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Mathematics for College Statistics
Version Description
In Mathematics for College Statistics, instructional time will emphasize four areas:
(1) analyzing and applying linear and exponential functions within the context of
statistics;
( 2 ) extending understanding of probability using data and various representations,
including two-way tables and Venn Diagrams;
( 3 ) representing and interpreting univariate and bivariate categorical and numerical data
and
( 4 ) determining the appropriateness of different types of statistical studies.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and
workforce-literacy skills; communication, reading, and writing skills; mathematics skills;
collaboration skills; contextual and applied-learning skills; technology-literacy skills;
information and media-literacy skills; and civic-engagement skills.
All clarifications stated, whether general or specific to Mathematics for College Statistics, are
expectations for instruction of that benchmark.
General Notes
Florida’s Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards: This course includes
Florida’s B.E.S.T. ELA Expectations (EE) and Mathematical Thinking and Reasoning Standards
(MTRs) for students. Florida educators should intentionally embed these standards within the
content and their instruction as applicable. For guidance on the implementation of the EEs and
MTRs, please visit https://www.cpalms.org/Standards/BEST_Standards.aspx and select the
appropriate B.E.S.T. Standards package.
English Language Development ELD Standards Special Notes Section: Teachers are required to
provide listening, speaking, reading and writing instruction that allows English language learners
(ELL) to communicate information, ideas and concepts for academic success in the content area
of Mathematics. For the given level of English language proficiency and with visual, graphic, or
interactive support, students will interact with grade level words, expressions, sentences and
discourse to process or produce language necessary for academic success. The ELD standard
should specify a relevant content area concept or topic of study chosen by curriculum developers
and teachers which maximizes an ELL’s need for communication and social skills. To access an
ELL supporting document which delineates performance definitions and descriptors, please click
on the following link:
https://cpalmsmediaprod.blob.core.windows.net/uploads/docs/standards/eld/ma.pdf.
General Information
Course Number: 12 10305 Course Type: Core Academic Course
Course Length: Year (Y) Course Level: 2
Grade Level(s): 9, 10, 11, 12
Graduation Requirement: Mathematics Number of Credits: One (1) credit
Course Path: Section | Grades PreK to 12 Education Courses > Grade Group | Grades 9 to 12
and Adult Education Courses > Subject | Mathematics > SubSubject | Probability
and Statistics > Abbreviated Title | MATH FOR COLL STATS
Educator Certification: Mathematics (Grades 6-12)
Course Standards and Benchmarks
Mathematical Thinking and Reasoning
MA.K12.MTR.1.1 Actively participate in effortful learning both individually and
collectively.
Mathematicians who participate in effortful learning both individually and with others:
Analyze the problem in a way that makes sense given the task.
Ask questions that will help with solving the task.
Build perseverance by modifying methods as needed while solving a challenging task.
Stay engaged and maintain a positive mindset when working to solve tasks.
Help and support each other when attempting a new method or approach.
Clarifications:
Teachers who encourage students to participate actively in effortful learning both individually and
with others:
Cultivate a community of growth mindset learners.
Foster perseverance in students by choosing tasks that are challenging.
Develop students’ ability to analyze and problem solve.
Recognize students’ effort when solving challenging problems.
MA.K12.MTR.4.1 Engage in discussions that reflect on the mathematical thinking of self
and others.
Mathematicians who engage in discussions that reflect on the mathematical thinking of self
and others:
Communicate mathematical ideas, vocabulary and methods effectively.
Analyze the mathematical thinking of others.
Compare the efficiency of a method to those expressed by others.
Recognize errors and suggest how to correctly solve the task.
Justify results by explaining methods and processes.
Construct possible arguments based on evidence.
Clarifications:
Teachers who encourage students to engage in discussions that reflect on the mathematical thinking of
self and others:
Establish a culture in which students ask questions of the teacher and their peers, and error is an
opportunity for learning.
Create opportunities for students to discuss their thinking with peers.
Select, sequence and present student work to advance and deepen understanding of correct and
increasingly efficient methods.
Develop students’ ability to justify methods and compare their responses to the responses of their
peers.
MA.K12.MTR.5.1 Use patterns and structure to help understand and connect
mathematical concepts.
Mathematicians who use patterns and structure to help understand and connect mathematical
concepts:
Focus on relevant details within a problem.
Create plans and procedures to logically order events, steps or ideas to solve problems.
Decompose a complex problem into manageable parts.
Relate previously learned concepts to new concepts.
Look for similarities among problems.
Connect solutions of problems to more complicated large-scale situations.
Clarifications:
Teachers who encourage students to use patterns and structure to help understand and connect
mathematical concepts:
Help students recognize the patterns in the world around them and connect these patterns to
mathematical concepts.
Support students to develop generalizations based on the similarities found among problems.
Provide opportunities for students to create plans and procedures to solve problems.
Develop students’ ability to construct relationships between their current understanding and more
sophisticated ways of thinking.
MA.K12.MTR.6.1 Assess the reasonableness of solutions.
Mathematicians who assess the reasonableness of solutions:
Estimate to discover possible solutions.
Use benchmark quantities to determine if a solution makes sense.
Check calculations when solving problems.
Verify possible solutions by explaining the methods used.
Evaluate results based on the given context.
Clarifications:
Teachers who encourage students to assess the reasonableness of solutions:
Have students estimate or predict solutions prior to solving.
Prompt students to continually ask, “Does this solution make sense? How do you know?”
Reinforce that students check their work as they progress within and after a task.
Strengthen students’ ability to verify solutions through justifications.
MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
Mathematicians who apply mathematics to real-world contexts:
Connect mathematical concepts to everyday experiences.
Use models and methods to understand, represent and solve problems.
Perform investigations to gather data or determine if a method is appropriate.
Redesign models and methods to improve accuracy or efficiency.
Clarifications:
Teachers who encourage students to apply mathematics to real-world contexts:
Provide opportunities for students to create models, both concrete and abstract, and perform
investigations.
Challenge students to question the accuracy of their models and methods.
Support students as they validate conclusions by comparing them to the given situation.
Indicate how various concepts can be applied to other disciplines.
ELA Expectations
ELA.K12.EE.1.1 Cite evidence to explain and justify reasoning.
ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.
ELA.K12.EE.3.1 Make inferences to support comprehension.
ELA.K12.EE.4.1 Use appropriate collaborative techniques and active listening skills
when engaging in discussions in a variety of situations.
MA.912.AR.1.2 Rearrange equations or formulas to isolate a quantity of interest.
𝑃𝑉
Algebra 1 Example: The Ideal Gas Law 𝑃𝑉 = 𝑛𝑅𝑇 can be rearranged as 𝑇 = to
𝑛𝑅
isolate temperature as the quantity of interest.
𝑛𝑡
𝑟
Example: Given the Compound Interest formula 𝐴 = 𝑃 ( 1 + ) , solve for 𝑃.
𝑛
Mathematics for Data and Financial Literacy Honors Example: Given the
𝑛𝑡
𝑟
Compound Interest formula 𝐴 = 𝑃 ( 1 + ) , solve for 𝑡.
𝑛
Benchmark Clarifications:
Clarification 1: Instruction includes using formulas for temperature, perimeter, area and volume; using
equations for linear (standard, slope-intercept and point-slope forms) and quadratic (standard, factored
and vertex forms) functions.
Clarification 2 : Within the Mathematics for Data and Financial Literacy course, problem types focus on
money and business.
MA.912.AR.2 Write, solve and graph linear equations, functions and inequalities in one
and two variables.
Solve and graph mathematical and real-world problems that are modeled with
MA.912.AR.2.5 linear functions. Interpret key features and determine constraints in terms of
the context.
Algebra 1 Example: Lizzy’s mother uses the function 𝐶(𝑝) = 450 + 7. 75 𝑝, where
𝐶(𝑝) represents the total cost of a rental space and 𝑝 is the
number of people attending, to help budget Lizzy’s 16
th
birthday
party. Lizzy’s mom wants to spend no more than $850 for the
party. Graph the function in terms of the context.
Benchmark Clarifications:
Clarification 1: Key features are limited to domain, range, intercepts and rate of change.
Clarification 2 : Instruction includes the use of standard form, slope-intercept form and point-slope form.
Clarification 3: Instruction includes representing the domain, range and constraints with inequality
notation, interval notation or set-builder notation.
Clarification 4 : Within the Algebra 1 course, notations for domain, range and constraints are limited to
inequality and set-builder.
Clarification 5 : Within the Mathematics for Data and Financial Literacy course, problem types focus on
money and business.
MA.912.AR.5 Write, solve and graph exponential and logarithmic equations and
functions in one and two variables.
Solve and graph mathematical and real-world problems that are modeled with
MA.912.AR.5.7 exponential functions. Interpret key features and determine constraints in
terms of the context.
Example: The graph of the function 𝑓(𝑡) = 𝑒
5 𝑡+ 2
can be transformed into the
straight line 𝑦 = 5 𝑡 + 2 by taking the natural logarithm of the function’s
outputs.
Benchmark Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is
increasing, decreasing, positive or negative; constant percent rate of change; end behavior and
asymptotes.
Clarification 2 : Instruction includes representing the domain, range and constraints with inequality
notation, interval notation or set-builder notation.
Clarification 3: Instruction includes understanding that when the logarithm of the dependent variable is
taken and graphed, the exponential function will be transformed into a linear function.
Clarification 4 : Within the Mathematics for Data and Financial Literacy course, problem types focus on
money and business.
Functions
MA.912.F.1 Understand, compare and analyze properties of functions.
Given a function represented in function notation, evaluate the function for an
MA.912.F.1.
input in its domain. For a real-world context, interpret the output.
Algebra 1 Example: The function 𝑓(𝑥) =
𝑥
− 8 models Alicia’s position in miles
7
relative to a water stand 𝑥 minutes into a marathon. Evaluate and
interpret for a quarter of an hour into the race.
Benchmark Clarifications:
Clarification 1: Problems include simple functions in two-variables, such as 𝑓(𝑥, 𝑦) = 3 𝑥 − 2 𝑦.
Clarification 2: Within the Algebra 1 course, functions are limited to one-variable such as 𝑓(𝑥) = 3 𝑥.
Data Analysis and Probability
MA.912.DP.1 Summarize, represent and interpret categorical and numerical data with
one and two variables.
Given a set of data, select an appropriate method to represent the data,
MA.912.DP.1.1 depending on whether it is numerical or categorical data and on whether it is
univariate or bivariate.
Benchmark Clarifications:
Clarification 1: Instruction includes discussions regarding the strengths and weaknesses of each data
display.
Clarification 2: Numerical univariate includes histograms, stem-and-leaf plots, box plots and line plots;
numerical bivariate includes scatter plots and line graphs; categorical univariate includes bar charts,
circle graphs, line plots, frequency tables and relative frequency tables; and categorical bivariate
includes segmented bar charts, joint frequency tables and joint relative frequency tables.
Clarification 3: Instruction includes the use of appropriate units and labels and, where appropriate, using
technology to create data displays.
Interpret data distributions represented in various ways. State whether the
MA.912.DP.1.
data is numerical or categorical, whether it is univariate or bivariate and
interpret the different components and quantities in the display.
Benchmark Clarifications:
Clarification 1: Within the Probability and Statistics course, instruction includes the use of spreadsheets
and technology.
Explain the difference between correlation and causation in the contexts of
MA.912.DP.1.
both numerical and categorical data.
Algebra 1 Example: There is a strong positive correlation between the number of
Nobel prizes won by country and the per capita chocolate
consumption by country. Does this mean that increased
chocolate consumption in America will increase the United
States of America’s chances of a Nobel prize winner?
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data.
For two or more sets of numerical univariate data, calculate and compare the
appropriate measures of center and measures of variability, accounting for
MA.912.DP.2.
possible effects of outliers. Interpret any notable features of the shape of the
data distribution.
Benchmark Clarifications:
Clarification 1: The measure of center is limited to mean and median. The measure of variation is
limited to range, interquartile range, and standard deviation.
Clarification 2: Shape features include symmetry or skewness and clustering.
Clarification 3 : Within the Probability and Statistics course, instruction includes the use of spreadsheets
and technology.
Fit a linear function to bivariate numerical data that suggests a linear
MA.912.DP.2. 4 association and interpret the slope and 𝑦-intercept of the model. Use the
model to solve real-world problems in terms of the context of the data.
Benchmark Clarifications:
Clarification 1: Instruction includes fitting a linear function both informally and formally with the use of
technology.
Clarification 2: Problems include making a prediction or extrapolation, inside and outside the range of
the data, based on the equation of the line of fit.
Given a scatter plot that represents bivariate numerical data, assess the fit of a
MA.912.DP.2. 5
given linear function by plotting and analyzing residuals.
Benchmark Clarifications:
Clarification 1: Within the Algebra 1 course, instruction includes determining the number of positive
and negative residuals; the largest and smallest residuals; and the connection between outliers in the data
set and the corresponding residuals.
Given a scatter plot with a line of fit and residuals, determine the strength and
MA.912.DP.2. 6 direction of the correlation. Interpret strength and direction within a real-
world context.
Benchmark Clarifications:
Clarification 1: Instruction focuses on determining the direction by analyzing the slope and informally
determining the strength by analyzing the residuals.
Compute the correlation coefficient of a linear model using technology.
MA.912.DP.2. 7 Interpret the strength and direction of the correlation coefficient.
Given marginal and conditional relative frequencies, construct a two-way
MA.912.DP.3.
relative frequency table summarizing categorical bivariate data.
Algebra 1 Example: A study shows that 9% of the population have diabetes and 91%
do not. The study also shows that 95% of the people who do not
have diabetes, test negative on a diabetes test while 80% who do
have diabetes, test positive. Based on the given information, the
following relative frequency table can be constructed.
Positive Negative Total
Has diabetes 7.2% 1.8% 9%
Doesn’t
have 4.55% 86.45% 91%
diabetes
Benchmark Clarifications:
Clarification 1 : Construction includes cases where not all frequencies are given but enough are provided
to be able to construct a two-way relative frequency table.
Clarification 2: Instruction includes the use of a tree diagram when calculating relative frequencies to
construct tables.
MA.912.DP.3.5 Solve real-world problems involving univariate and bivariate categorical data.
Benchmark Clarifications:
Clarification 1: Instruction focuses on the connection to probability.
Clarification 2: Instruction includes calculating joint relative frequencies or conditional relative
frequencies using tree diagrams.
Clarification 3: Graphical representations include frequency tables, relative frequency tables, circle
graphs and segmented bar graphs.
MA.912.DP.4 Use and interpret independence and probability.
Describe events as subsets of a sample space using characteristics, or
categories, of the outcomes, or as unions, intersections or complements of
MA.912.DP.4.
other events.
MA.912.DP.4.
Determine if events A and B are independent by calculating the product of
their probabilities.
MA.912.DP.4.
Calculate the conditional probability of two events and interpret the result in
terms of its context.
MA.912.DP.4.4 Interpret the independence of two events using conditional probability.
Given a two-way table containing data from a population, interpret the joint
and marginal relative frequencies as empirical probabilities and the
MA.912.DP.4.5 conditional relative frequencies as empirical conditional probabilities. Use
those probabilities to determine whether characteristics in the population are
approximately independent.
Example: A company has a commercial for their new grill. A population of people
are surveyed to determine whether or not they have seen the commercial
and whether or not they have purchased the product. Using this data,
calculate the empirical conditional probabilities that a person who has
seen the commercial did or did not purchase the grill.
Benchmark Clarifications:
Clarification 1: Instruction includes the connection between mathematical probability and applied
statistics.
MA.912.DP.4.
Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations.
MA.912.DP.4.
Apply the addition rule for probability, taking into consideration whether the
events are mutually exclusive, and interpret the result in terms of the model
and its context.
MA.912.DP.4.
Apply the general multiplication rule for probability, taking into
consideration whether the events are independent, and interpret the result in
terms of the context.
Apply the addition and multiplication rules for counting to solve
mathematical and real-world problems, including problems involving
MA.912.DP.4.
probability.
Given a mathematical or real-world situation, calculate the appropriate
MA.912.DP.4.10 permutation or combination.
MA.912.DP.5 Determine methods of data collection and make inferences from collected
data.
MA.912.DP.5.1 Distinguish between a population parameter and a sample statistic.
Explain how random sampling produces data that is representative of a
MA.912.DP.5.2 population.
Logic and Discrete Theory
MA.912.LT.5 Apply properties from Set Theory to solve problems.
Perform the set operations of taking the complement of a set and the union,
MA.912.LT.5.
intersection, difference and product of two sets.
Benchmark Clarifications:
Clarification 1: Instruction includes the connection to probability and the words AND, OR and NOT.
Explore relationships and patterns and make arguments about relationships
MA.912.LT.5.5 between sets using Venn Diagrams.
