Probability, Grade 7 Workbook

The concepts covered in Probability, Grade 7 Workbook are very likely new to your student. However, most students have an intuitive understanding of probability based on hearing the terms “probably” and “likely,” listening to weather forecasts, and so on.

In the past, probability wasn’t taught until high school - for example, I personally encountered it for the first time in 12th grade. However, since probability is such a useful and easily accessible field of math, it was felt that it should be introduced sooner, so during the 1990s and 2000s it “crept” down the grade levels until many states required probability even in elementary school. The Common Core Standards include probability starting in 7th grade. I feel that is good timing because by 7th grade students have studied fractions, ratios, and proportions, so they have the tools they need to study probability. Moreover, they will need an understanding of the basic concepts of probability in order to understand the statistical concepts that they will study in middle school and high school.

In this workbook, we start with the concept of simple (classic) probability, which is defined as the ratio of the number of favorable outcomes to the number of all possible outcomes. Students calculate probabilities that involve common experiments, which include flipping a coin, tossing a pair of dice, picking marbles, and spinning a spinner.

The lesson Probability Problems from Statistics introduces probability questions involving the phrase “at least,” which are often solved by finding the probability of the complement event. For example, it might be easier to count the number of students who got at most D+ on a test than to count the number of students who got at least C-.

In the next lesson, Experimental Probability, students conduct experiments, record the outcomes, and calculate both the theoretical and experimental probabilities of events, in order to compare the two. They will draw a card from a deck or roll a die hundreds of times.

Next, we study compound events, which combine two or more individual simple events. Tossing a die twice or choosing first a girl then a boy from a group of people are compound events. Students calculate the probabilities of compound events by using the complete sample space (a list of all possible outcomes). They construct the sample space in several ways: by drawing a tree diagram, by making a table, or simply by using logical thinking to list all the possible outcomes.

The last major topic in this workbook is simulations. Students design simulations to find the probabilities of events. For example, we let heads represent “female” and tails represent “male,” so we can toss a coin to simulate the probability of choosing a person of either sex at random.

Later in the lesson, students design simulations that use random numbers. They generate those numbers by using either the free tool at a link that is provided in the lesson or a spreadsheet program on a computer.

In the last lesson of the workbook, Probabilities of Compound Events, we learn to calculate the probability of a compound event by multiplying the probabilities of the individual events (assuming the outcomes of the individual events are independent of each other). This topic exceeds the Common Core Standards for 7th grade and thus is optional. I have included it here because the idea studied in the lesson is very simple and I feel many students will enjoy it.