Common Core High School Statistics & Probability Teaching and Learning Resources
Domain: IC: Making Inferences and Justifying Conclusions
Select the cluster for resources on this page:
IC-A: Understand and evaluate random processes underlying
statistical experiments
IC-B: Make inferences and justify conclusions from sample surveys,
experiments, and observational studies
IC-A: Understand and evaluate random processes underlying
statistical experiments
Standards:
- IC-A.1. Understand statistics as a process
for making inferences about population parameters based on a random
sample from that population.
- IC-A.2. Decide if a specified model is
consistent with results from a given data-generating process, e.g.,
using simulation. For example, a model says a spinning coin falls
heads up with probability 0.5. Would a result of 5 tails in a row
cause you to question the model?
Technology-enhanced investigations:
Stattrek.com Statistics Dictionary contains the following key vocabulary for this domain.
Select the term from the Stattrek pull-down menu. Use with IC-A, IC-B:
|
experiment |
observational study |
population |
mean |
|
margin of error |
parameter |
random sample |
statistics |
|
significance level |
randomization |
sample survey |
treatment |
Calculator.net:
Sample
Size Calculator
Imagine Learning Classroom (formerly LearnZillion) subscription
needed:
- Lesson set:
Understand statistics as a process for making inferences:
Seven video lessons: Distinguish between population and sample,
take a simple random sample; take a systematic, stratified,
convenience, voluntary sample; choose a sampling method given a
situation. Aligns with IC-A.1.
- Lesson set:
Understand statistics as a process for making inferences about
populations: Four video lessons: Determine the population
and parameter from a statistical question, take a random sample,
obtain a random sample from a simulation, reduce variation by
increasing sample size. Aligns with IC-A.1.
- Lesson set:
Decide if a model is consistent with results: Five video
lessons: Test a model using samples, using a simulation with
random numbers, using a simple simulation, against given
results; test a hypothesis for a population parameter.
Aligns with IC-A.2.
- Lesson set:
Decide if a specified model is consistent with results: Four
video lessons: Compare theoretical and empirical results,
explain and use the Law of Large Numbers, evaluate the
effectiveness of a treatment, design a simulation. Aligns
with IC-A.2.
MIT BLOSSOMS: Video lessons with additional teacher and learner
resources. Descriptions are from the video summaries.
- Flu Math Games:
"This video lesson shows students that math can play a role in
understanding how an infectious disease spreads and how it can be
controlled." Additional simulations are included. Aligns
with Algebra standards SSE-B.3.c and REI-A.1; Function standards
IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics and Probability
standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.
-
Averages: Still Flawed: "This learning video continues the
theme of an early BLOSSOMS lesson, Flaws of Averages, using new
examples—including how all the children from Lake Wobegon can be
above average, as well as the Friendship Paradox. As mentioned
in the original module, averages are often worthwhile
representations of a set of data by a single descriptive number.
The objective of this module, once again, is to simply point out
a few pitfalls that could arise if one is not attentive to
details when calculating and interpreting averages."
Aligns with IC-A.2.
PhET Interactive Simulations:
Plinko Probability. Per its description: "Drop balls through a triangular grid of pegs and
see them accumulate in containers. Switch to a histogram view and compare the
distribution of balls to an ideal binomial distribution. Adjust the binary probability
and develop your knowledge of statistics!" Aligns with ID-A.1, ID-A.2,
and IC-A.2.
Statistics Canada: Statistics: Power from Data:
Sampling Methods.
Use with IC-A.1.
Stat Trek: Tutorial:
Simulation of Random Events
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives. Note: Within the
Wolfram Demonstration Project are
7 manipulatives addressing IC-A.1 and
2 manipulatives addressing IC-A.2: Among those are:
Multiple Choice:
Constructed-response:
Performance tasks:
Illustrative Mathematics:
Statistics and
Probability:
Mathematics Vision Project,
Secondary
3 Student Edition:
-
Module 8: Statistics: This module contains 8 classroom tasks. Task
5 and task 7 align with standard IC-A.1. Tasks 6-8 address IC-A.2.
Additionally task 8 also addresses IC-B.3.
NCTM's Reasoning and Sense Making Task Library: Eruptions: Old Faithful includes the task overview, teacher notes for its use
in the classroom, and student activity sheet. Aligns with IC-A.1,
ID-A.1, and mathematical practice standards 1, 3, and 5.
Statistics in Schools from the U.S. Census Bureau:
Activities:
Math: 9-12:
-
Educational Attainment and Marriage: Testing a Correlation
Coefficient's Significance. Students "develop,
justify, and evaluate conjectures about the relationship between
two quantitative variables over time in the United States: the
median age (in years) when women first marry and the percentage
of women aged 25–34 with a bachelor’s degree or higher. Students
will write a regression equation for the data, interpret in
context the linear model’s slope and y-intercept, and find the
correlation coefficient (r), assessing the strength of the
linear relationship and whether a significant relationship
exists between the variables. Students will then summarize their
conclusions and consider whether correlation implies causation."
Aligns with standards ID-C.8, ID-C.9, and IC-A.1.
Related to the above task is the article: What
Is The Aim Of Finding Correlation? Why Is It Used If Correlation
Doesn’t Imply Causation? posted at ScienceABC. Author Argha Sengupta (2022,
July 8) delved into Finding Meaning From Random Data: Exploratory
Analysis and Correlation May Not Imply Causation, the latter of which
might be owing to an influence of a third variable.
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IC-B: Make inferences and justify conclusions from sample surveys,
experiments, and observational studies
Standards:
- IC-B.3. Recognize the purposes of and
differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each.
- IC-B.4. Use data from a sample survey to
estimate a population mean or proportion; develop a margin of error
through the use of simulation models for random sampling.
- IC-B.5. Use data from a randomized
experiment to compare two treatments; use simulations to decide if
differences between parameters are significant.
- IC-B.6. Evaluate reports based on data.
Technology-enhanced investigations:
Khan Academy: Videos:
Bernoulli distributions and margins of error. Use with IC-B.4.
Imagine Learning Classroom (formerly LearnZillion) subscription
needed:
- Lesson set:
Distinguish between surveys, experiments, and observational
studies; relate randomization to each: Four video lessons:
Conduct a survey and select a sampling method; develop and
conduct a statistical experiment, an observational study; select
a type of study. Aligns with IC-B.3.
- Lesson set:
Recognize the purposes of and differences among research
methods, including how they relate to randomization: Five
video lessons: Distinguish between observational studies,
surveys, and experiments, determine whether an investigation
uses a simple random sample or a systematic sample, determine
the differences between a cluster sample and a stratified
sample, understand sources and types of bias, avoid bias.
Aligns with IC-B.3.
- Lesson set:
Use survey data to estimate means and proportions, develop a
margin of error through simulation models, and evaluate reports
based on data: Three video lessons: Determine the likelihood
that a hypothesis is reasonable, approximating a sampling
distribution from a simulation, decrease the size of a
confidence interval. Aligns with IC-B.4.
- Lesson set:
Use data from a sample survey and evaluate reports based on data:
Six video lessons: Distinguish between descriptive and
inferential statistics, between different types of survey
research; generate survey data through simulations, use
comparative box plots to compare data sets, interpret margin of
error, construct and interpret a confidence interval.
Aligns with IC-B.4 and IC-B.6.
- Lesson set:
Use data from a randomized experiment to compare treatments;
evaluate reports based on data: Five video lessons: Design
and select a design method for a statistical experiment; compare
experimental treatments by comparing box plots, state null and
alternative hypotheses, compare treatments using a resampling
strategy. Aligns with IC-B.5.
MIT BLOSSOMS: Video lesson with additional teacher and learner
resources. Description is from the video summary. Flu Math Games:
"This video lesson shows students that math can play a role in
understanding how an infectious disease spreads and how it can
be controlled." Additional simulations are included.
Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function
standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics
nd Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.
Shodor Interactivate:
Statistics and Probability
Making Inferences and Justifying Conclusions:
Understand and evaluate random processes underlying statistical
experiments. This includes 10 lessons and 22 activities with
virtual manipulatives involving simulations and experiments.
Statistics How To: Misleading Graphs:
Real Life Examples
Stat Trek: Tutorials on Surveys and Experiments: Surveys:
Data Collection Methods: This tutorial presents four main methods of
data collection: census, sample surveys, experiments, and observational studies;
What is an experiment?; and
Experimental Design in Statistics
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives. Note: Within the
Wolfram Demonstration Project are
1 manipulative addressing IC-B.3,
3 manipulatives addressing IC-B.4, and
2 manipulatives addressing IC-B.5. Among those are:
Multiple Choice:
Khan Academy: Practice questions with videos.
Interpret graphs from the Earth Observatory at NASA. Analyze
some temperature and precipitation graphs from different cities and match
them up to the correct biome.
Constructed-response:
Performance tasks:
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Common Core Math:
Intro | HS Statistics & Probability Domain:
ID | IC | CP | MD |
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