Intermediate Test Prep Math 8 (Grade 6)Use arrangements and combinations (e.g. tree diagram)

Tree Diagrams
Lesson
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treediagram A tree diagram is a diagram showing all possible outcomes of an event. This type of diagram shows one branch for each possible outcome.

It is often easy to list the outcomes for a single experiment. It can be more complicated to list the outcomes for a series of experiments.

When trying to determine the possible outcomes from an experiment, it is often helpful to draw a diagram which illustrates how to arrive at the answer.

Example 1

You need to decide on your snack. You can have white or chocolate milk to drink. To eat you can have chocolate chip or oatmeal cookies. How many different choices do you have?

drink		food	combinations
2	x	2	4

Example 2

	If you flip a penny, dime, and a quarter, how many different ways can the three coins land? There are two ways the penny, dime, and quarter can land: heads or tails.
Make a tree diagram There are eight different possible outcomes.
Multiply to find the number of possible outcomes	penny	x	dime	x	quarter	possible outcomes
Multiply to find the number of possible outcomes	2	x	2	x	2 =	8

Remember:
A tree diagram is a branching, tree-like diagram showing all possible outcomes of a situation.

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