Geometry for Teachers, Math 257, Kriloff
Objectives
Section 9.1
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Know basic facts about probability and definitions of key terms.
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Be able to compute basic probabilities.
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Understand the difference between exact and experimental probabilities
and the issue of constructing and testing a model for an experimental probability.
Section 9.2
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Know the definition of an event and properties of probabilities of events.
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Be able to calculate probabilities of events.
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Be able to record data and estimate probabilities from a simulation.
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Be able to explain clearly in words how to set up a simulation to estimate
the probability of a given event.
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Know basic properties of probabilities of events.
Section 9.3
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Be able to construct a tree for a multistage experiment with or without
replacement.
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Know how to compute probabilities of outcomes or events in a multistage
experiment using a probability tree or using the multiplication rule for
probabilities.
Section 9.4
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Be able to compute numbers of combinations where order does and does not
matter.
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Be able to compute probabilities of events when there are many equally
likely outcomes using numbers of combinations.
Section 9.5
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Know how to compute expected values and decide whether a game is fair or
not.
Section 10.1
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Know basic types of graphs, diagrams, and plots, and advantages and disadvantages
of each.
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Be able to identify ways in which a graph is misleading or clear.
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Be able to construct plots of data.
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Be able to read information from a graph, diagram, or plot.
Section 10.2
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Know how to compute the mean, median, and mode of a set of data.
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Understand the effects of outlying data on the mean, median, and mode.
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Know how to compute lower and upper quartiles.
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Be able to construct and interpret box and whisker plots.
Section 10.3
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Know how to compute variance and standard deviation.
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Understand the effects of shifting or scaling data on the mean and standard
deviation.
Section 10.4
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Know the shape and properties of normally distributed data.
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Know and be able to use or find percentages of data in certain ranges assuming
data is normally distributed.
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Understand the purpose of z-scores and how to find them.
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Be aware that proper and careful analysis of data depends on a deep study
of statistics and probability.
Section 11.1
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Know some reasons why it is important to study geometry.
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Know what ideal figures are meant by point, line, plane, space.
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Know what is meant by the adjectives (non)intersecting, (non)collinear,
(non)concurrent, coplanar, parallel, and skew, and be able to use
them correctly.
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Be able to look for patterns and make conjectures based on examples of
simple geometric relationships.
Section 11.2
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Know and be able to correctly use definitions of half line, ray, and types
of segments.
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Know and be able to correctly use definitions of half planes; angle; vertex,
sides, interior, and exterior of angles; adjacent angles; linear pair;
vertical angles.
Section 11.3
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Know and be able to correctly use definitions of:
types of curves (planar, closed, simple, simple closed)
types of polygons (triangle, quadrilateral, pentagon, etc.)
connected, convex, dimensions.
Section 12.1
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Know what it means for two figures to be congruent.
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Know how to perform rigid motions
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Know how to specify rigid motions precisely in words.
Section 12.2
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Know and understand basic properties of a measure function.
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Understand the importance of using standardized units in measurement and
the need to report units.
Section 12.3
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Know standard formulas for linear measurements (including arc length) and
why they are true.
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Be able to use standard formulas to calculate linear measurements (including
arc length).
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Know how to report linear measurements correctly.
Section 12.4
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Know standard formulas for area measurements (including surface area of
figures in space) and why they are true.
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Be able to use standard formulas to calculate area measurements of two
dimensional figures in the plane and in space.
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Know how to report area measurements correctly.
Section 12.5
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Know standard formulas for volumes of prisms, cylinders, cones, sphere
and believe those for the first three.
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Be able to use standard formulas to calculate volume measurements.
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Be able to report volume measurements correctly.
Section 13.1
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Know basic properties of measures of angles.
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Be able to use basic properties to find measures of angles.
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Know how to use notation for angles and measures of angles correctly.
Section 13.2
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Know the names, shapes, and properties of basic polygons and polyhedra.
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Be able to classify polygons.
Section 13.3
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Know the basic units in the metric system.
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Be able to compare and convert between and within metric units and standard
units.
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Have an intuitive sense for the sizes of metric units.
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Be able to make calculations using metric or customary units using dimensional
analysis.
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Know how to calculate using smaller units of angle measure.
Section 13.4
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Know the difference between precision and accuracy.
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Be able to calculate precision unit, greatest possible error, and relative
error.
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Be able to compare precision and accuracy of measurements and know when
measurements are incomparable.
Section 13.5
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Be able to describe symmetries precisely in words.
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Be able to list all symmetries of a figure.
Section 14.1
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Be able to perform basic constructions with compass and straightedge.
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Be able to combine basic constructions to construct other geometric objects.
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Understand the technical meaning of the term constructible.
Section 14.2
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Know the parallel postulate and definitions of transversal, alternate interior
angles, alternate exterior angles, and corresponding angles.
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Know that lines are parallel if and only if any pair of such angles are
congruent.
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Know how to construct parallel lines and partition a segment.
Section 14.3
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Know and understand the six basic angle properties given in this section.
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Be able to use the properties to justify or construct arguments or make
calculations.
Section 14.4
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Know which side and angle conditions guarantee congruence and which do
not.
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Be able to correctly conclude and report congruence using conditions like
SAS, ASA, SSS, and CPCTC.
Section 14.6
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Be able to scale a drawing given a projection point and scale factor.
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Be able to locate the projection point and find the scale factor given
two similar figures.
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Know the effect of dilation on length, area, volume, and angle measure.
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Be able to calculate lengths, areas, and volumes using similarity.
Section 14.7
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Know the relationships between corresponding sides and angles of similar
triangles.
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Know and understand the similarity criteria SAS, SSS, AA.
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Be able to use the similarity criteria to draw conclusions or make calculations.