Students randomly sample candy pieces, record frequencies, compute part-to-whole ratios and percentages, and predict the most and least common colors before comparing the sample to the whole package. Students collect every 5th customer sales data in the food-truck example and use the sample histogram, mean, and measures of variability to make an inference (for example, predicting about $2500 if there are 100 customers). Students perform repeated sampling in the word-length activity (every 20th, every 15th, and discussion of every 5th or 50th) and compute sample means to compare to the population mean, observing sampling variability and how larger samples reduce it.

Students flip a coin repeatedly and record results in a table for sets of 5, 10, 50, and 100 tosses, converting counts to fractions, decimals, and percentages (Activity 2). They are asked to compare experimental probability to the theoretical probability (½) and are told that as they do more flips the experimental probability should get closer to theoretical. Students also play a die-rolling game where they predict outcomes each round and record whether they were correct, collecting data on predictions and results. In Activity 3 students compute theoretical probabilities for spinner sections and express them as fractions, decimals, and percents.

Students conduct repeated trials by spinning a three-color spinner 10, 50, and 100 times and record tallies for each color. Students calculate experimental probability using Number of times it happened / Total number of spins and convert results to fraction, decimal, and percent. Students use their experimental probabilities to predict the approximate number of outcomes out of 600 spins using Prediction = Experimental Probability × 600 and are asked to round and note that results will not be exact. The materials also prompt students to observe how results stabilize as the number of trials increases (long-run relative frequency).

Students perform repeated trials and record outcomes (rolling a six-sided die for 30, 60, and 120 rolls; spinning a non-uniform spinner 50 times; surveying classroom choices) and compute relative frequencies from their tallies. Students use theoretical probability to make numeric predictions by multiplying probability by number of trials (examples: 1/6 × 30 = 5, coin: 1/2 × 500 = 250, spinner: 1/8 × 64 = 8). Students compare experimental relative frequencies to theoretical predictions, discuss the Law of Large Numbers, and analyze discrepancies using guided questions and the "What Went Wrong?" activities.

The lesson has students compute probabilities and then predict expected counts when an experiment is repeated (e.g., the snack example: compute P(Juice and Chips)=1/6 and predict 120 × 1/6 = 20 occurrences). Activity pages repeatedly ask students to build a probability model and "predict how many times the outcome would occur if the situation was repeated" (examples use 75, 90, 100, 120 trials). The Making Inferences activity has students use a sample proportion (14 of 60 students) to estimate counts in a larger population (≈266 of 1,143), showing practice applying observed sample frequencies to predict larger-group frequencies.

Students run repeated trials using random tools (marbles, a 10-sided die) and record outcomes: Activity 1 has students repeat 10 trials recording pulls until a Blue marble; Activity 2 and 3 require 20 trials recording number of rolls until a target outcome; Activity 4 has students count how many of 20 trials take 4 or more rolls and convert that fraction to a percent. Students compute averages, fractions, and percents and are asked to compare their simulation results to their original hypotheses or to changed probabilities (e.g., if Instrumentals were 20% instead of 10%).

Students compute experimental probabilities from collected data in multiple problems (e.g., rolling a die 60 times with fifteen 6s and rolling a die 100 times with twenty 3s where they calculate 15/60 and 20/100). Students compare experimental results to theoretical probabilities and explain differences (questions ask for theoretical 1/6 and ask why experimental may differ; answer key explains convergence with more trials). Students design and run simulations (tasks: run at least 10 trials for scenarios like "If 40% of marbles are red..." and "If 30% of coins are copper...") and the materials include explicit guidance to predict approximate counts from probability (the example of predicting about 200 threes or sixes in 600 rolls appears repeatedly).

Students compute empirical probabilities from the shelter counts by writing each size+color combination and calculating percentage chances (e.g., 9/60 = 15%). Students build a probability model (size+color) and answer questions about most/least likely outcomes and equal-likelihood pairs. In Part 4 students run simulations using a 10-sided die (mapping die faces to events like small black or large black dogs), record the number of rolls until the target outcome across repeated trials, compute averages, and compare the simulation results to the model's predictions.

Students construct two-way frequency tables and convert counts into relative frequencies (decimals or percentages) across multiple activities. In Activity 4 the example explicitly computes an empirical probability by dividing 18 bikers who caught a cold by 90 bikers to get 0.20 and then uses those proportions to compare groups. Multiple exercises require students to fill in relative frequency tables and interpret those proportions as measures of likelihood or association.

Students plan and carry out data collection from people (e.g., timing 20 friends doing jumping jacks and recording heart rates, and asking 20 people categorical survey questions). Students record counts with tally charts, convert counts into percentages, and build two-way relative frequency tables. Students compute and interpret those relative frequencies (percentages) to describe which category combinations are most or least common and to summarize patterns in their data.

Students compute experimental probability from provided data (spinner spun 25 times with yellow occurring 7 times) and write it as a fraction and decimal. Students consider a game with theoretical probability 1/4 and calculate the expected number of wins in 20 trials, explicitly stating they would not expect exactly 5 wins and explaining variability. The materials discuss that as the number of trials increases the experimental probability tends to get closer to the theoretical probability.

Students are given an experimental outcome (a spinner spun 25 times landing on yellow 7 times) and asked to compute the experimental probability and explain how it might differ from theoretical probability (Question 43). Students label points on a probability line, find theoretical probabilities for marbles and dice, list sample spaces, and create a probability model for a bag of shapes (Questions 38–46). Students are also asked to explain how a spinner with 10 equal sections could model a 40% probability (Question 49), which links probability to expected counts in a finite model.

Students are asked in Problem 50 to use column totals and calculate relative frequencies as decimals from a contingency table of observed counts (Favorite Snack and Where It is Eaten). Unit 8 contains multiple data analysis tasks (mean, median, mode, range, MAD, IQR, box plot, and interpretation questions) that require students to compute and interpret empirical summaries of observed data. The relative frequency table task explicitly has students convert observed counts into proportions, which is an empirical probability computation.