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RCHS Rev. 06/2011 Geometry B Unit 4 Expressing Geometric Properties With Equations Length of Unit KY Common Core Academic Standards ___weeks 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). Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Vocabulary: side length, vertex, first quadrant, slope, distance, midpoint, parallel, perpendicular, intersecting Activities/Assessments/ Resources Note: Same with Unit 5 Unit Learning targets Students will be able to: I can recall previous understandings of coordinate geometry (including, but not limited to: distance, midpoint and slope formula, equation of a line, definitions of parallel and perpendicular lines, etc.) (K) From Appendix A: This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; I can represent the vertices of a figure in the coordinate plane using variables. (R) I can connect a property of a figure to the tool needed to verify that property. (R) I can use coordinates and the right tool to prove or disprove a claim about a figure. For example: Use slope to determine if sides are parallel, intersecting, or perpendicular; Use the distance formula to determine if sides are congruent or to decide if a point is inside a circle, outside a circle, or on the circle; Use the midpoint formula or the distance formula to decide if a side has been bisected. (R) Page 1 RCHS Rev. 06/2011 Geometry B Unit 4 Expressing Geometric Properties With Equations Length of Unit KY Common Core Academic Standards ___weeks 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). Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: slope, parallel, perpendicular, product, line, linear equation, slope-intercept form, point slope form Unit Learning targets Students will be able to: I can recognize that slopes of parallel lines are equal. (K) I can recognize that slopes of perpendicular lines are opposite reciprocals (i.e, the slopes of perpendicular lines have a product of -1). (K) I can find the equation of a line parallel to a given line that passes through a given point. (K) I can find the equation of a line perpendicular to a given line that passes through a given point. (K) I can prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. (R) From Appendix A: Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra 1 involving systems of equations having no solution or infinitely many solutions. Parallel Lines: I can draw a line on a coordinate plane and translate that line to produce its image. (K) I can explain that these lines are parallel since translations preserve angle. (K) I can determine the slope of the original line and its image after translation and show they have the same slope using specific examples and general coordinates (x,y). (R) I can state that parallel lines have the same slope. (K) I can determine if lines are parallel using their slopes. (R) Page 2 RCHS Rev. 06/2011 Geometry B I can write an equation for a line that is parallel to a given line that passes through a given point. (R) Perpendicular Lines: I can draw a line on a coordinate plane and rotate that line 90° to produce a perpendicular image. (K) I can determine the slope of the original line and its image after a 90° rotation and show they have the opposite reciprocal slopes using specific examples and general coordinates (x,y). (R) I can state that perpendicular lines have the opposite reciprocal slopes. (K) I can determine if lines are perpendicular using their slopes. (R) I can write an equation for a line that is perpendicular to a given line that passes through a given point. (R) Rowan County Senior High School 2010-2011 Page 3 RCHS Rev. 06/2011 Geometry B Unit 4 Expressing Geometric Properties With Equations Length of Unit KY Common Core Academic Standards ___weeks G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: directed line segment, endpoint, ratio Unit Learning targets Students will be able to: I can recall the definition of ratio. (K) I can recall previous understandings of coordinate geometry. (K) I can calculate the point(s) on a directed line segment whose endpoints are (x1 ,y1) and (x2,y2) that partitions the line segment into a given ratio, r1 to r2 using the formula x = r2x1 +r1x2 and y = r2y1 + r1y2 r1 + r2 r 1 + r2 (e.g., For the directed line segment whose endpoints are (0,0) and (4,3), the point that partitions the segment into a ratio of 3 to 2 can be found: x = (2•0 + 3• 4) = 12 and y = (2•0 + 3• 3) = 9 (3+2) 5 (3 + 2) 5 So the point is (12/5, 9/5).) (R) Rowan County Senior High School 2010-2011 Page 4 RCHS Rev. 06/2011 Geometry B Unit 4 Expressing Geometric Properties With Equations Length of Unit KY Common Core Academic Standards ___weeks G.GPE.7 Use coordinates to compute perimeters of polygons and area of triangles and rectangles, e.g., using the distance formula.*(*Modeling Standard) Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: coordinate plane, coordinates, distance formula, perimeter, polygon, area, triangle, rectangle Unit Learning targets Students will be able to: Formulate a model of figures in contextual problems to compute area and/or perimeter. (R) From Appendix A: G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem. I can use coordinates of the vertices of a polygon graphed in the coordinate plane and use the distance formula to compute the perimeter. (S) I can use the coordinates of the vertices of triangles and rectangles graphed in the coordinate plane to compute area. (S) Unit 4 Expressing Geometric Properties With Equations Length of Unit KY Common Core Academic Standards ___weeks G.GPE.2 Derive the equation of a parabola given a focus and directrix. Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: parabola, focus, directrix, distance formula, factor, perfect square trinomial Unit Learning targets Page 5 RCHS Rev. 06/2011 Geometry B Students will be able to: I can define a parabola including the relationship of the focus and the equation of the directrix to the parabolic shape. From Appendix A: The directrix should be parallel to a coordinate axis. (K) I can find the distance from a point on the parabola (x,y) to the directrix. (S) I can find the distance from a point on the parabola (x,y) to the focus using the distance formula (Phytagorean Theorem). (S) I can equate the two distance expressions for a parabola to write its equation. (S) I can identify the focus and directrix of a parabola when given its equation. (R) Unit 5 Circles Length of Unit KY Common Core Academic Standards ___weeks G.C.1 Prove that all circles are similar. Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: circle, similar figures, rigid motion, dilation, angle measure, preimage, image, central angle Unit Learning targets Students will be able to: I can recognize when figures are similar. (Two figures are similar if one is the image of the other under a Rowan County Senior High School 2010-2011 Page 6 RCHS Rev. 06/2011 Geometry B transformation from the plane into itself that multiplies all distances by the same positive scale factor, k. That is to say, one figure is a dilation of the other. ) (K) I can compare the ratio of the circumference of a circle to the diameter of the circle. (R) I can discuss, develop and justify this ratio for several circles. (R) Determine that this ratio is constant for all circles. (R) I 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 measure. (R) Unit 5 Circles Length of Unit ___weeks KY Common Core Academic Standards G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: central angle, inscribed angle, circumscribed angle, diameter, radius, chord, tangent, circle, intersect, endpoints, right angle, perpendicular Unit Learning targets Students will be able to: I can identify inscribed angles, radii, chords, central Page 7 RCHS Rev. 06/2011 Geometry 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. B angles, circumscribed angles, diameter, and tangent. (K) I can examine the relationship between central, inscribed and circumscribed angles by applying theorems about their measures. (R) I can describe the relationship between a central angle and the arc it intercepts. (R) I can describe the relationship between an inscribed angle and the arc it intercepts. (R) I can describe the relationship between a circumscribed angle and the arcs it intercepts. (R) I can recognize that an inscribed angle whose sides intersect the endpoints of the diameter of a circle is a right angle. (K) I can recognize that the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (K) Unit 5 Circles Length of Unit ___weeks KY Common Core Academic Standards Vocabulary/Learning Targets G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Vocabulary: inscribed, circumscribed, angle bisector, perpendicular bisector, construction, compass, straightedge, intersection, incenter, circle, circumcenter, quadrilateral, arc, inscribed angle, ARC Addition Postulate, equation, opposite angles, supplementary Activities/Assessments/ Resources Unit Learning targets Students will be able to: I can define the terms inscribed, circumscribed, angle bisector, and perpendicular bisector (K) I can construct the inscribed circle whose center is the Rowan County Senior High School 2010-2011 Page 8 RCHS Rev. 06/2011 Geometry B point of intersection of the angle bisectors (the incenter). (P) I can construct the circumscribed circle whose center is the point of intersection of the perpendicular bisectors of each side of the triangle (the circumcenter). (P) I can apply the Arc Addition Postulate to solve for missing arc measures. (S) I can prove that opposite angles in an inscribed quadrilateral are supplementary. (R) Unit 5 Circles Length of Unit ___weeks KY Common Core Academic Standards G.C. 4 (+) Construct a tangent line from a point outside a given circle to the circle. Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: tangent line, circle, perpendicular, radius, endpoint, midpoint, line segment, point Unit Learning targets Students will be able to: I can recall vocabulary: tangent, radius, perpendicular bisector, and midpoint (K) I can identify the center of the circle. (K) I can define and identify a tangent line. (K) I can synthesize theorems that apply to circles and tangents, such as: Tangents drawn from a common external point are congruent. A radius is perpendicular to a tangent at the point of tangency. (R) Rowan County Senior High School 2010-2011 Page 9 RCHS Rev. 06/2011 Geometry B I can construct the perpendicular bisector of the line segment between the center C to the outside point P. (P) I can construct arcs on circle C from the midpoint Q, having length of CQ. (P) I can construct a tangent line from a point outside the circle to the circle using construction tools or computer software. (P) Unit 5 Circles Length of Unit ___weeks KY Common Core Academic Standards 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. Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: similarity, rigid motion, dilation, angle measure, length, proportional, arc, constant of proportionality, radian, angle, area, circle, sector, formula, intercepted arc Unit Learning targets Students will be able to: I can recall how to find the area and circumference of a circle.(K) I can explain that 1° = Π/180 radians (K) I can recall (from G.C.1) that all circles are similar. (K) I can determine the constant of proportionality (scale factor). (K) I can justify the radii of any two circles (r1 and r2) and the arc lengths (s1 and s2) determined by congruent central angles are proportional, such that r1 /s1 = r2/s2 (R) I can verify that the constant of a proportion is the same as the radian measure, Θ, of the given central angle. Conclude s = r Θ (R) From Appendix A: Emphasize the similarity of all circles. Page 10 RCHS Rev. 06/2011 Geometry B Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. I can define similarity as rigid motions with dilations, which preserves angle measures and make lengths proportional (K) I can use similarity to calculate the length of an arc. (S) I 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. (R) I can convert degrees to radians using the constant of proportionality (2π x angle measure / 360° ). (K) I can calculate the area of a circle.(S) I can define a sector of a circle. (K) I can calculate the area of a sector using the ratio of the intercepted arc measure and 360° multiplied by the area of the circle. (R) Rowan County Senior High School 2010-2011 Page 11 RCHS Rev. 06/2011 Geometry B Unit 5 Expressing Geometric Properties with Equations Length of Unit ___weeks KY Common Core Academic Standards 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. Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: distance formula, Pythagorean Theorem, difference, coordinates, radius, circle, hypotenuse, equation, center, complete the square, quadratic equation, conic equation, standard form, general form Unit Learning targets Students will be able to: I can define a circle. (K) I can use Pythagorean Theorem. (K) I can complete the square of a quadratic equation. (K) I can derive equation of a circle using the Pythagorean Theorem – given coordinates of the center and length of the radius. (R) I can determine the center and radius by completing the square. (R) From Appendix A: Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. I can identify the center and radius of a circle given its equation. (K) I can draw a right triangle with a horizontal leg, a vertical leg, and the radius of a circle as its hypotenuse. (K) I can use the distance formula (Pythagorean Theorem), the coordinates of a circle’s center, and the circle’s radius to write the equation of the circle. (R) I can convert an equation of a circle in general (quadratic) Page 12 RCHS Rev. 06/2011 Geometry B form to standard form by completing the square. (S) I can identify the center and radius of a circle given its equation. (R) Unit 5 Expressing Geometric Properties with Equations Length of Unit ___weeks KY Common Core Academic Standards 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). Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: side length, vertex, first quadrant, slope, distance, midpoint, parallel, perpendicular, intersecting Unit Learning targets Students will be able to: I can recall previous understandings of coordinate geometry (including, but not limited to: distance, midpoint and slope formula, equation of a line, definitions of parallel and perpendicular lines, etc.) (K) I can use coordinates to prove simple geometric theorems algebraically. (R) 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). From Appendix A: Include simple proofs involving circles. I can represent the vertices of a figure in the coordinate plane using variables. (R) I can connect a property of a figure to the tool needed to verify that property. (R) I can use coordinates and the right tool to prove or Page 13 RCHS Rev. 06/2011 Geometry B disprove a claim about a figure. For example: Use slope to determine if sides are parallel, intersecting, or perpendicular; Use the distance formula to determine if sides are congruent or to decide if a point is inside a circle, outside a circle, or on the circle; Use the midpoint formula or the distance formula to decide if a side has been bisected. (R) Unit 5 Modeling with Geometry Length of Unit ___weeks KY Common Core Academic Standards 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).*(*Modelin g Standard) Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: circumference, area, perimeter, volume Unit Learning targets Students will be able to: I can use measures and properties of geometric shapes to describe real world objects. (K) Given a real world object, I can classify the object as a known geometric shape - use this to solve problems in context. (R) From Appendix A: Focus on situations in which the analysis of circles is required. I can represent real-world objects as geometric figures. (R) I can estimate measure (circumference, area, perimeter, volume) of real-world objects using comparable geometric shapes or three-dimensional figures. (R) I can apply the properties of geometric figures to comparable real-world objects (e.g., The spokes of a wheel of a bicycle are equal lengths because they Rowan County Senior High School 2010-2011 Page 14 RCHS Rev. 06/2011 Geometry B represent the radii of a circle.). (R) Unit 6 Conditional Probability and the Rules of Probability Length of Unit KY Common Core Academic Standards ___weeks 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”). ___weeks 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 Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: event, sample space, subset union, intersection, complement Unit Learning targets Students will be able to: I can define event and sample space. (K) I can establish events as subsets of a sample space. (S) I can define union, intersection, and complement. (K) I can establish events as subsets of a sample space (the set of outcomes) using characteristics of the outcomes, based on the union, intersection, or complement of other events (‘or’, “and”, “not’). (S) Vocabulary: independent events, probability, product, event Unit Learning targets Students will be able to: I can define and identify independent events. (K) I can explain and provide an example to illustrate that for Page 15 RCHS Rev. 06/2011 Geometry this characterization to determine if they are independent. Statistics and B two dependent events, the probability of the events occurring together is the product of the probability of each event. (R) I 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(A and B) and P(A) x P(B). (R) Unit 6 Conditional Probability and the Rules of Probability Length of Unit ___weeks KY Common Core Academic Standards 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. Statistics and Probability is a Modeling Conceptual Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: probability, dependent events, conditional probability, independent events Unit Learning targets Students will be able to: I can define dependent events and conditional probability. (K) 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. (R) I 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(A and B) and give examples to show how P(B) to use the formula (R) Page 16 RCHS Rev. 06/2011 Geometry Category. B I 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 (i.e., A and B are independent events if P(B│A) = P(B) and P(A│B) = P(A)). (R) I can determine if two events are independent and justify my conclusion. (R) Unit 6 Conditional Probability and the Rules of Probability Length of Unit ___weeks KY Common Core Academic Standards S.CP. 4 Construct and interpret twoway 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 Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Vocabulary: two-way frequency table, display, data, variable, category, random sample, probability, event, independent events, formula, conditional probability Unit Learning targets Students will be able to: I can determine when a two-way frequency table is an appropriate display for a set of data. (R) I can collect data from a random sample. (S) I can construct a two-way frequency table for the data using the appropriate categories for each variable. (S) 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). (R) I can calculate the conditional probability of A given B using the formula P(A│B) = P(A and B) . (S) P(B) I can pose a question for which a two-way frequency is appropriate, use statistical technique to sample the population, and design an appropriate product to Activities/Assessments/ Resources Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. From Appendix A: Build on work with two-way tables from Algebra 1 Unit 3 (S.ID.5) to develop understanding of conditional probability and independence. Interpret two-way frequency tables of data when two categories are associated with each object being classified. (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 Page 17 RCHS Rev. 06/2011 Geometry selected student from your school will favor science given that the student is in 10th grade. Do the same for other subjects and compare the results. summarize the process and report the results. (P) B school will favor science given that the student is in 10th grade. Do the same for other subjects and compare the results.) Unit 6 Conditional Probability and the Rules of Probability Length of Unit ___weeks KY Common Core Academic Standards S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Statistics and Probability is a Modeling Conceptual Category. Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: conditional probability, dependent events, independence, independent events Unit Learning targets Students will be able to: I can illustrate the concept of conditional probability using everyday examples of dependent events. (R) I can illustrate the concept of independence using everyday examples of independent events. Page 18 RCHS Rev. 06/2011 Geometry B Unit 6 Conditional Probability and the Rules of Probability Length of Unit KY Common Core Academic Standards ___weeks 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. Statistics and Probability is a Modeling Conceptual Category. Rowan County Senior High School 2010-2011 Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: probability, event, dependent event, conditional probability, intersection, set Unit Learning targets Students will be able to: I can find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A. I can interpret the answer in terms of the model. I can calculate the probability of the intersection of two events. (S) I can calculate the conditional probability of A given B using the model P(A│B) = P(A and B) . (S) P(B) I can interpret probability based on the context of the given problem. (R) Page 19 RCHS Rev. 06/2011 Geometry B Unit 6 Conditional Probability and the Rules of Probability Length of Unit ___weeks ___weeks KY Common Core Academic Standards Vocabulary/Learning Targets S.CP.7 Apply the Additional Rule, P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in terms of the model. Statistics and Probability is a Modeling Conceptual Category. Vocabulary: probability, event, intersection, union, Addition Rule 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 Vocabulary: probability, event, conditional probability, General Multiplication Rule, intersection Rowan County Senior High School 2010-2011 Activities/Assessments/ Resources Unit Learning targets Students will be able to: I can 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). (S) I can interpret the probability of unions and intersections based on the context of the given problem. (R) Unit Learning targets Students will be able to: Page 20 RCHS Rev. 06/2011 Geometry interpret the answer in terms of the model. Statistics and Probability is a Modeling Conceptual Category. B I can use the multiplication rule with correct notation. I can apply the general Multiplication Rule to calculate the probability of the intersection of two events using the formula P(A and B) = P(A)P(B|A) = P(B)P(A|B). I can Interpret conditional probability based on the context of the given problem. Unit 6 Conditional Probability and the Rules of Probability Length of Unit ___weeks KY Common Core Academic Standards S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. Statistics and Probability is a Modeling Conceptual Category. Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: fundamental counting principle, outcomes, sample space, factorial, permutation, combination, compound event, probability Unit Learning targets Students will be able to: I can apply the fundamental counting principle to find the total number possible outcomes in a sample space. (S) I can define factorial, permutation, combination and compound event. (K) I can distinguish between situations that require permutations and those that require combinations. (R) I can apply the permutation formula to determine the number of outcomes in an event nPr =n!/(n-r)! (S) I can apply the combination formula to determine the number of outcomes in an event. Rowan County Senior High School 2010-2011 Page 21 RCHS Rev. 06/2011 Geometry B nCr =n!/(n-r)!r! (S) I can compute probabilities of compound events. (S) I can solve problems involving permutations and combinatations. (S) I can write and solve original problems involving compound events, permutations, and/or combinations (P) Unit 6 Using Probability to Make Decisions Length of Unit KY Common Core Academic Standards Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: probability, event, theoretical probability, ___weeks S.MD.6 (+) Use probabilities to make fair decisions (e.g. drawing by lots, using a random number generator.) This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with conclusions drawn from sample data (i.e. incomplete information) requires an understanding of probability concepts. experimental probability, Unit Learning targets Students will be able to: I can compute Theoretical and Experimental Probabilities. (K) I can use probabilities to make fair decisions (e.g. drawing by lots, using a random number generator.) (R) I can analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game.) From Appendix A: This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with Rowan County Senior High School 2010-2011 Page 22 RCHS Rev. 06/2011 Geometry B conclusions drawn from sample data (i.e. incomplete information) requires an understanding of probability concepts. Unit 6 Using Probability to Make Decisions Length of Unit ___weeks KY Common Core Academic Standards S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game.) Statistics and Probability is a Modeling Conceptual Category. Vocabulary/Learning Targets Activities/Assessments/ Resources Vocabulary: probability, event, product testing, medical testing Unit Learning targets Students will be able to: I can recall prior understandings of probability. I can analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game.) From Appendix A: This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with conclusions drawn from sample data (i.e. incomplete information) requires an understanding of probability Rowan County Senior High School 2010-2011 Page 23 RCHS Rev. 06/2011 Geometry B concepts. Rowan County Senior High School 2010-2011 Page 24