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Mathematics Content Expectations

Form A: Math Alignment Table
Alignment to Math High School Content Expectations
Math High School Content Expectations Prealgebra
Math 050 to
Summer 2006
Prealgebra
Math 050 to
Fall 2006
Introductory
Algebra
Math 107
Summer and
Fall
2006
Math 112 ACCUPLACER
Tests
STANDARD S1: UNIVARIATE DATA –
EXAMINING DISTRIBUTIONS

Students plot and analyze univariate data by
considering the shape of distributions and analyzing
outliers; they find and interpret commonly -used
measures of center and variation; and they explain
and use properties of the normal distribution.
         
S1.1 Producing and Interpreting Plots          
S1.1.1 Construct and interpret dot plots, histograms,
relative frequency histograms, bar graphs, basic
control charts , and box plots with appropriate labels
and scales; determine which kinds of plots are
appropriate for different types of data; compare data
sets and interpret differences based on graphs and
summary
statistics.
         
S1.1.2 Given a distribution of a variable in a data
set, describe its shape, including symmetry or
skewness, and state how the shape is related to
measures of center (mean and median) and
measures of variation (range and standard deviation)
with particular attention to the effects of outliers on
these measures.
         
S1.2 Measures of Center and Variation          
S1.2.1 Calculate and interpret measures of center
including: mean, median, and mode; explain uses,
advantages and disadvantages of each measure
given a particular set of data and its context.
         
S1.2.2 Estimate the position of the mean, median,
and mode in both symmetrical and skewed
distributions, and from a frequency distribution or
histogram.
         
S1.2.3 Compute and interpret measures of variation,
including percentiles, quartiles, interquartile range,
variance, and standard deviation.
         
S1.3 The Normal Distribution          
S1.3.1 Explain the concept of distribution and the
relationship between summary statistics for a data
set and parameters of a distribution.
         
S1.3.2 Describe characteristics of the normal
distribution, including its shape and the relationships
among its mean, median, and mode.
         
S1.3.3 Know and use the fact that about 68%, 95%,
and 99.7% of the data lie within one, two, and three
standard deviations of the mean, respectively in a
normal distribution.
         
S1.3.4 Calculate z-scores, use z-scores to recognize
outliers, and use z-scores to make informed
decisions.
         
STANDARD S2: BIVARIATE DATA – EXAMINING
RELATIONSHIPS
Students plot and interpret
bivariate data by constructing scatterplots,
recognizing linear and nonlinear patterns, and
interpreting correlation coefficients; they fit and
interpret regression models, using technology as
appropriate.
         
S2.1 Scatterplots and Correlation          
S2.1.1 Construct a scatterplot for a bivariate data set
with appropriate labels and scales.
         
S2.1.2 Given a scatterplot, identify patterns,
clusters, and outliers; recognize no correlation, weak
correlation, and strong correlation.
         
S2.1.3 Estimate and interpret Pearson’s correlation
coefficient for a scatterplot of a bivariate data set;
recognize that correlation measures the strength of
linear association.
         
S2.1.4 Differentiate between correlation and
causation; know that a strong correlation does not
imply a cause-and-effect relationship; recognize the
role of lurking variables in correlation.
         
S2.2 Linear Regression          
S2.2.1 For bivariate data which appear to form a
linear pattern, find the least squares regression line
by estimating visually and by calculating the equation
of the regression line; interpret the slope of the
equation
for a regression line.
         
S2.2.2 Use the equation of the least squares
regression line to make appropriate predictions.
         
STANDARD S3: SAMPLES, SURVEYS, AND
EXPERIMENTS

Students understand and apply sampling and various
sampling methods, examine surveys and
experiments, identify bias in methods of conducting
surveys, and learn strategies to minimize bias. They
understand basic principles of good experimental
design.
         
S3.1 Data Collection and Analysis          
S3.1.1 Know the meanings of a sample from a
population and a census of a population, and
distinguish between sample statistics and population
parameters.
         
S3.1.2 Identify possible sources of bias in data
collection and sampling methods and simple
experiments; describe how such bias can be reduced
and controlled by random sampling; explain the
impact of such bias on conclusions made from
analysis of the data; and know the effect of
replication on the precision of estimates.
         
S3.1.3 Distinguish between an observational study
and an experimental study, and identify, in context,
the conclusions that can be drawn from each .
         
STANDARD S4: PROBABILITY MODELS AND
PROBABILITY CALCULATION

Students understand probability and find probabilities
in various situations, including those involving
compound events , using diagrams, tables, geometric
models and counting strategies; they apply the
concepts of probability to make decisions.
         
S4.1 Probability          
S4.1.1 Understand and construct sample spaces in
simple situations (e.g., tossing two coins, rolling two
number cubes and summing the results).
         
S4.1.2 Define mutually exclusive events,
independent events, dependent events, compound
events, complementary events and conditional
probabilities; and use the to compute probabilities.
         
S4.2 Application and Representation          
S4.2.1 Compute probabilities of events using tree
diagrams, formulas for combinations and
permutations
, Venn diagrams, or other counting
techniques.
         
S4.2.2 Apply probability concepts to practical
situations, in such settings as finance, health,
ecology, or epidemiology, to make informed
decisions.
         
RECOMMENDED:          
*S3.1.4 Design simple experiments or investigations
to collect data to answer questions of interest;
interpret and present results.
         
*S3.1.5 Understand methods of sampling, including
random sampling, stratified sampling, and
convenience samples, and be able to determine, in
context, the advantages and disadvantages of each.
         
*S3.1.6 Explain the importance of randomization,
double-blind protocols, replication, and the placebo
effect in designing experiments and interpreting the
results of studies.
         
*S3.2.1 Explain the basic ideas of statistical process
control, including recording data from a process over
time.
         
*S3.2.2 Read and interpret basic control charts;
detect patterns and departures from patterns.
         
*S4.1.3 Design and carry out an appropriate
simulation using random digits to estimate answers
to questions about probability; estimate probabilities
using results of a simulation; compare results of
simulations to theoretical probabilities.
         

 

11/15/2006 bls BUSINESS and ED          
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