May 24th
May 24th
High School Math A & B
Key Idea 4
Modeling/Multiple Representation
Students use mathematical modeling/multiple representation
to provide a means
of presenting, interpreting, communicating, and connecting mathematical
information
and relationships.
| PERFORMANCE INDICATORS |
INCLUDES |
EXAMPLES |
4A. Represent problem situations symbolically
by using algebraic expressions,
sequences, tree diagrams, geometric figures,
and graphs. |
• Use of variables/Algebraic representations.
• Inequalities.
• Formulas and literal equations.
• Undefined terms: point, line, and p l a n e.
• Parallel and intersecting lines and
perpendicular lines.
• Angles: degree measure, right,
acute, obtuse, straight, supplementary,
complementary, vertical, alternate
interior and exteriors, and
corresponding.
• Simple closed curves : polygons
and circles.
• Sum of interior and exterior angles
of a polygon.
• Study of triangles: classifications of
scalene, isosceles, equilateral,
acute, obtuse, and right; triangular
inequality; sum of the measures of
angles of a triangle; exterior angle
of a triangle, base angles of an
isosceles triangle.
• Study of quadrilaterals: classification
and properties of paralle lograms ,
rectangles, rhombi, squares,
and trapezoids.
• Study of solids: classification of prism,
rectangular solid, pyramid, right circular
cylinder, cone, and sphere .
• Sample spaces: list of ordered pairs
of n-tuples, tree diagrams. |
See Assessment Example 4A. |
4B. Justify the procedures for basic geometric
constructions. |
• Basic constructions: copy line and
angle, bisect line segment and
angle, perpendicular lines and parallel
lines.
• Comparison of triangles : congruence
and similarity. |
See Classroom Idea 4B. |
4C. Use transformations in the coordinate
plane. |
• Reflection in a line and in a point.
• Translations.
• Dilations |
See Assessment Example 4C. |
4D. Develop and apply the concept of basic
loci to compound loci. |
• Locus.
• At a fixed distance from a point.
• At a fixed distance from a line.
• Equidistant from two points.
• Equidistant from two parallel lines.
• Equidistant from two intersecting
lines.
• Compound locus. |
See Assessment Example 4D. |
4E. Model real-world problems with systems
of equations and inequalities. |
• Systems of linear equations and
inequalities. |
See Assessment Example 4E. |
Key Idea 5
Measurement
Students use measurement in both metric and English
measure to provide a major
link between the abstractions of mathematics and the real world in order to
describe and compare objects and data.
| PERFORMANCE INDICATORS |
INCLUDES |
EXAMPLES |
5A. Apply formulas to find measures such as
length, area, volume, weight, time, and
angle in real-world contexts. |
• Perimeter of polygons and circumference
of circles.
• Area of polygons and circles.
• Volume of solids.
• Pythagorean theorem. |
See Assessment Example 5A. |
5B. Choose and apply appropriate units and
tools in measurement situations. |
• Converting to equivalent measurements
within metric and English
measurement systems.
• Direct and indirect measure. |
See Classroom Idea 5B. |
| 5C. Use dimensional analysis techniques. |
• Dimensional analysis. |
See Assessment Example 5C. |
5D. Use statistical methods including the
measures
of central tendency to describe and
compare data. |
• Collecting and organizing data:
sampling, tally, chart , frequency
table, circle graphs , broken line
graphs, frequency histogram, box
and whisker plots, scatter plots,
stem and leaf plots, and cumulative
frequency histogram.
• Measures of central tendency:
mean, median, mode.
• Quartiles and percentiles. |
See Assessment Example 5D. |
5E. Use trigonometry as a method to measure
indirectly. |
• Right triangle trigonometry. |
See Assessment Example 5E. |
5F. Apply proportions to scale drawings and
direct variation. |
• Ratio.
• Proportion.
• Scale drawings.
• Percent.
• Similar figures.
• Similar polygons: ratio of perimeters
and areas.
• Direct variation. |
See Assessment Example 5F. |
5G. Relate absolute value, distance between
two points, and the slope of a line to the
coordinate plane. |
• Absolute value and length of a line
segment.
• Midpoint of a segment.
• Equation of a line: point-slope and
slope intercept form.
• Comparison of parallel and perpendicular
lines. |
See Assessment Example 5G. |
5H. Explain the role of error in measurement
and its consequence on subsequent
calculations. |
• Error of measurement and its consequences
on calculation of
perimeter of polygons and circumference
of circles.
• Area of polygons and circles.
• Volume of solids.
• Percent of error in measurements. |
See Classroom Idea 5H. |
5I. Use geometric relationships in relevant
measurement problems involving geometric
concepts. |
• Similar polygons: ratio of perimeters
and areas.
• Similar figures.
• Comparison of volumes of similar
solids. |
See Assessment Example 5I. |
Key Idea 6
Uncertainty
Students use ideas of uncertainty to illustrate that
mathematics involves more than
exactness when dealing with everyday situations.
| PERFORMANCE INDICATORS |
INCLUDES |
EXAMPLES |
6A. Judge the reasonableness of results
obtained from applications in algebra,
geometry, trigonometry, probability, and
statistics. |
6A. Judge the reasonableness of results
obtained from applications in algebra,
geometry, trigonometry, probability, and
statistics. |
See Classroom Idea 6A. |
6B. Use experimental and theoretical probability
to represent and solve problems
involving uncertainty. |
• Single and compound events.
• Problems involving and and or.
• Probability of the complement of
an event. |
See Assessment Example 6B. |
6C. Use the concept of random variable in
computing probabilities. |
• Mutually exclusive and independent
events.
• Counting principle.
• Sample space.
• Probability distribution.
• Probability of the complement of
an event. |
See Assessment Example 6C. |
6D. De termine probabilities , using permutations
and combinations . |
• Factorial notation.
• Permutations: nPn and nPr.
• Combinations: nCn and nCr. |
See Assessment Example 6D. |
Key Idea 7
Patterns/Functions
Students use patterns and functions to develop
mathematical power, appreciate the
true beauty of mathematics, and construct generalizations that describe patterns
simply and efficiently.
| PERFORMANCE INDICATORS |
INCLUDES |
EXAMPLES |
7A. Represent and analyze functions, using
verbal descriptions, tables, equations, and
graphs. |
• Techniques for solving equations
and inequalities.
• Techniques for solving factorable
quadratic equations.
• Graphs of linear relations: slope
and intercept.
• Graphs of conics: circle and
parabola .
• Graphic solution of systems of linear
equations, inequalities, and
quadratic-linear pair.
• Algebraic solution of systems of
linear equations, inequalities, and
quadratic-linear pair by substitution
method and addition -subtraction
method. |
See Assessment Example 7A. |
7B. Apply linear and quadratic functions in
the solution of problems.7C. Translate among the verbal descriptions,
tables, equations, and graphic forms of
functions. |
• Graphic and algebraic solutions of
linear and quadratic functions in
the solution of problems. |
See Assessment Example 7B. |
7C. Translate among the verbal descriptions,
tables, equations, and graphic forms of
functions. |
• Translate linear and quadratic functions,
systems of equations,
inequalities and quadratic linear
pairs between representations that
are verbal descriptions, tables,
equations, or graphs. |
See Assessment Example 7C. |
7D. Model real-world situations with the
appropriate function. |
• Determine and model real-life situations
with appropriate functions. |
See Assessment Example 7D. |
| 7E. Apply axiomatic structure to algebra. |
• Solve linear equations with integral,
fraction , or decimal coefficients.
• Solve linear inequalities.
• Solve factorable quadratic equations.
• Solve systems of linear equations,
inequalities, and quadratic-linear
pair. |
See Assessment Example 7E. |
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