## chapter 5 outline

**Section 5.1:**This section introduces a linear diagram that you will use to represent relationships between parts and the whole to solve problems.

**Section 5.2:**You will investigate probability using a deck of cards and a random number generator. You will learn to represent multiple events using a probability tree, a list, and a table. You will also revisit the idea of the fairness of events and compare experimental and theoretical probabilities.

**Section 5.3:**This section will introduce the 5‑D Process as a problem-solving method. You will learn how to understand a problem by drawing, describing, and defining its elements. You will learn strategies that lead to writing and solving equations later in the course.

## Big Ideas

Find and use percentages to solve problems.

Calculate the probability of compound (multiple) events.

Use experimental results to make and test conjectures about unknown sample spaces.

Describe how the relationship between experimental and theoretical probabilities for an experiment changes as the experiment is conducted many times.

Solve situational problems using the 5‑D Process.

Calculate the probability of compound (multiple) events.

Use experimental results to make and test conjectures about unknown sample spaces.

Describe how the relationship between experimental and theoretical probabilities for an experiment changes as the experiment is conducted many times.

Solve situational problems using the 5‑D Process.

## Guiding Questions

What is the part?

What is the whole?

Which is more likely?

Is it fair?

How can I represent the relationship?

How can I organize my thinking?

What is the whole?

Which is more likely?

Is it fair?

How can I represent the relationship?

How can I organize my thinking?

## vocabulary

5-D Process

consecutive integers

complement

compound events

dependent events

desired outcomes

equivalent ratios

experimental probability

independent events

mutually exclusive

outcome

partition

percent

possible outcomes

probability

probability table

probability tree

proportional relationship

ratio

sample space

scalene triangle

simplify

simulation

single event

systematic list

theoretical probability

variable

consecutive integers

complement

compound events

dependent events

desired outcomes

equivalent ratios

experimental probability

independent events

mutually exclusive

outcome

partition

percent

possible outcomes

probability

probability table

probability tree

proportional relationship

ratio

sample space

scalene triangle

simplify

simulation

single event

systematic list

theoretical probability

variable

## CCSS Standards in Unit

- 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
*For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.* - 7.RP.2d. Explain what a point
*(x, y)*on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1,*r)*where*r*is the unit rate. - 7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
*For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.* - 7.SP.7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
*For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.* - 7.SP.7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
*For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?* - 7.SP.8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
- 7.SP.8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
- 7.SP.8c. Design and use a simulation to generate frequencies for compound events.
*For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?*