Standard
4.11:
All Students Will Develop An Understanding Of Patterns,
Relationships, And Functions And Will Use Them To Represent
And Explain Real-World Phenomena |
Standard
4.12:
All Students Will Develop An Understanding Of Statistics
And Probability And Will Use Them To Describe Sets Of Data,
Model Situations, And Support Appropriate Inferences And
Arguments |
|
Descriptive Statement:
Patterns, relationships, and functions constitute
a unifying theme of mathematics. From the earliest age,
students should be encouraged to investigate the patterns
that they find in numbers, shapes, and expressions, and,
by doing so, to make mathematical discoveries. They should
have opportunities to analyze, extend, and create a variety
of patterns and to use pattern-based thinking to understand
and represent mathematical and other real-world phenomena.
These explorations present unlimited opportunities for
problem-solving, making and verifying generalizations,
and building mathematical understanding and confidence.
Building upon knowledge and skills gained in the preceding
grades, by the end of grade 12, students: |
Descriptive Statement:
Probability and statistics are the mathematics used
to understand chance and to collect, organize,
describe, and analyze numerical data. From weather reports
to sophisticated studies of genetics, from election results
to product preference surveys, probability and statistical
language and concepts are increasingly present in the
media and in everyday conversations. Students need this
mathematics to help them judge the correctness of an argument
supported by seemingly persuasive data.
Building upon knowledge and skills gained in the preceding
grades, and demonstrating continued progress in Indicator
6
above, by the end of grade 12, students: |
|
Cumulative Progress Indicators
| 14. |
Analyze and describe
how a change in an independent variable can
produce a change in a dependent variable. |
| 15. |
Use polynomial, rational,
trigonometric, and exponential functions to model
real-world phenomena. |
| 16. |
Recognize that a variety
of phenomena can be modeled by the same
type of function. |
| 17. |
Analyze and explain
the general properties and behavior of
functions, and use appropriate graphing technologies
to represent
them. |
| 18. |
Analyze the effects
of changes in parameters on the graphs of
functions. |
| 19. |
Understand the role
of functions as a unifying concept in
mathematics. |
|
Cumulative Progress Indicators
| 17. |
Estimate probabilities and predict outcomes
from actual data. |
| 18. |
Understand sampling and recognize its
role in statistical claims. |
| 19. |
Evaluate bias, accuracy, and reasonableness
of data in real-world
contexts. |
| 20. |
Understand and apply measures of dispersion
and correlation. |
| 21. |
Design a statistical experiment to study
a problem, conduct the experiment, and interpret and
communicate the outcomes. |
| 22. |
Make predictions using curve fitting
and numerical procedures to
interpolate and extrapolate from known data. |
| 23. |
Use relative frequency and probability,
as appropriate, to represent
and solve problems involving uncertainty. |
| 24. |
Use simulations to estimate probabilities. |
| 25. |
Create and interpret discrete and continuous
probability distributions,
and understand their application to real-world situations. |
| 26. |
Describe the normal curve in general
terms, and use its properties to
answer questions about sets of data that are assumed
to be normally
distributed. |
| 27. |
Understand and use the law of large numbers
(that experimental
results tend to approach theoretical probabilities
after a large number of trials). |
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