Get a statistical snapshot of a population using simplified versions of the random, systematic, and stratified sampling techniques commonly used by researchers around the world!

- Sampling Methods
- Populations

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Standard- Science and Engineering Practices: 1. Asking Questions and Defining Problems 2. Developing and Using Models 3. Planning and Carrying Out Investigations 4. Analyzing and Interpreting Data 5. Using Mathematics and Computational Thinking 6. Constructing Explanations and Designing Solutions 7. Engaging in Argument from Evidence 8. Obtaining, Evaluating, and Communicating Information ||Next Generation Science Standards||Middle School||Science and Engineering Practices
- Develop Understanding Of Statistical Variability||Common Core Mathematics||Grade 6||Statistics And Probability
- Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices
- 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ""The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."" ""For every vote candidate A received, candidate C received nearly three votes.""||Common Core Mathematics||Grade 6||Ratios And Proportional Relationships||Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems
- Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices
- 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.||Common Core Mathematics||Grade 7||Ratios And Proportional Relationships||Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems
- 7.RP.2. Recognize and represent proportional relationships between quantities.||Common Core Mathematics||Grade 7||Ratios And Proportional Relationships||Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems
- 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.||Common Core Mathematics||Grade 7||Statistics And Probability||Use Random Sampling To Draw Inferences About A Population
- 7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.||Common Core Mathematics||Grade 7||Statistics And Probability||Use Random Sampling To Draw Inferences About A Population
- 7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.||Common Core Mathematics||Grade 7||Statistics And Probability||Draw Informal Comparative Inferences About Two Populations
- Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices
- 8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?||Common Core Mathematics||Grade 8||Statistics And Probability||Investigate Patterns Of Association In Bivariate Data
- Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices
- Science and Engineering Practices: 1. Asking Questions and Defining Problems 2. Developing and Using Models 3. Planning and Carrying Out Investigations 4. Analyzing and Interpreting Data 5. Using Mathematics and Computational Thinking 6. Constructing Explanations and Designing Solutions 7. Engaging in Argument from Evidence 8. Obtaining, Evaluating, and Communicating Information ||Next Generation Science Standards||High School||Science and Engineering Practices
- HS.S.CP.4. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.||Common Core Mathematics||High School||Conditional Probability And The Rules Of Probability||Understand Independence And Conditional Probability And Use Them To Interpret Data

- 1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).||CA Mathematics||Grade 6||01. Number Sense||1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.
- 2.2 Identify different ways of selecting a sample (e.g., convenience sampling, respond to a survey, random sampling) and which method makes a sample more representative for a population.||CA Mathematics||Grade 6||04. Statistics, Data Analysis, and Probability||2.0 Students use data samples of a population and describe the characteristics and limitations of the samples.
- 7. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will: ||CA Science||Grade 6||07. Investigation and Experimentation
- 7. Scientific progress is made by asking meaningful questions & conducting careful investigations. As a basis for understanding this concept, and to address the content of the other strands, students will develop questions & perform investigations.||CA Science||Grade 7||07. Investigation and Experimentation
- 9. Investigation and Experimentation||CA Science||Grade 8||01. Physical Sciences
- 1. Scientific progress is made by asking meaningful questions & conducting careful investigations. As a basis for understanding this concept, & to address the content of the other strands, students should develop questions & perform investigations.||CA Science||Grade 9-12||05. Investigation and Experimentation

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