d2ct263enury6r.cloudfront.net · Web viewConstruct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way

MONROVIA UNIFIED SCHOOL DISTRICT INSTRUCTIONAL PACING GUIDE

“World Class Schools for World Class Students”Standard Resources Essential Questions/Vocabulary

(Concepts to be Understood)Timing(Days)

Skills/Procedures DifferentiationIntervention

(SIOP, SDAIE, RTI)G.CO.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.

CORE 1-1 How do you use the undefined terms as the basic elements of geometry.

Point, line, line segment

2 days• Name geometric figures

G.CO.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.

CORE 1-2 What tools and methods can you use to copy a segment, bisect a segment, and construct a circle?

Distance along a line, circle

2 days • Copy, bisect and construct a line segment.

G.CO.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.

CORE 1-3 What tools and methods can you use to copy an angle and bisect an angle?

Angle

2 days • Copy an angleConstruct the bisector of an angle

Monrovia Unified School District Page 1 of 20Instructional Pacing Guide Geometry Last Revised: August 5, 2014

*** This guide is intended to be a guide only. The timing is recommended so that the material is learned by the indicated benchmark assessment. Teachers will use their professional judgement to modify the time given to ensure students have adequate time to learn the material.

GeometryDepartment MathCourse Name GeometryGrade Level 9-12Instructional Reference Material(s)

CORE in CORE MathHolt Geometry

Standard Resources Essential Questions/Vocabulary(Concepts to be Understood)

Timing(Days)


(SIOP, SDAIE, RTI)A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.G.CO.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.Foundation for G.CO.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.

CORE 1-4 How can you use angle pairs to solve problems?

2 days • Measure angles• Identify angles and angle pairs• Find angle measures

A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

CORE 1-5 How can you express formulas in different ways?

2 days • Solving formulas for specified variables

• Rewriting formulas to solve problems

G.GPE.6 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.G.GPE.4 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

CORE 1-6 How can you find midpoints of segments and distances in the coordinate plane.

1 day • Find the mid-point of line segments

• Use the midpoint formula• Find a distance in the

coordinate planeG.CO.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.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.Prep for G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

CORE 1-7 How do you identify transformations that are rigid motions?

1 day • Classify transformations• Identify rigid motions

Performance Task and Test Review 1 dayChapter 1 Cumulative Test - Target Date - 9/12/14 1 day



Timing(Days)


(SIOP, SDAIE, RTI)G.CO.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.

CORE 2-1 How can you use examples to support or disprove a conjecture?

1 day • Make conjectures about bisectors of obtuse angles

• Make conjectures about double angles of acute angles

Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others.

CORE 2-2 How can you effectively justify arguments and critique the arguments of others?

2 days • Use a Venn diagram to analyze conditional statements


CORE 2-3 How can you connect statements to visualize a chain of reasoning?

2 days • Show logical reasoning• Complete a chain of reasoning


CORE 2-4 How can you analyze and critique the reasoning of others?

2 days • Analyze bi-conditionals and definitions

G.CO.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.

CORE 2-5 What kinds of justifications can you use in writing algebraic and geometric proofs?

2 days


CORE 2-6 How can you organize the deductive reasoning of a geometric proof?

2 days • Apply linear pair theorem when writing proofs

`


CORE 2-7 What are some formats you can use to organize geometric proofs?

Skip • Apply vertical angles and common segments theorems when writing proofs

Performance Task and Test Review 1 dayChapter 2 Cumulative Test - Target Date - 10/2/14 1 dayPrep for G.CO.9 CORE 3-1 How many distinct angle

measures are formed when three lines in a plane intersect in different ways?

1 day • Sketch different triangle possibilities

• Sketch different intersection possibilities



Timing(Days)


(SIOP, SDAIE, RTI)G.CO.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.

CORE 3-2 How can you prove and use theorems about angles formed by transversals that intersect parallel lines?

1 day • Know and apply the same-side interior angles postulate

• Know and apply the alternate interior angles theorem

• Know and apply the corresponding angles theorem

• Know and apply the equal-measure linear pair theorem

• Know the converse of the same-side interior angles, alternate interior angles and corresponding angles theorems

G.CO.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.

CORE 3-3 How can you construct a line parallel to another line that passes through a given point?

2 days • Construct a parallel line

G.CO.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.

CORE 3-4 How can you construct perpendicular lines and prove theorems about perpendicular bisectors?

1 day • Construct a perpendicular bisector

• Know and apply the perpendicular bisector theorem

• Know and apply the converse of the perpendicular bisector theorem

• Construct a perpendicular to a line

G.GPE.6 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

CORE 3-5 How do you find the point on a directed line segment that partitions the segment in a given ratio?

1 day • Partition a segment



Timing(Days)


(SIOP, SDAIE, RTI)G.GPE. 5 - Prove the slope criteria for parallel and perpendicular lines 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).

CORE 3-6 Write equations of parallel linesWrite equation perpendicular lines

2 days

Chapter 3 Cumulative Test - Target Date - 10/17/14 1 dayAssessed Performance Task - Given with Interim 1 1 day1st Interim Benchmark October 20th-October 24th 5 daysG.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.G.CO.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.

CORE 4-1 How can you use transformations to determine whether figures are congruent?

2 days • Determine if figures are congruent

• Find a sequence of rigid motions

G.GPE.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).G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

CORE 4-2 How can you classify triangles in the coordinate plane?

2 days • Classify triangles by side lengths

• Classify triangles by angles using side lengths

G.CO.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.

CORE 4-3 What are some theorems about angle measure in triangles?

Prove the triangle sum theorem

Prove the exterior angle theorem

Prove the quadrilateral sum theorem

2 days

G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

CORE 4-4 How can you use properties of rigid motions to draw conclusions about corresponding sides and corresponding angles in congruent triangles?

1 day • Find an unknown dimension• Use CPCTC (Corresponding

parts of congruent triangles are congruent theorem)



Timing(Days)


(SIOP, SDAIE, RTI)G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.G.CO.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.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 4-5 How can you establish the SSS and SAS triangle?

1 day • Know and apply SSS congruence criterion

• Know and apply the angle bisection theorem

• Know and apply the reflected points on an angle theorem

• Know and apply the SAS congruence criterion

• Know and apply the SSS congruence criterion

G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.G.CO.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.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 4-6 How can you establish and use the ASA and AAS triangle congruence criteria?

2 days • Know and apply the ASA and AAS congruence criterion

G.GPE. 5 - Prove the slope criteria for parallel and perpendicular lines 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).

CORE 4-7 How can CPCTC be used in proving slope criteria for parallel and perpendicular lines?

Prove that parallel lines have the same slope

Prove that lines with the same slope are parallel

Prove that perpendicular lines have slopes whose product is -1

2 days

G.GPE.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).

CORE 4-8 How do you write a coordinate proof?

2 days • Prove or disprove a statement• Write a coordinate proof

G.CO.10 - Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles

CORE 4-9 What special relationships exist among the sides and angles of

1 day



Timing(Days)


(SIOP, SDAIE, RTI)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.

isosceles triangles?

Prove the isosceles triangle theorem

Prove the converse of the isosceles triangle theorem

Performance Task and Test Review 1 dayChapter 4 Cumulative Test - Target Date - 11/21/14 1 dayG.GPE.2 - Derive the equation of a parabola given a focus and directrix. CORE 5-1 How do you write the equation of

a parabola given its focus and directrix?

2 days • Create a parabola• Derive the equation of a

parabola• Write the equation of a

parabolaG.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CORE 5-2 How do you construct the circle that circumscribes a triangle?How do you inscribe a circle in a triangle?

1 day • Construct a circumscribed circle

• Construct an inscribed circle

G.CO.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.


CORE 5-3 What can you conclude about the medians of a triangle?

Prove the concurrency of medians theorem.

1 day

G.GO.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.G.GPE.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).

CORE 5-4 What must be true about the segment that connects the midpoints of two sides of a triangle?

Prove the mid-segment theorem

1 day



Timing(Days)


(SIOP, SDAIE, RTI)G.GO.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.

CORE 5-5 How can you use inequalities related to triangle side lengths and angle measures in proofs?

1 day • Prove side relationships.• Prove angle relationships.

G.GO.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.

CORE 5-6 When two sides of a triangle have fixed lengths and the angle included by them changes, how does the third side change?

1 day

Review for Test 1 dayCumulative Test ( We are not yet at the end of chapter 5, but may want to administer cumulative test to help review for finals.

1 day

Assessed Performance Task - Given with Interim 2 ———-

2nd Interim (Benchmark) December 15th- December 19th (Finals) 5 daysG.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

CORE 5-7 How can you apply the Pythagorean Theorem?

1 day • Use Pythagorean Theorem with lengths.

• Use Pythagorean Theorem with velocities.

G.SRT.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.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

CORE 5-8 What can you say about the side lengths associated with special right triangles?

2 days • Solve special triangles.

Review for TestChapter 5 Cumulative Test - Target Date - 01/13/14 1 dayG.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

CORE 6-1 How do you inscribe a regular polygon in a circle?

1 day • Inscribe a regular polygon.• Inscribe a square.

G.CO.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.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 6-2 What can you conclude about the sides, angles, and diagonals of a parallelogram?

2 days • Prove opposite sides of a parallelogram are congruent.

• Prove diagonals of a parallelogram bisect each other.



Timing(Days)


(SIOP, SDAIE, RTI)G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 6-3 What criteria can you use to prove that a quadrilateral is a parallelogram?

2 days • Prove opposites criterion for a parallelogram.

• Prove opposite angles criterion for a parallelogram.

G.CO.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.G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 6-4 What are the properties of a rectangles and rhombuses?

1 day • Prove the rectangle theorem.• Prove diagonals of a rhombus

are perpendicular.


CORE 6-5 How can you use slope in coordinate proofs?

2 days • Prove a quadrilateral is a parallelogram.

• Prove a quadrilateral is a rectangle.


CORE 6-6 How can auxiliary segments be used in proofs?

2 days • Prove using reasoning between congruent angles and congruent sides.

Performance Task and Review 1 dayChapter 6 Cumulative Test - Target Date - 1/30/14 1 dayPrep for G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.Prep for G.SRT.1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

CORE 7-1 How can you use ratios of corresponding side lengths to solve problems involving similar polygons?

1 day • Determine polygon similarity.• Find unknown lengths in

similar polygons.

G.CO.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.SRT.1 - Verify experimentally the properties of dilations given by a center and a scale factor.G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all

CORE 7-2 What are the key properties of dilations, and how can dilations be used to show figures are similar?

2 days • Determine if figures are similar.

• Prove all circles are similar.



Timing(Days)


(SIOP, SDAIE, RTI)corresponding pairs of sides.G.C.1 - Prove that all circles are similar.G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations 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.3 - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

CORE 7-3 What can you conclude about similar triangles and how can you prove triangles are similar?

2 days • Apply similarity to triangles.• Identify congruent angles and

proportional sides.• Prove AA Similarity criterion.

G.SRT.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.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 7-4 How does a line that is parallel to one side of a triangle divide the two sides that it intersects?

1 day • Prove triangle proportionality theorem.

• Prove the converse of the triangle proportionality theorem.

G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.G.MG.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).*

CORE 7-5 How can you use similar triangles and similar rectangles to solve problems?

2 days • Find an unknown distance.• Find an unknown height.• Solve a problem about similar

triangles.

G.CO.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).

CORE 7-6 How can you represent dilations in the coordinate plane?

1 day • Draw a dilation in a coordinate plane.

Performance Task 1 dayChapter 7 Cumulative Test - Target Date - 2/19/14 1 dayG.SRT.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.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CORE 8-1 How can you use right triangle similarity to prove the Pythagorean Theorem?

Prove the Pythagorean Theorem

2 day

G.SRT.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.7 - Explain and use the relationship between the sine and cosine of complementary angles.G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to

CORE 8-2 How do you find the tangent, sine, cosine ratios for acute angles in a right triangle?

2 day • Find the tangent of an angle.• Solve a real-world problem.• Find the sine and cosine of an

angle.



Timing(Days)


(SIOP, SDAIE, RTI)solve right triangles in applied problems.G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

CORE 8-3 How do you find an unknown angle measure in a right triangle?

1 day • Use an inverse trigonometric ratio.

G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Mathematical Practice 4 - Model with mathematics.

CORE 8-4 How can you use trigonometric ratios to solve problems involving angles of elevation and depression?

1 day • Solve a problem with an angle of depression.

• Solve a problem with an angle of elevation.

G.SRT.10 - Prove the Laws of Sines and Cosines and use them to solve problems.

Mathematical Practice 8 - Look for and express regularity in repeated reasoning.

CORE 8-5 How can you find the side lengths and angle measures of non-right triangles?

1 day

G.SRT.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).

CORE 8-6 How can you apply trigonometry to solve vector problems?

1 day • Solve a vector problem.

Chapter 8 Cumulative Test - Target Date - 3/6/14 1 dayS.CP.9 - Use permutations and combinations to compute probabilities of compound events and solve problems.

Mathematical Practice 7 - Look for and make use of structure.

CORE 13-1 What are permutations and combinations and how can you use them to calculate probabilities?

2 days • Find permutations.• Use permutations to calculate a

probability.• Find combinations.• Use combinations to calculate

a probability.S.MD.6 - Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

CORE 13-2 How can you use probabilities to help you make fair decisions?

2 days • Use a random sample.• Use a convenience sample.



Timing(Days)


(SIOP, SDAIE, RTI)S.CP.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.S.CP.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.S.CP.8 - Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.Mathematical Practice 1 - Make sense of problems and persevere in solving them.

CORE 13-3 How do you find the probability of independent and dependent events?

2 days • Determine if events are independent.

• Use the probability of independent events formula.

• Show that events are independent.

• Find the probability of dependent events.

• Use the multiplication rule.

S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.S.CP.6 - Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

CORE 13-4 How do you calculate a conditional probability?

2 days • Find conditional probabilities.• Use the formula for conditional

probability.

S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

CORE 13-5 How do you find the probability of mutually exclusive events and overlapping events?

1 day • Find the probability of mutually exclusive events.

• Find the probability of overlapping events.

• Use the addition rule.Performance Task and Review 1 dayChapter 13 Cumulative Test - Target Date - 4/21/14 1 day



Timing(Days)


(SIOP, SDAIE, RTI)G.CO.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.4 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.G.CO.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.Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others.

CORE 9-1 How do you draw the image of a figure under a reflection?

2 days • Draw a reflection image.• Construct a reflection image.• Draw a reflection in the

coordinate plane.

G.CO.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.4 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.G.CO.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.

CORE 9-2 How do you draw the image of a figure under a translation?

2 days • Name a vector.• Construct a translation image.• Draw a translation in the

coordinate plane.

G.CO.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.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.

CORE 9-3 How do you draw the image of a figure under a rotation?

1 day • Draw a rotation image.

CAHSEE REVIEW (10th Grade CAHSEE - 3/17-3/18) 2 daysG.CO.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.

CORE 9-4 How can you use more than one transformation to map one figure onto another?

1 day

G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular CORE 9-5 How do you determine whether a 1 day • Identify line symmetry.Monrovia Unified School District Page 13 of 20Instructional Pacing Guide Geometry Last Revised: August 5, 2014


Timing(Days)


(SIOP, SDAIE, RTI)polygon, describe the rotations and reflections that carry it onto itself. figure has line symmetry or

rotational symmetry?• Identify rotational symmetry.

G.CO.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.

CORE 9-6 How can you use transformations to describe tessellations?

1 day • Describe tessellations.

G.CO.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).

CORE 9-7 How do you draw the image of a figure under a dilation.

1 day • Construct a dilation image.

Assessed Performance Task - Given with Interim 3 ———-

3rd Interim - SUMMATIVE (Benchmark) March 23rd - 26th 3 daysG.SRT.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.

CORE 10-1 What formula can you use to find the area of a triangle if you know the length of two sides and the measure of an included angle.

2 days • Use an area formula.

G.GMD.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.MG.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).*Mathematical Practice 8 - Look for and express regularity in repeated reasoning.

CORE 10-2 How do you justify and use the formula for the circumference of a circle?

1day • Justify the circumference formula.

G.MG.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.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).*

CORE 10-3 How can you find areas of irregular shapes?

2 days • Find area using addition.• Find area using subtraction.

G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*G.MG.2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

CORE 10-4 How do you find the perimeter and area of polygons in the coordinate plane?

2 days • Find perimeters.• Approximating a population

density.



Timing(Days)


(SIOP, SDAIE, RTI)G.CO.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).

CORE 10-5 What happens when you change the dimensions of a figure using different scale factors along two dimensions?

2 days

S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CORE 10-6 How can you use set theory to help you calculate theoretical probabilities?

1 day • Calculate theoretical probability.

Performance Task and Review 1 dayChapter 10 Cumulative Test - Target Date - 5/9/14 1 dayG.GMD.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.

CORE 11-1 How do you identify cross sections of three-dimensional figures and how do you use rotations to generate three-dimensional figures?

2 days • Identify cross sections of a cylinder.

• Generate three dimensional figures.

G.GMD.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.2 - Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.G.MG.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.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).

CORE 11-2 How do you calculate the volume of a prism or cylinder and use volume formulas to solve design problems?

Design a box with maximum volume.

2 days • Compare densities.• Find the volume of an oblique

cylinder.

G.GMD.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.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

CORE 11-3 How do you calculate the volume of a pyramid or cone and use volume to solve problems?

2 days • Solve a volume problem.

G.GMD.2 - Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

CORE 11-4 How do you calculate the volume of a sphere and use the volume formula to solve problems?

2 days • Solve a volume problem.

Performance Task 1 dayChapter 11 Cumulative Test - Target Date - 5/23/14 1 day



Timing(Days)


(SIOP, SDAIE, RTI)G.C.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.

CORE 12-1 What is the relationship between a tangent line to a circle and the radius drawn from the center too the point of tangency?

Prove the tangent-radious theorem.

If time permits

G.C.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.

CORE 12-2 How are arcs and chords of circles associated with central angles?

If time permits

G.CO.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.G.C.5 - Derive using similarity the fact that the length of the arc 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.G.GMD.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.

CORE 12-3 How do you find the area of a sector of a circle, and how do you calculate arc length in a circle?

If time permits

• Find the area of a sector. Find arc length.

• Convert to radian measure.

G.C.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.3 - Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CORE 12-4 What is the relationship between central angles and inscribed angles in a circle?

If time permits

• Find arc and angle measures.

G.CO.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.C.4 - Construct a tangent line from a point outside a given circle to the circle.

CORE 12-5 When two tangents are drawn to a circle, how do you find the measure of the angle formed at their intersections?

Prove circumscribed angle theorem.

If time permits



Timing(Days)


(SIOP, SDAIE, RTI)G.C.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.MG.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).*

CORE 12-6 How can you estimate the distance to the horizon using results about segments related to circles?

Secant-tangent product theorem

If time permits

• Approximate distance to the horizon.

A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.G.GPE.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.G.GPE.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).

CORE 12-7 How can you write and use equations of circles in the coordinate plane?

Derive the equation of a circle.

If time permits

• Find the center and radius of a circle.

• Write a coordinate proof.• Solve a system by graphing.

Chapter 12 Cumulative Test - Target Date - 5/23/14Assessed Performance Task to be given with the Summative Assessment

1 day

SUMMATIVE ASSESSMENT (Benchmark) June 4th- June 6th 3 days


Department Policies

Grading Scale:97% - 100% A+93% - 96% A90% - 92% A- 87% - 89% B+83% - 86% B80% - 82% B-77% - 79% C+73% - 76% C70% - 72% C-67% - 69% D+66% - 60% D0% - 50% F

Grade Weights :

Assignment Type Percent of Grade Assessments/Projects 35%Assignments 30%Interim #1/#3 10%Interim #2/#4 25%

Makeup Work: Makeup work is accepted for full credit if the student have an excused absence. The student will have an amount of time equal to the number of days absent to complete any missed assignments.

Late Work Policy: Late work may be accepted at the discretion of the teacher.

Testing Policy: Students will be allowed to make-up a test if they have an excused absence. They will have the amount of days equal to the days they were absent to prepare for the test.

Teacher Policies: [please insert relevant policy]


Documents

d2ct263enury6r.cloudfront.net · Web viewConstruct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way