### Clarifications

*Clarification 1:*Instruction includes representing probability as a fraction, percentage or decimal between 0 and 1 with probabilities close to 1 corresponding to highly likely events and probabilities close to 0 corresponding to highly unlikely events.

*Clarification 2: *Instruction includes P(event) notation.

*Clarification 3:* Instruction includes representing probability as a fraction, percentage or decimal.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**7

**Strand:**Data Analysis and Probability

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Event
- Theoretical Probability

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students interpret the probability of a chance event and the likelihood of it occurring. In grade 8, students will solve problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability.- An event is a set of outcomes.
- For example, if the experiment is to roll a six-sided die, possible events could be:
- “rolling a 3 or a 4;”
- “rolling an even number;” or
- “not rolling a 2.”

- For example, if the experiment is to roll a six-sided die, possible events could be:
- Instruction includes the understanding that some events can have a probability of 1 or 0. Students should understand that if an event has a probability of zero, the event is impossible or will not occur. If an event has a probability of one, the event is certain or must occur.
- For example, in the experiment of rolling a 6-sided die, the event of rolling a 1, 2, 3, 4, 5 or 6 would have a probability of 1.
- For example, when rolling a 6-sided fair die, the event of rolling a 7 would have a probability of 0.

- Instruction includes having students use probabilities of 1, 0.5 and 0 as benchmark probabilities to interpret the likelihood of other events.
- For example, if a student wants to interpret the likelihood represented by the probability of 80%, they can compare 80% to the benchmark probabilities of 50% and 100%.

- If an event has a probability of 0.5, it can be interpreted that is has the same likelihood as its opposite.
- For example, in the experiment of picking a card from a standard 52-card deck, the event of picking a red card has a probability of 0.5, which can be interpreted as having the same likelihood as the opposite event, which is picking a black card.

### Common Misconceptions or Errors

- Students may invert the meaning of an event and an experiment.
- Students may confuse the mathematical meaning of a word like “event” with the everyday meaning.
- Students may incorrectly convert forms of probability between fractions and percentages. To address this misconception, scaffold with more familiar values initially to facilitate the interpretation.
- Students may incorrectly interpret a value with a negative sign as a possible probability.
- For example, −$\frac{\text{1}}{\text{2}}$ cannot represent a probability since negative values are less than 0.

### Strategies to Support Tiered Instruction

- Teacher creates and posts an anchor chart with visual representations of probability terms to assist students in correct academic vocabulary when solving real-world problems.
- Teacher provides opportunities for students to use a 100 frame to review place value for and the connections to decimal, fractional and percentage forms of probabilities.
- Instruction includes the use of a 100 frame to review place value for tenths, hundredths, and if needed, thousandths and the connections for decimal and fractional forms of probabilities.
- When students incorrectly convert from one form to another (i.e, fraction to percentage), the teacher scaffolds with more familiar values initially to facilitate the interpretation.

### Instructional Tasks

*Instructional Task 1*

**(MTR.1.1)**Determine which of the following could represent the probability of an event. For those that can, provide a possible event that would fit the probability given.

### Instructional Items

*Instructional Item 1*

In each scenario, a probability is given. Describe each event as likely, unlikely or neither.

- a. The probability of a hurricane being within 100 miles of a location in two days is 40%.
- b. The probability of a thunderstorm being located within 5 miles of your house sometime tomorrow is $\frac{\text{9}}{\text{10}}$
- c. The probability of a given baseball player getting at least three hits in the game today is 0.08.

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Experts

## Text Resource

## Tutorial

## STEM Lessons - Model Eliciting Activity

Students will decide what is the best month to celebrate an outdoor wedding. The couple is looking for the perfect wedding day. What is the definition of a perfect day? It has to be a Saturday or Sunday with a 20% or less probability of rain and sunny but not too hot. Based on the information provided , students will find the month in which the probability of having a rainy day and the probability of having a super hot day (temperature higher than 75º F) are minimal.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are asked to determine the likelihood of an event given a probability.

Students are asked to determine the likelihood of an event given a probability.

Students are asked to determine whether or not a given number could represent the probability of an event.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial