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&Fdd$If[$\$gd#E $Ifgd#E $Ifgd&g556;7l7;222 $Ifgd&gkd$$Ifִdk!`'-4^^^< 2-4ayt#El72:;=?&?b?t??@@NAzABC*
&Fdd$If[$\$gd#E $Ifgd#E $Ifgd&gdd$If[$\$gdY?@@@@zA~ABBCCD(*,@*,24}}}}}}&h#EB*CJH*OJQJ^JaJphh#ECJaJ'h#E0JB*CJOJQJ^JaJph,jh#EB*CJOJQJU^JaJph)h#E5B*CJOJQJ\^JaJphU#h#EB*CJOJQJ^JaJph#h#EB*CJOJQJ^JaJph1the ratio of the portion to the whole circle to create a formula for the area of a sector.Students understand that:
l Radians measure the ratio of the arc length to the radius for an intercepted arc,
l The ratio of the area of a sector to the area of a circle is proportional to the ratio of the central angle to a complete revolution.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54219" \t "_blank" ALEX Resources30. 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.Expressing Geometric Properties with EquationsTranslate between the geometric description and the equation for a conic section.GeometryG-GPE.1Students: Given the center (h,k) and radius (r) of a circle,
l Explain and justify that every point on the circle is a combination of a horizontal and vertical shift from the center with a length equal to the radius,
l Create a right triangle from the center of a circle to a general point on the circle, and show that the legs of the right triangle are the absolute values of x-h and y-k, and the hypotenuse is r, then apply Pythagorean theorem to show that r2 = (x - h)2 + (y - k)2.
Given an equation of a circle in general form,
l Complete the square to rewrite the equation in the form r2 = (x - h)2 + (y - k)2 and determine the center and radius.Students know:
l Key features of a circle,
l The Pythagorean Theorem,
l The technique of completing the square.Students are able to:
l Create a right triangle in a circle using the horizontal and vertical shifts from the center as the legs and the radius of the circle as the hypotenuse,
l Convert an equation of a circle from general form to standard form using the method of completing the square.Students understand that:
l Circles represent a fixed distance in all directions in a plane from a given point, and a right triangle may be created to show the relationship of the horizontal and vertical shift to the distance,
l Rewriting algebraic expressions or equations in equivalent forms often reveals significant features of the expression, (i.e., circles written in standard form are useful for recognizing the center and radius of a circle).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54221" \t "_blank" ALEX Resources31. Use coordinates to prove simple geometric theorems algebraically. 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).Expressing Geometric Properties with EquationsUse coordinates to prove simple geometric theorems algebraically. (Include distance formula; relate to Pythagorean Theorem.)GeometryG-GPE.4Students: Given coordinates and geometric theorems and statements defined on a coordinate system,
l Use the coordinate system and logical reasoning to justify (or deny) the statement or theorem, and to critique arguments presented by others.l Simple geometric theoremsStudents know:
l Relationships (e.g. distance, slope of line) between sets of points,
l Properties of geometric shapes,
l Coordinate graphing rules and techniques,
l Techniques for presenting a proof of geometric theorems.Students are able to:
l Accurately determine what information is needed to prove or disprove a statement or theorem,
l Accurately find the needed information and explain and justify conclusions,
l Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.Students understand that:
l Modeling geometric figures or relationships on a coordinate graph assists in determining truth of a statement or theorem,
l Geometric theorems may be proven or disproven by examining the properties of the geometric shapes in the theorem through the use of appropriate algebraic techniques.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54223" \t "_blank" ALEX Resources32. 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).Expressing Geometric Properties with EquationsUse coordinates to prove simple geometric theorems algebraically. (Include distance formula; relate to Pythagorean Theorem.)GeometryG-GPE.5Students: Given a line,
l Create lines parallel to the given line and compare the slopes of parallel lines by examining the rise/run ratio of each line,
l Create lines perpendicular to the given line by rotating the line 90 degrees and compare the slopes by examining the rise/run ratio of each line,
l Use understandings of similar triangles and logical reasoning to prove that parallel lines have equal slopes and the slopes of perpendicular lines are negative reciprocals.
Given a geometric problem involving parallel or perpendicular lines,
l Apply the appropriate slope criteria to solve the problem and justify the solution including finding equations of lines parallel or perpendicular to a given line.l Slope criteria for parallel and perpendicular linesStudents know:
l Techniques to find the slope of a line,
l Key features needed to solve geometric problems,
l Techniques for presenting a proof of geometric theorems.Students are able to:
l Explain and justify conclusions reached regarding the slopes of parallel and perpendicular lines,
l Apply slope criteria for parallel and perpendicular lines to accurately find the solutions of geometric problems and justify the solutions,
l Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.Students understand that:
l Relationships exist between the slope of a line and any line parallel or perpendicular to that line,
l Slope criteria for parallel and perpendicular lines may be useful in solving geometric problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54225" \t "_blank" ALEX Resources33. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.Expressing Geometric Properties with EquationsUse coordinates to prove simple geometric theorems algebraically. (Include distance formula; relate to Pythagorean Theorem.)GeometryG-GPE.6Students: Given two points and a ratio that partitions the segment between the points,
l Construct a circle using one of the given points as the center and the distance between the points as the radius,
l Construct a dilation of the circle using the given ratio as the scale factor and find the intersection between the dilation and the equation of the line passing through the given points,
l Justify and explain the reasons for each step in the process of finding a point that partitions a segment in a given ratio.l Directed line segment
l PartitionsStudents know:
l Techniques for finding the distance between two points and the equation of a line passing through two points,
l Forms for writing the equation of a circle dependent on the information given to find the equation of the dilation of a circle,
l Techniques to find the intersection between a line and a circle.Students are able to:
l Accurately find the distance between two points and the equation of a line passing through two points,
l Accurately find the equation of a dilation of a circle,
l Find the intersection point(s) of a line and a circle.Students understand that:
l A radius of a circle may be used to show the distance between two points,
l A dilation of a circle may be used to partition a line segment by making it the radius, in a given ratio.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54226" \t "_blank" ALEX Resources34. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.&Expressing Geometric Properties with EquationsUse coordinates to prove simple geometric theorems algebraically. (Include distance formula; relate to Pythagorean Theorem.)GeometryG-GPE.7Students: Given a contextual situation that requires the perimeter and/or area of a polygon as part of its solution,
l Find the solution to the situation through the use of coordinates and the distance formula as appropriate, through modeling the situation in a Cartesian coordinate system and explain and justify the solution.Students know:
l The distance formula and its applications,
l Techniques for coordinate graphing.Students are able to:
l Create geometric figures on a coordinate system from a contextual situation,
l Accurately find the perimeter of polygons and the area of triangles and rectangles from the coordinates of the shapes,
l Explain and justify solutions in the original context of the situation.Students understand that:
l Contextual situations may be modeled in a Cartesian coordinate system,
l Coordinate modeling is frequently useful to visualize a situation and to aid in solving contextual problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54227" \t "_blank" ALEX Resources35. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)Geometric Measurement & DimensionUse coordinates to prove simple geometric theorems algebraically. (Alabama)GeometryG-GMD.5Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54229" \t "_blank" ALEX Resources36. Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments.Geometric Measurement & DimensionExplain volume formulas and use them to solve problems.GeometryG-GMD.1Students: Given a circle,
l Use repeated reasoning from multiple examples of the ratio of circle circumference to the diameter, to informally conjecture that the circumference of any circle is a little more than three times the diameter,
l Divide the circle into an equal number of sectors, and rearrange the sectors to form a shape that is approaching a parallelogram,
l Make conjectures about the area and perimeter of the new shape as the number of sectors becomes larger, and relate those conjectures to the original circle.
Given a cylinder,
l Explain how a cylinder could be divided into an infinite number of circles, and the area of those circles multiplied by the height is the volume of the cylinder, and use Cavalieri s Principle to demonstrate that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
Given a pyramid or cone,
l Explain that the shapes could be divided into cross-sections, and the area of the cross-sections is decreasing as the cross-sections become further away from the base, and the area of an infinite number of cross-sections is the volume of a pyramid or cone.l Dissection arguments
l Cavalieri s Principle
l Cylinder
l Pyramid
l ConeStudents know:
l Techniques to find the area and perimeter of parallelograms,
l Techniques to find the area of circles or polygons.Students are able to:
l Accurately decompose circles, cylinders, pyramids, and cones into other geometric shapes,
l Explain and justify how the formulas for circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone may be created from the use of other geometric shapes.Students understand that:
l Geometric shapes may be decomposed into other shapes which may be useful in creating formulas,
l Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54231" \t "_blank" ALEX Resources37. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.&Geometric Measurement & DimensionExplain volume formulas and use them to solve problems.GeometryG-GMD.3Students: Given a contextual situation that requires finding the volume of a cylinder, pyramid, cone, or sphere as part of its solution,
l Use an appropriate shape or 2-D drawing to model the situation,
l Solve using the appropriate formula,
l Justify and explain the solution and solution path in the context of the given situation.Students know:
l Volume formulas for cylinders, pyramids, cones, and spheres,
l Techniques for modeling 3-D objects with shapes or 2-D drawings, and for using these models to identify specific values for use in volume formulas.Students are able to:
l Accurately model a contextual situation with a cylinder, pyramid, cone, sphere, or a 2-D drawing,
l Use the model or drawing to find values needed for use in the volume formula,
l Accurately find a solution to the given situation, and explain the solution in the context of the situation.Students understand that:
l A contextual situation involving cylinders, pyramids, cones, and spheres may be modeled by shapes or 2-D drawings, and the model may provide insight into the solution of the problem,
l Formulas are useful for efficiency when many problems of the same type need to be solved.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54232" \t "_blank" ALEX Resources38. Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) &Geometric Measurement & DimensionExplain volume formulas and use them to solve problems.GeometryG-GMD.6Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54233" \t "_blank" ALEX Resources39. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.Geometric Measurement & DimensionVisualize relationships between two-dimensional and three-dimensional objects.GeometryG-GMD.4Students: Given 3-D objects,
l Conjecture about the characteristics of geometric shapes formed if a cross-section of a 3-D shape is taken,
l Take 2-D cross-sections at different angles of cut,
l Explain the shape formed by taking 2-D cross-sections,
l Compare and contrast the figures formed when the angle of the cut changes.
Given 2-D objects,
l Conjecture about the characteristics of geometric shapes formed from rotating a 2-D shape about a line,
l Rotate the object about given lines,
l Explain the 3-D objects formed if the 2-D object is rotated about a line.l Two-dimensional cross-sections
l Two-dimensional objects
l Three-dimensional objects
l RotationsStudents know:
l Characteristics of 2-D and 3-D geometric objects,
l Techniques for finding a cross-section of a 3-D object,
l Techniques for rotating a 2-D object about a line.Students are able to:
l Conjecture about the characteristics of geometric shapes formed from taking a cross-section of a 3-D shape, or rotating a 2-D shape about a line,
l Accurately determine the geometric shapes formed from taking a cross-section of a 3-D shape, or rotating a 2-D shape about a line.Students understand that:
l 3-D objects can be created from 2-D plane figures through transformations such as rotations,
l Cross-sections of 3-D objects can be formed in a variety of ways, depending on the angle of the cut with the base of the object.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54235" \t "_blank" ALEX Resources40. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).&Modeling with GeometryApply geometric concepts in modeling situations.GeometryG-MG.1Students: Given a real-world object,
l Select an appropriate geometric shape to model the object,
l Provide a description of the object through the measures and properties of the geometric shape which is modeling the object,
l Explain and justify the model which was selected.Students know:
l Techniques to find measures of geometric shapes,
l Properties of geometric shapes.Students are able to:
l Model a real-world object through the use of a geometric shape,
l Justify the model by connecting its measures and properties to the object.Students understand that:
l Geometric shapes may be used to model real-world objects,
l Attributes of geometric figures help us identify the figures and find their measures, therefore matching these figures to real world objects allows the application of geometric techniques to real world problems.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54237" \t "_blank" ALEX Resources41. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).&Modeling with GeometryApply geometric concepts in modeling situations.GeometryG-MG.2Students:Given a contextual situation involving density,
l Model the situation by creating an average per unit of area or unit of volume,
l Generate questions raised by the model and defend answers they produce to the generated questions (e.g., should population density be given per square mile or per acre? What insights might one yield over the other?),
l Explain and justify the model in terms of the original context.l DensityStudents know:
l Geometric concepts of area and volume,
l Properties of rates,
l Modeling techniques.Students are able to:
l Accurately model a situation involving density,
l Justify how the model is an accurate representation of the given situation.Students understand that:
l Situations involving density may be modeled through a representation of a concentration per unit of area or unit of volume.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54238" \t "_blank" ALEX Resources42. 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).&Modeling with GeometryApply geometric concepts in modeling situations.GeometryG-MG.3Students:Given a contextual situation involving design problems,
l Create a geometric method to model the situation and solve the problem,
l Explain and justify the model which was created to solve the problem.l Geometric methods
l Design problemsStudents know:
l Properties of geometric shapes,
l Characteristics of a mathematical model.Students are able to:
l Accurately model and solve a design problem,
l Justify how their model is an accurate representation of the given situation.Students understand that:
l Design problems may be modeled with geometric methods,
l Geometric models may have physical constraints,
l Models represent the mathematical core of a situation without extraneous information, for the benefit in a problem solving situation.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54239" \t "_blank" ALEX Resources43. 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.Conditional Probability & the Rules of ProbabilityUnderstand independence and conditional probability and use them to interpret data. (Link to data from simulations or experiments.)Statistics & ProbabilityS-CP.3Students:Given scenarios involving two events A and B both when A and B are independent and when A and B are dependent,
l Determine the probability of each individual event, then limit the sample space to those outcomes where B has occurred and calculate the probability of A, compare the P(A) and the P(A given B), and explain the equality or difference in the original context of the problem,
l Justify that P(A given B) = P(A)"B)/P(B).l Conditional probability
l IndependenceStudents know:
l Methods to find probability of simple and compound events,
l Techniques to find conditional probability.Students are able to:
l Accurately determine the probability of simple and compound events,
l Accurately determine the conditional probability P(A given B)from a sample space or from the knowledge of P(A)"B) and the P(B).Students understand that:
l The independence of two events is determined by the effect that one event has on the outcome of another event,
l The occurrence of one event may or may not influence the likelihood that another event occurs (e.g., successive flips of a coin - the first toss exerts no influence on whether a head occurs on the second, drawing an ace from a deck changes the probability that the next card drawn is an ace).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54241" \t "_blank" ALEX Resources44. 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. 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.Conditional Probability & the Rules of ProbabilityUnderstand independence and conditional probability and use them to interpret data. (Link to data from simulations or experiments.)Statistics & ProbabilityS-CP.4Students:Given a situation in which it is meaningful to collect categorical data for two categories
l Collect data and create two-way frequency tables,
l Determine probabilities of simple events and conditional events from the table, explain whether the events are independent based on the context and the probability calculations.l Two way frequency tables
l Sample space
l Independent
l Conditional probabilitiesStudents know:
l Techniques to construct two-way frequency tables,
l Techniques to find simple and conditional probability in two-way frequency tables.Students are able to:
l Accurately construct a two-way frequency table,
l Accurately find simple and conditional probability from a two-way frequency table.Students understand that:
l Two-way frequency tables show conditional probability and can be used to test for independence.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54242" \t "_blank" ALEX Resources45. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. 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.Conditional Probability & the Rules of ProbabilityUnderstand independence and conditional probability and use them to interpret data. (Link to data from simulations or experiments.)Statistics & ProbabilityS-CP.5Students:Given a contextual situation and scenarios involving two events,
l Explain the meaning of independence from a formula perspective P(A)"B) = P(A) x P(B) and from the intuitive notion that A occurring has no impact on whether B occurs or not,
l Compare these two interpretations within the context of the scenario.l Conditional probability
l IndependenceStudents know:
l Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.Students are able to:
l Communicate the concepts of conditional probability and independence using everyday language by discussing the impact of the occurrence of one event on the likelihood of the other occurring.Students understand that:
l The occurrence of one event may or may not influence the likelihood that another event occurs (e.g., successive flips of a coin - first toss exerts no influence on whether a head occurs on the second, drawing an ace from a deck changes the probability that the next card drawn is an ace),
l Events are independent if the occurrence of one does not affect the probability of the other occurring.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54244" \t "_blank" ALEX Resources46. 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.Conditional Probability & the Rules of ProbabilityUse the rules of probability to compute probabilities of compound events in a uniform probability model.Statistics & ProbabilityS-CP.6Students:Given a contextual situation consisting of two events,
l Determine the probability of each individual event, then limit the sample space to those outcomes where B has occurred and calculate the probability of A, compare the P(A) and the P(A given B), and explain the equality or difference in the original context of the problem,
l Determine the probability of each individual event, then limit the sample space to those outcomes where B has occurred and calculate the P(A and B), compare the ratio of P(A and B) and P(B) to P(A given B), and explain the equality or difference in the original context of the problem.l Conditional probabilityStudents know:
l Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.Students are able to:
l Accurately determine the probability of simple and compound events,
l Accurately determine the conditional probability P(A given B) from a sample space or from the knowledge of P(A)"B) and the P(B).Students understand that:
l Conditional probability is the probability of an event occurring given that another event has occurred.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54247" \t "_blank" ALEX Resources47. 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.Conditional Probability & the Rules of ProbabilityUse the rules of probability to compute probabilities of compound events in a uniform probability model.Statistics & ProbabilityS-CP.7Students:Given a contextual situation consisting of two events,
l Determine the simple probability of each event,
l Determine the P(A or B) and P(A and B),
l Interpret the Addition Rule by counting outcomes in the four events A, B, A and B, A or B and showing the relationship to P(A or B) = P(A) + P(B) - P(A and B),
l Interpret the Addition Rule in the case that the P(A and B) = 0.l Addition RuleStudents know:
l Techniques for finding probabilities of simple and compound events.Students are able to:
l Accurately determine the probability of simple and compound events.Students understand that:
l Formulas are useful to generalize regularities, but must be justified,
l The Addition Rule may be used for finding compound probability.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54248" \t "_blank" ALEX Resources48. (+) 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.Conditional Probability & the Rules of ProbabilityUse the rules of probability to compute probabilities of compound events in a uniform probability model.Statistics & ProbabilityS-CP.8Students:Given a contextual situation consisting of two events A and B,
Use the definition of conditional probability P(B|A) = P(A and B)/P(A) to determine the probability of the compound event (A and B) when the P(A|B) and the P(A) are known or may be determined. Interpret the probability as it relates to the context.Uniform probability model
General Multiplication Rule
Probability
Simple events
Conditional eventsStudents know:
Techniques for finding probabilities of simple and conditional events.Students are able to:
Determine the probability of a single event.
Determine the probability of a conditional event.Students understand that:
The general Multiplication Rule for probability is a manipulation of the formula for conditional probability.
The formula P(A and B) = P(A)P(B|A) will always apply regardless of whether the events are independent or dependent.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54249" \t "_blank" ALEX Resources49. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.Conditional Probability & the Rules of ProbabilityUse the rules of probability to compute probabilities of compound events in a uniform probability model.Statistics & ProbabilityS-CP.9Students:Given a contextual situation,
Choose the appropriate counting technique (permutation or combination),
Find the number of ways an event(s) can occur,
Use these counts to determine probabilities of the event, including compound events.Permutations
Combinations
Compound events
Probability
Possible outcomesStudents know:
Order is the determining factor in whether a event requires a permutation or a combination to count the number of possible outcomes of the event.
Techniques for finding probabilities of simple and compound events.
Techniques for finding the number of permutations or combinations of an event.Students are able to:
Evaluate factorial expressions.
Apply the multiplication and addition rules to determine probabilities.
Interpret and apply the different notations for combinations and permutations.
Perform procedures to evaluate expressions involving the number of combinations and permutations of n things taken r at a time. Students understand that:
There are contextual situations that can be interpreted through the use of combinations and permutations.
The contextual situation determines whether combinations or permutations must be utilized.
Mathematics is a coherent whole. Structure within mathematics allows for procedures or models from one concept to be applied elsewhere (e.g., Pascal's triangle as it applies to the number of combinations).Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54250" \t "_blank" ALEX Resources50. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).Using Probability to Make DecisionsUse probability to evaluate outcomes of decisions. (Introductory; apply counting rules.)Statistics & ProbabilityS-MD.6Students:Given a contextual situation in which a decision needs to be made,
Use a random probability selection model to produce unbiased decisions.Fair decisions
Probability
Fair decisions
RandomStudents know:
The characteristics of a random sample.Students are able to:
Randomly select a sample from a population (using technology when appropriate).Students understand that:
Multiple factors may ultimately determine the decision one makes other than the probability of events, such as ethical constraints, social policy, or feelings of others.
Probabilities can be used to explain why a decision was considered to be fair or objective.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54252" \t "_blank" ALEX Resources51. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).Using Probability to Make DecisionsUse probability to evaluate outcomes of decisions. (Introductory; apply counting rules.)Statistics & ProbabilityS-MD.7Students:Given a contextual situation in which a decision needs to be made,
Use probability concepts to analyze, justify, and make objective decisions.ProbabilityStudents know:
Techniques for finding probabilities of simple, compound, and conditional events and from probability distributions. Students are able to:
Choose the appropriate probability concept for the given situation.
Use and apply the selected probability rule.
Communicate the reasoning behind decisions.Students understand that:
Objective decision making can be mathematically based, often using analysis involving probability concepts.
Multiple factors may ultimately determine the decision one makes other than the probability of events, such as ethical constraints, social policy, or feelings of others.Click below to access all ALEX resources aligned to this standard.
HYPERLINK "http://alex.state.al.us/all.php?std_id=54253" \t "_blank" ALEX Resources
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
HYPERLINK "http://alex.state.al.us/insight/lauderdaleco/standardprint/getstandards" \l "#" print
Geometry Mathematics CCRS Standards and Alabama COS
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