Chapter 1. Probability, Percent, Rational Number EquivalenceSeventh grade begins with problem solving as students review and apply arithmetic with whole numbersas they investigate chance processes. Probability provides students with opportunities to build fluencywith fractions, percents, and decimals from previous grades - and recognize equivalent forms of rationalnumbers. Number line models are appropriate. In addition to covering basic counting techniques andlisting outcomes in a sample space, students distinguish theoretical probabilities from experimental(frequentist) approaches to estimate probabilities. This chapter concludes with a section specificallyabout solving percent problems, including those involving discounts, interest, taxes, tips, and percentincrease or decrease.Section 1.1: Investigate chance processes. Develop/use probability models.•Understand that the probability of a chance event is a number between 0 and 1 that expresses thelikelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near0 indicates an unlikely event, a probability around12indicates an event that is neither unlikelynor likely, and a probability near 1 indicates a likely event. 7SP5.•Approximate the probability of a chance event by collecting data on the chance process that pro-duces it and observing its long-run relative frequency, and predict the approximate relative fre-quency given the probability. For example, when rolling a number cube 600 times, predict that a3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7SP6BackgroundThis is the students’ first formal introduction to probability.The mathematics emphasized in thischapter reflects the importance in today’s society of being able to understand basic concepts of proba-bility. Also, probability is a vehicle for students to engage in a new mathematical topic while reviewingand practicing whole number and rational number arithmetic. This enables the teacher to assess stu-dent proficiency with the skills while introducing mathematics that is new and yet familiar to most7th graders because of their life experience.The mathematical study of probability dates to the 15th century and is based on problems involvinggambling.Most historians think that it originated in an unfinished dice game.The French math-ematician Blaise Pascal received a letter from his friend Chevalier de M´er´e, a professional gambler,who asked how to divide the stakes if two players start, but fail to complete, a game consisting offive matches in which the winner is the one who wins three out of five matches. The players decidedto divide the stakes according to their chances of winning the game. Pascal shared the problem withPierre Fermat and together they solved the problem, which is often marked as the beginning of theera of mathematical theory related to probability.