**Math Topics**- Common Core
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Select the cluster for resources on this page:

**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 | randomization | significance level |

margin of error | parameter | random sample | statistics |

mean | population | sample survey | treatment |

McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 11 Data Analysis and Statistics for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook. Use with IC-A.

LearnZillion:

- 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 examplesâ€”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.

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:

- Random samples and random permutations: "This demonstration is intended for its usefulness to instructors and students in elementary statistics to replace the use of random number tables." Aligns with IC-A.1.
- Decisions based on p-values and significance levels: Aligns with IC-A.1, IC-A.2.
- Confidence Intervals: Confidence Level, Sample Size, and Margin of Error: Aligns with IC-A.1, IC-A.2.
- Confidence intervals for the mean: Aligns with IC-A.1, IC-B.4.
- Hypothesis tests about a population mean: Aligns with IC-A.1, IC-B.5.
- The Power of a Test Concerning the Mean of a Normal Population: Aligns with IC-A.1, IC-B.5.

**Multiple Choice:**

Glencoe Online Learning Center, Geometry (2010) self-check quizzes: Ch. 13, Lesson 4: Simulations Aligns with IC-A.2.

Khan Academy: Practice questions with videos.

- Valid claims: Aligns with IC-A.1.
- Simple hypothesis testing: Aligns with IC-A.2.

McDougal Littell ClassZone, Algebra 2, 2011: Ch. 11.5 Quiz: Choose the Best Model for Two-Variable Data

OpenEd:

- Making inferences and justify conclusions: 5 multiple choice questions. Includes related review resources. Aligns with IC-A.1.
- Is the model consistent: 5 questions combine multiple choice and free response. Includes related review resources. Aligns with IC-A.2.

**Constructed-response:**

**Performance tasks:**

Illustrative Mathematics:

- Strict Parents: This task aligns with standards IC-A.1 and IC-B.3.
- Sarah, the Chimpanzee: This task aligns with standard IC-A.2.

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.

**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.

LearnZillion:

- 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.

McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 11 Data Analysis and Statistics for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook. Use with IC-B.

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.

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:

- Randomly filling an array: Aligns with IC-B.3, IC-B.4.
- Confidence intervals for the mean: Aligns with IC-A.1, IC-B.4.
- The Central Limit Theorem: "The central limit theorem states that the sampling distribution of the sample mean approaches a normal distribution as the size of the sample grows." Aligns with IC-B.4.
- Hypothesis tests about a population mean: Aligns with IC-A.1, IC-B.5.
- The Power of a Test Concerning the Mean of a Normal Population: Aligns with IC-A.1, IC-B.5.

**Multiple-choice:**

Glencoe Online Learning Center, Algebra 2 (2010) self-check quiz: Ch. 12, Lesson 1: Experiments, Surveys, and Observational Studies

Khan Academy: Practice questions with videos.

- Types of statistical studies: Aligns with IC-B.3, IC-B.6.
- Hypothesis testing in experiments: Aligns with IC-B.5.

McDougal Littell ClassZone, Algebra 2, 2011: Ch. 11.4 Quiz: Select and Draw Conclusions from Samples

OpenEd:

- Surveys, experiments and observations: 5 multiple choice questions. Includes related review resources. Aligns with IC-B.3.
- Using data from a sample survey: 5 questions combine multiple choice and free response. Includes related review resources. Aligns with IC-B.4.
- Evaluating reports: 5 multiple choice questions. Includes related review resources. Aligns with IC-B.6.

**Constructed-response:**

OpenEd: Using data from randomized experiments: 2 free response questions and 1 true-false. Includes related review resources. Aligns with IC-B.5.

**Performance tasks:**

Illustrative Mathematics:

- Strict Parents: Aligns with IC-B.3 and IC-A.1.
- Words and Music II: Aligns with IC-B.3.

Mathematics Assessment Project: Standards: High School: Statistics & Probability: http://map.mathshell.org/stds.php?standardid=1233 Task 217: Interpreting Statistics: A Case of Muddying the Waters

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.

Back to top Common Core Math: Intro | HS Statistics & Probability Domain: ID | IC | CP | MD |