The lesson explicitly defines population and sample and states that "When a sample is used in statistics, it is meant to provide insights into what is likely true for the entire population," directly tying sample results to population information. It teaches that a sample must be representative and warns about bias, including intentional and unintentional bias, with examples (e.g., asking only 10-year-old campers or only sports fans). The lesson defines random sampling as giving every member an equal chance, shows a marble-bag random sampling illustration, and asks students to choose/randomly select names (every hundredth citizen, random names, sampling from registration lists) in activities that practice selecting representative random samples. Practice pages (Dr. Franklin, Shayna, economist, Marlon) ask students to decide when to use samples, identify biased versus representative sampling methods, and select the most representative/random options.

Students identify whether a data set is a sample or the whole population (Scenario 3 asks, "Is this data from all the visitors at the amusement park or a sample?" with answer "a sample"). Students label the attribute and state where the data came from (dot plot titles and category labels ask for the attribute and source, e.g., camper votes, dog heights). Students count and report the number of observations by creating frequency tables and adding frequencies to find totals (several activities ask for the total number of responses or total games/days).

Students are explicitly asked to determine whether a data set represents a whole population or a sample (Activity 1 question 2 and its answer key). The activity asks students to identify attributes, decide if data are numerical or categorical, and classify data as primary or secondary, so students practice distinguishing kinds of data sources. Several student tasks require reading stem-and-leaf plots to report counts and totals, reinforcing interpretation of data sets that could be populations or samples.

Students answer Quiz questions that ask them to decide when to use a population or a sample (Question 3) and to choose which sampling method is least biased for finding the most popular pet in a town (Question 4). The answer key explicitly identifies a random sampling of 100 citizens from the census as the non-biased choice. Several activities ask students to label situations as 'sample' or 'population' and to choose appropriate sampling approaches.

The lesson includes a scenario in which "the water company randomly selected 100 homeowners in town" and asks students to interpret the resulting box plot, so students work with a sample described as randomly selected. The wrapping-up paragraph states that patterns in a data distribution can be used to draw understandings about the population represented by the data set. The skills list and activities have students summarize numerical data in context and use sample data (dot plots, stem-and-leaf, box plots) to compute measures that describe a data set.

Students practice taking random samples (for example, reaching into a candy package without looking and counting every 20th or 15th word in a passage) and record sample data in dot plots, frequency tables, and calculate ratios, percentages, and means. Students compare sample results to the whole population by separating and counting all candies in the package, and they calculate the actual population mean for the word-length activity to see how close samples come to the population. Students examine a food-truck example where every fifth customer is sampled, compute measures of center and variability, and write inferences about the population based on that sample; they also reflect on how sample size and multiple samples affect sampling variability.

Students use sample data (dot plots, box plots, and tables) to draw inferences about populations in multiple activities (pumpkins, zucchini, heights of 10- and 11-year-olds, cat/dog adoptions). Students compute and compare summary statistics (means and mean absolute deviations) and use overlap and a ratio of mean difference to variability to judge how confident they can be in conclusions about populations. The lesson repeatedly prompts students to avoid bias by using the same sampling methods when comparing populations (Questions to Discuss; Things to Review).

Students identify populations and samples (e.g., Samuel's neighborhood, people at the county fair) and classify sample types (convenience vs. random) on activity pages. Students choose which sampling methods are most likely to be representative (e.g., every 5th or every 50th person) and identify biased or convenience samples (asking only neighbors, surveying families with children). Students use data from stated random samples to make inferences (e.g., movie-goers' favorite day, deciding the busiest day) and answer questions about sampling variability when sample size changes.

Students are asked to identify the population and the attribute of interest (Step 1) and to record their methods of data collection and unit of measure (Step 2). Students collect a sample of data (aiming for 10–20 values), organize it, compute summary statistics and create graphs, and answer a prompt asking, "What general inferences can you make about the population of your statistical study?" The materials also remind students to make sampling methods consistent to avoid unintentional bias and to note risks of low participation with certain survey methods.

Students run repeated experiments with a three-color spinner (10, 50, 100 spins), record tallies, and compute experimental probabilities as fractions, decimals, and percents. Students use the experimental probability from their 100-spin sample to predict outcomes for 600 spins (Prediction = Experimental Probability × 600). The lesson repeatedly has students observe relative frequency and notes that with more trials results tend to settle toward expected values.

Students run repeated experiments (rolling dice, spinning spinners, sampling tokens) and compute experimental probabilities to compare with theoretical probabilities, applying the Law of Large Numbers. Students build probability models from actual counts (e.g., 16 choir, 10 band, 8 orchestra) and calculate probabilities from those real-world data. Activities and the quiz ask students to explain discrepancies and list causes such as small sample size, biased/unfair method, or recording error, and an example references selecting a student at random from a class.

Activity 4 explicitly defines population and sample and states that "if the sample is chosen randomly—meaning each individual has an equal chance of being selected—then we can often expect the sample to represent the population accurately." The Timpony example has students compute a sample proportion (14 out of 60 → 23.3%) and apply it to the whole population (0.233 × 1,143 ≈ 266), showing how to use sample statistics to estimate a population quantity. Student activity pages and answer keys give multiple practice problems where students calculate proportions from samples and multiply to predict counts in larger populations.

Students set up and run multiple simulations using random tools (marbles, a 10-sided die, and random digits) to model real-world situations and collect data. They repeat trials (10, 20) and record frequencies, compute averages, and convert counts to fractions and percents (e.g., Library Hunt: count trials with 4 or more rolls and convert to percent). The Parent Plan and activity instructions explicitly ask students to design and use simulations to generate frequencies to approximate probabilities (for example, using random digits to approximate finding a donor with type A blood).