Students are taught the formula "Probability = Number of favorable outcomes / Total outcomes" in the Spinners activity and practice converting counts to fractions, decimals, and percents. Multiple activities ask students to list complete sample spaces (coin flips, dice, spinners, and a combined coin-and-spinner challenge) and the Sample Space answer key explicitly lists combined outcomes like {Heads-Green, Heads-Orange, Tails-Green, Tails-Orange}. The Coin Toss and Spinners activities have tables where students record counts and turn them into probabilities (e.g., heads 6/10 → 0.6 → 60%).

Students identify sample spaces and compute probabilities by counting favorable outcomes and dividing by the total number of outcomes (e.g., die sample space {1,…,6} and P(any number)=1/6). Students group outcomes and compute probabilities for compound events such as "even number or a multiple of 3" by listing outcomes, accounting for overlap, and producing a fraction of the sample space (example: 7 favorable outcomes out of 10 → 7/10). Students also use complements and unions in real contexts (e.g., "not in choir" = band + orchestra) and make predictions by multiplying the probability (fraction of the sample space) by the number of trials.

The Compound Probability section gives the probability formula (Probability = number of items in a group / total number of items) and walks students through counting favorable outcomes and total outcomes (e.g., Juice & Chips: 1 out of 6). Multiple worked examples show students building the sample space (spinner + coin S = {(R,H),...}) and then computing probabilities as fractions and percents (e.g., P(Blue and Tails)=1/8, P(Red and Heads)=3/8). Student activities require learners to build sample spaces with lists, tables, or tree diagrams and then calculate the probability as a fraction for specified compound events.

Students run multiple simulations (Activities 2–4) that map digits 0–9 to outcomes (e.g., 0–3 = Pop = 4/10) and then count frequencies. Activity 4 explicitly directs students to count how many of 20 trials took 4 or more rolls and write the result as a fraction (# of trials with 4 or more rolls/20) and convert it to a percent. Several activities ask students to record outcomes, compute totals and averages, and interpret the fraction/percent of trials meeting a condition.

The materials include tasks that require students to represent sample spaces for compound events (e.g., Problem 8: coin and die sample space listed as 12 ordered pairs; Problem 9: tree diagram for coin and spinner showing (H,G),(H,O),(T,G),(T,O)). Multiple problems ask students to use lists, tables, or tree diagrams to show all outcomes (e.g., coin+die, two coins, spinner+die). The answer key repeatedly computes compound probabilities by counting favorable outcomes over total outcomes (e.g., doubles: 6/36 = 1/6; exactly one head: 2/4 = 1/2), and the Parent Plan explicitly states that the probability of a compound event is the fraction of outcomes in the sample space that match the event.

Students construct complete sample spaces of compound outcomes (sex × size × color) as a full list of 30 combinations and as tables and tree diagrams. Students build a probability model for size+color combinations by listing each of the 15 outcomes and computing probabilities using the formula (number in group / 60) × 100, with worked examples such as (Medium, White) = 9/60 = 15%. Students then use those computed probabilities to set up and run simulations (using a 10-sided die) that model the likelihoods of compound events like getting a small black dog or a large black dog.

Students construct two-way frequency tables from raw survey lists (Activity 3) and fill the counts into cells to represent combined categories (e.g., boy & morning). The lesson defines relative frequency as frequency/total and has students convert frequency tables into relative frequency tables (Activity 4 and Day 3), including the explicit computation 18/90 = 0.20 for bikers who caught a cold. Several activities (Activity 5, Making Relative Frequency Tables) ask students to compute row- or column-based relative frequencies (e.g., 18/24 = 0.75 for pet owners who like science) and interpret those proportions as comparisons of likelihoods.

Students construct and interpret two-way frequency and relative frequency tables (Activity 17 and multiple music/sport tables) and compute cell fractions such as "What fraction of evening viewers chose soccer?" (0.33). Students read and use table entries that represent joint outcomes (for example, "12 students like pop music and prefer quiet while studying") and are asked to fill a relative frequency table and answer fraction/decimal questions. Several problems require finding relative frequencies and using them as fractions of the total (answer keys show fractions/decimals like 0.33, 0.45, etc.).

Students construct two-way relative frequency tables and are instructed to "Calculate Percentages" so that each cell shows the percent of all 20 people in that activity–time combination. The materials state explicitly that "Each cell represents the percentage of all 20 people who fit into that activity–time combination," and include prompts asking students which combination had the highest or lowest percentage. The Parent Plan and activity pages tell students to use relative frequencies for rows or columns to describe association between two categorical variables.

Students list complete sample spaces for compound actions (coin + spinner, coin + die, two dice) and count total outcomes (e.g., 8 outcomes for coin + 4-section spinner, 12 for coin + 6-sided die). Students use tree diagrams to organize outcomes (coin + spinner with red/blue sections) and identify favorable outcomes, then compute probabilities as fractions (examples: Heads and C = 1/8; Tails and 4 = 1/12; sum of 9 = 4/36 = 1/9; Red and Heads = 3/10). The materials explicitly state that sample spaces and tree diagrams help organize all possible outcomes so none are missed, supporting the fraction-based calculation of compound probabilities.

Students list the sample space for flipping one coin and spinning a 4-section spinner (problem 41) and use that list to compute the probability of tails and landing on C as 1/8 (problem 42 and answer key). Students draw a tree diagram for a spinner with 3 red and 2 blue sections combined with a coin flip (problem 46a), count outcomes (46b), and compute the probability of red and heads as 3/10 (46c). Additional tasks (problem 47 and others) ask students to find probabilities for two-dice outcomes and create probability models, all using counts of favorable outcomes over total outcomes.

Students work with a two-way relative-frequency table in Activity 4 and compute cell fractions such as 12/50 = 0.24 (24%) to describe how many evening students prefer gaming. The activity asks students to use relative frequencies (fractions and decimals) to identify which activity is most popular in a given time column and to draw conclusions from those fractions. The parent plan and answer key explicitly show computations of joint/category counts divided by column totals to produce proportions.