

G.SRT.6I can use characteristics of similar figures to justify the trig. ratios.I can define the trig ratios for acute angles in a right triangle.

66Unit 2-

Trigonometry

G.SRT.6I can use division and the Pythagorean Theorem to prove that sin2 + cos2 = 1

67Unit 2-

Trigonometry

G.SRT.7I can define complementary angles.I can calculate sine and cosine ratios for acute angles in a right triangle when given two side lengths.

68Unit 2-

Trigonometry

G.SRT.7I can define complementary angles.I can calculate sine and cosine ratios for acute angles in a right triangle when given two side lengths.

69Unit 2-

Trigonometry

G.SRT.7I can use a diagram of a right triangle to explain that for a pair of complementary angles A and B, the sine of A is equal to the cosine of B and vice versa.

70Unit 2-

Trigonometry

G.SRT.8I can use angle measures to estimate side lengths.

71 72 73 74 75

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 Unit 2-

Trigonometry

G.SRT.8I can use side lengths to estimate angle measures.

Quiz

Unit 2-

Trigonometry

G.SRT.8I can solve right triangles by finding the measures of all sides and all angles.I can use sine, cosine, tangent, and their inverses to solve for the unknown side lengths and angle measures of a right triangle.I can use the Pythagorean theorem to solve for an unknown side length of a right triangle.

Unit 2-

Trigonometry

G.SRT.8I can draw right triangles that describe real world problems and label the sides and angles with their given measures.I can solve application problems involving right triangles. Including angle of elevation and depression, navigation, and surveying.

Unit 2-

Trigonometry

G.SRT.8I can draw right triangles that describe real world problems and label the sides and angles with their given measures.I can solve application problems involving right triangles. Including angle of elevation and depression, navigation, and surveying.

Unit 2-

Segment Partitioning

G.GPE.6I can calculate the point(s) on a directed line segment whose endpoints are (x1,y1) and (x2,y2) that partitions the segment into a given ration, r1 to r2 using a formula.

76Unit 2-

Segment Partitioning

G.GPE.6I can calculate the point(s) on a directed line segment whose endpoints are (x1,y1) and (x2,y2) that partitions the segment into a given ration, r1 to r2 using a formula.



79Exam

80Exam


91Unit 3-

Polygons

I can define and identify polygons.I can classify quadrilaterals.

92Unit 3-

Polygons

I can define and identify polygons.I can classify quadrilaterals.

93Unit 3-

Quadrilaterals

G.CO.11I can prove the following theorems.

Opposite sides of a parallelogram are congruent

Opposite angles of a parallelogram are congruent

I can use properties of quadrilaterals to solve.

94Unit 3-

Quadrilaterals


Opposite sides of a parallelogram are congruent

Opposite angles of a parallelogram are congruent


95Unit 3-

Quadrilaterals


Diagonals of a parallelogram bisect each other

Rectangles are parallelograms with congruent diagonals.


96Unit 3-

Quadrilaterals


Diagonals of a parallelogram bisect each other

Rectangles are parallelograms with congruent diagonals.

I can use properties of quadrilaterals to

97Unit 3-

Parallel and Perpendicular

G.GPE.5-I can determine if lines are parallel using their slopes.

-I can determine if lines are perpendicular using their slopes.

Quiz

98Unit 3-


G.GPE.5I can write an equation of a parallel line through a specific point.

99Unit 3-


G.GPE.5I can write an equation of a perpendicular line through a specific point.

Quiz

100Unit 3-

Classifying Quadrilaterals

G.GPE.4I can represent the vertices of a figure in the coordinate plane using variables.I can use coordinates to prove or disprove a claim about a figure.*slope to determine parallel or perpendicular*distance for congruence*midpoint for bisectors


solve.101

Unit 3-

Classifying Quadrilaterals

G.GPE.4I can represent the vertices of a figure in the coordinate plane using variables.I can use coordinates to prove or disprove a claim about a figure.*slope to determine parallel or perpendicular*distance for congruence*midpoint for bisectors

Quiz

102Unit 3-

Perimeter and Area

G.GPE.7I can use the coordinates of the vertices of a polygon graphed in the coordinate plane and use the distance formula to compute the perimeter.I can use coordinates of the vertices of triangles and rectangles graphed in the coordinate plane to compute area.

103Unit 3-

Volume

G.GMD.1I can define Pi as the ratio of a circle’s circumference to its diameter.I can use algebra to demonstrate that circumference = pi * dI can find the area of a circle.

104Unit 3-

Volume

G.GMD.1I can break a regular polygon into triangles to find its area.I can use the Area formula for a regular polygonI can explain that as a polygon increases its number of sides it approaches the area of a circle.

Quiz

105Unit 3-

Volume

G.GMD.1I can identify the base for prisms, cylinders, pyramids, and cones.I can calculate the area of the base for prisms, cylinders, pyramids, and cones.

106Unit 3-

Volume

G.GMD.1I can develop the formula for the volume of a prism and cylinder. I can compare the two formulas and defend that they are the same.

107Unit 3-

Volume

G.GMD.1I can explain and use the property that a pyramid and cone are 1/3 the volume of a prism and cylinder.I can compare the two formulas and defend that they are the same.

108Unit 3-

Volume

G.GMD.2I can state that if two solid figures have the same total height and their cross-sectional areas are identical at every level, the figures have the same volume.I can use a deck of cards to demonstrate.

109Unit 3-

Volume

G.GMD.2I can find cross sectional area using Pythagorean theorem and area formulas.

110Unit 3-

Volume

G.GMD.2I can find cross sectional area using Pythagorean theorem and area formulas.

111Unit 3-

112Flex day use for remediation and


114MIDTERM EXAM

115Unit 3-

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 Volume

G.GMD.2I can develop the formula for the volume of a sphere.

differentiation. differentiation. Volume

G.GMD.3I can use the formulas for the volume of 3-D figures.

116Unit 3-

Volume


117Unit 3-

Volume


118Unit 3-

Volume


119Unit 3-

Volume


120Unit 3-

Volume

G.GMD.4I can identify the shapes of two-dimensional cross-sections of three-dimensional objects.I can rotate a 2-D figure and identify the 3-D object formed.

121Unit 3-

Volume

G.GMD.4I can identify the shapes of two-dimensional cross-sections of three-dimensional objects.I can rotate a 2-D figure and identify the 3-D object that is formed.

122Unit 3-

Volume

G.GMD.4I can identify the shapes of two-dimensional cross-sections of three-dimensional objects.I can rotate a 2-D figure and identify the 3-D object that is formed.

123Unit 3-

Volume

G.MG.2I can decide whether it is best to calculate or estimate the area or volume of a geometric figure and perform the calculation or estimation.

I can convert units of measure.

124Unit 3-

Volume

G.MG.2I can break composite geometric figures into manageable pieces.

125Unit 3-

Volume

G.MG.2I can apply area and volume to situation involving density.

126Unit 3-

127Unit 3-



130Nine Weeks Exam

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 Volume

G.MG.3I can create a visual representation of a design problem.I can solve design problems using a geometric model.

Volume

G.MG.3I can interpret the results and make conclusions based on the geometric model.

differentiation. differentiation.

131Unit 4-

Circles

G.C.1I can prove that all circles are similar by showing that for a dilation centered at the center of a circle, the preimage and the image have equal central angle measures.

132Unit 4-

Circles

G.C.1I can prove that all circles are similar by showing that for a dilation centered at the center of a circle, the preimage and the image have equal central angle measures.

133Unit 4-

Circles

G.C.2I can identify central angles, inscribed angles, circumscribed angles, diameters, radii, chords, and tangents.

134Unit 4-

Circles

G.C.2I can describe the relationship between a central angle and the arc it intercepts.

I can describe the relationship between and inscribed angle and the arc it intercepts.

I can recognize that an inscribed angle whose sides intersect the endpoints of the diameter of a circle is a right angle.

135Unit 4-

Circles

G.C.2I can describe the relationship between a circumscribed angle and the arcs it intercepts.

Quiz

136Unit 4-

Circles

137Unit 4-

Circles/Constructions

138G.C.3I can apply the Arc Addition Postulate to solve for missing arc measures.

139Unit 4-

Circles/Arc Length

140Unit 4-

Circles/Sector Area

North Laurel High SchoolGeometry Daily Pacing Map Last Revised: 5/15/12 G.C.2I can recognize that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

G.C.3I can define the terms: inscribed, circumscribed, angle bisector, and perpendicular bisector.

I can construct the inscribed circle.

I can construct the circumscribed circle.

I can prove that opposite angles in an inscribed quadrilateral are supplementary.

G.C.5I can use similarity to calculate the length of an arc.

G.C.5I can define and calculate the area of a sector of a circle.

141Unit 4-

Circles/Radians

G.C.5I can define the radian measure of an angle as the ratio of an arc length to its radius and calculate a radian measure when given an arc length and its radius.

I can convert degrees to radians using the constant of proportionality

Quiz

142Unit 4-

Circles/Constructions

G.CO.13I can construct the following:

Equilateral triangle inscribed in a circle.

Square inscribed in a circle.

Hexagon inscribed in a circle.

143Unit 4-

Circles/Equations

G.GPE.1I can draw a right triangle with a horizontal leg, a vertical leg, and the radius of a circle as its hypotenuse.

I can use the distance formula, the coordinates of a circle’s center and the circle’s radius to write the equation of the circle.

I can convert an equation of a circle in general form to standard form by completing the square.

144Unit 4-

Circles/Equations

G.GPE.1I can identify the center and radius of a circle given its equation.

I can identify the center and radius of a circle given its equation.

Quiz

145Unit 4-

Parabolas

G.GPE.2I can define a parabola.I can find the distance from a point on the parabola to the directrix.

I can find the distance from a point on the parabola to the focus using the distance formula.


146Unit 4-

Parabolas

G.GPE.2I can equate the two distance expressions for a parabola to write its equation.

I can identify the focus and directrix of a parabola when given its equation.

147Unit 4-

Ellipses

G.GPE.3I can define an ellipse and a hyperbola.

I can define and identify the foci of an ellipse and a hyperbola.

148Unit 4-

Ellipses

G.GPE.3I can use the distance formula to write an expression for the sum of the distances from a point on the ellipse to each focus and equate it to the given constant sum.

I can use algebra to convert the derived equation for a hyperbola to standard form.I can identify the center, foci, and axes of an ellipse when give the standard form equation.

149Unit 4-

Ellipses

G.GPE.3I can use the distance formula to write an expression for the difference of the distances from a point on the hyperbola to each focus and equate it to the given constant sum.

I can use algebra to convert the derived equation for a hyperbola to standard form.

I can identify the center, foci, axes, and asymptotes of a hyperbola when given the standard form equation.

150Mid Term Test

151Unit 5-

Probability

S.CP.1I can define event and sample space.I can establish events as subsets of a sample space.

152Unit 5-

Probability

S.CP.1I can define union, intersection, and complement.

153Unit 5-

Probability

S.CP.1I can establish events as subsets of a sample space based on the union, intersection, and/or complement of other events.

154Unit 5-

Probability

S.CP.2I can define and identify independent events.

I can explain and provide an example to illustrate that for two independent events, the

155Unit 5-

Probability

S.CP.2I can calculate the probability of an event.

I can predict if two events are independent, explain my reasoning, and check my


Quiz probability of the events occurring together is the product of the probability of each event.

statement by calculating P(AandB) and P(A)xP(B)

156Unit 5-

Probability

S.CP.2I can calculate the probability of an event.

I can predict if two events are independent, explain my reasoning, and check my statement by calculating P(AandB) and P(A)xP(B)

157Unit 5-

Probability

S.CP.3I can define dependent events and conditional probability.

I can explain that conditional probability is the probability of an event occurring given the occurrence of some other event and give examples that illustrate conditional probability.

158Unit 5-

Probability

S.CP.3I can explain that for two events A and B, the probability of event A occurring given the occurrence of event B is P(A|B)= P(AandB)/P(B) and give examples.

159Unit 5-

Probability

S.CP.3I can explain that A and B are independent events if the occurrence of A does not impact the probability of B occurring and vice versa. P(A|B)=P(A) and P(B|A)=P(B).

I can determine if two events are independent and justify my conclusion.

Quiz

160Unit 5-

Probability

S.CP.4I can determine when a two-way frequency table is an appropriate display for a set of data.

I can collect data from a random sample.

I can construct a two-way frequency table for the data using the appropriate categories for each variable.

I can pose a question for which a two-way frequency is appropriate, use statistical techniques to sample the population, and design a n appropriate product to summarize the process and report the results.


161Unit 5-

Probability

S.CP.4Using a two-way frequency table:

I can decide if events are independent of each other by comparing P(B|A) and P(B) or P(A|B) and P(A).

I can calculate the conditional probability of A given B using the formula P(A|B)=P(AandB)\P(B)

162Unit 5-

Probability

S.CP.5I can illustrate the concept of a conditional probability using everyday examples of dependent events.

I can illustrate the concept of independence using everyday examples of independent events.

163Unit 5-

Probability

S.CP.6I can calculate the probability of the intersection of two events.

164Unit 5-

Probability

S.CP.6I can calculate the conditional probability of A given B.

165Unit 5-

Probability

S.CP.6I can interpret probability based on the context of the given problem.

Quiz

166Unit 5-

Probability

S.CP.7I can apply the Apply the Addition Rule to determine the probability of the union of two events using the formula.P(A or B)=P(A) + P(B) – P(A and B)

167Unit 5-

Probability

S.CP.7I can interpret the probability of unions and intersections based on the context of the given problem.


169Flex day use for remediation and differentiation

170Final Exam

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