Sample Spaces and Tree Diagrams - Grade 7

6th - 8th

Probability pros conduct a variety of experiments and solve them using tree diagrams and sample spaces to make predictions. They define key vocabulary terms, and observe how to diagram the theoretical probability of tossing a coin three times. To conclude, they design their own probability experiment. The lesson plan is thoroughly written so that you can implement it easily. Let the games begin!

Resource Details

1 hr
Alaska Department of Education and Early Development

Cafe 240

An engaging task awaits your starting statisticians: design a menu for a new cafe that offers a total of 240 combinations of a main dish, a side, a dessert, and a beverage. Creative juices will flow as collaborative groups employ lists, tables, or diagrams to come up with the possibilities. This is a delicious challenge for your math class when learning how to work with sample spaces and compound events.

Sample Space Diagrams and Probability - Independent Events

Six tasks make probability models come to life with this activity. Sample space diagrams and tree diagrams help statisticians compute probabilities of drawing red, blue, or white beads from a bag. Bold font makes this easy to read, and the problems that learners work through are practical. 

Aging of Trees

Young scholars examine tree rings to determine its age.  In this tree ring instructional activity, students examine core tree samples, identify the tree rings, and then determine its age. Young scholars complete a worksheet, deciding which of the two core sample is the oldest tree. 

Finding the Probability of Combined Events

Eighth graders investigate the probability of combined events.  In this eight grade probability lesson, 8th graders use a sample space, two events, and their intersections to determine the probability of each event, their intersection, and their union.   


In need of a probability resource that has it all? Take a look at a full textbook chapter on teaching and engaging learners in mathematical probability and data analysis. It begins with a teacher preparation section, and then moves into several multi-part lessons that include activities, tools, manipulatives, worksheets, and assessments. The best thing about the resource is that it is full of research-based strategies proven to help learners access content. The entire packet is 54 pages in length, can be printed or saved, and comes from a reputable source that adheres to standards-based teaching.

Keys To Trees: Dichotomous Tree Identification

Ninth graders gather samples of different tree leaves in their neighborhoods, and on school grounds, and identify several species of common South Carolina trees using leaf and growth characteristics with aid of dichotomous key.

Real-World Probability

Students explore the concept of probability.  In this probability lesson, students create a video, poster, or podcast explaining what experiments, sample space, events, and outcomes are in relation to probability.  Students create a brochure or PowerPoint explaining the counting rules.  Students make a video, photostory, or use moviemaker to show teaching a probability lesson or how to find the probability of an event.

Probability- Many Stage Experiments

Learners list the sample space of an experiment. In this statistics lesson, students calculate the number of favorable outcome in a given sample space. They define and apply mutually exclusive events versus not mutually exclusive events.

Investigation - What's in the Bag?

If you have or can create a set of tiles, numbered one through eight, then you can implement this hands-on lesson about probability models. Individuals draw a tile from a bag, record its number, and then return it to the bag. They predict the probability of the product of three draws equalling an odd number. Teach them how to use sample spaces and tree diagrams to do so. The notes for the lesson are fairly simple, but include two assessment questions and an extension suggestion.

Sample Space and Probability Distribution

Young scholars use the sample space to make predictions and analyze data. In this statistics lesson plan, students apply properties of the probability of an event occurring to solve problems.

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