### Clarifications

*Clarification 1:*Instruction includes representing probability as a fraction, percentage or decimal.

*Clarification 2:* Simple experiments include tossing a fair coin, rolling a fair die, picking a card randomly from a deck, picking marbles randomly from a bag and spinning a fair spinner.

**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 find the theoretical probability of an event related to a simple experiment, and in grade 8, they will find the theoretical probability of an event related to a repeated experiment.- Instruction builds on finding sample spaces from MA.7.DP.2.1. Have students discuss their understanding of the words “theoretical” and “probability” to build toward a formal definition of theoretical probability.
- When finding theoretical probability, have students work from their sample space. Doing so will lead to the understanding that since experiments for this benchmark are fair, the probability of an event is equivalent to $\frac{\text{number of outcomes in the event}}{\text{number of outcomes in the sample space}}$.
- For example, if rolling a fair 6-sided die, the sample space is {1, 2, 3, 4, 5, 6,}. If one wants to find $P$($rollinganoddnumber$), students can circle all of the odd numbers from the sample space to determine the probability as , or 0.5.

- While the benchmark does focus on fair experiments, instruction could include spinners with unequal sections making the connection to angle measures and to circle graphs.
- Instruction focuses on the simple experiments listed in Clarification 2.
- For example, when tossing a coin with one side colored yellow and the other side colored red, $P$($landingonblue$) = 0.
- For example, when rolling a 10-sided die, $P$($notrollingamultipleof$ 3) = 0.7.
- For example, when picking a card from a deck that contains each of the letters of the alphabet, $P$($pickingaconstant$) = $\frac{\text{21}}{\text{26}}$.
- For example, when picking a tiles from a bag that contains a set of chess pieces, $P$($pickingapawn$) = 50%.
- For example, when spinning a spinner that contains 5 sections where two of the sections are green and the remaining sections are red, white and blue,

$P$($landingonacolorfromtheAmericanflag$) = $\frac{\text{3}}{\text{5}}$.

### Common Misconceptions or Errors

- 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 count outcomes when one outcome appears more than once in the sample space.
- For example, if the sample space is {red, red, blue} and one wants to find $P$($red$), a student may incorrectly state $\frac{\text{1}}{\text{2}}$ or $\frac{\text{1}}{\text{3}}$ instead of $\frac{\text{2}}{\text{3}}$.

### Strategies to Support Tiered Instruction

- Teacher provides instruction in converting between fractions and percentages, by using more familiar values.
- For example, $\frac{\text{1}}{\text{2}}$ = 50%, $\frac{\text{1}}{\text{4}}$ = 25%, $\frac{\text{1}}{\text{3}}$ ≈ 33.3%, etc.

- Teacher co-creates a T-chart (like the one below) to list the experiment and the sample space necessary for the examples provided.

### Instructional Tasks

*Instructional Task 1*

**(MTR.4.1, MTR.7.1)**Look at the shirt you are wearing today and determine how many buttons it has. Then complete the following table for all the members of your class.

- Part A. What is the probability that the student whose card is selected is wearing a shirt with no buttons?
- Part B. What is the probability that the student whose card is selected is female and is wearing a shirt with two or fewer buttons?

Instructional Task 2

Instructional Task 2

**(***, MTR.5.1)***MTR.4.1**There is only one question on the next quiz and it will be true or false.

- Part A. If a student randomly answers the question, what is the probability of earning a score of 100%?
- Part B. What is the probability of earning a 50%?

### Instructional Items

*Instructional Item 1*

What is the probability of choosing a 9 from a standard deck of 52 cards?

*Instructional Item 2*

There are 7 red, 5 blue and 12 green marbles in a bag.

- Part A. What is the probability of choosing a red marble?
- Part B. What is the probability of not choosing a green marble?
- Part C. What is the probability of choosing a yellow marble?
- Part D. What is the probability of choosing a red or blue marble?

**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

## Perspectives Video: Expert

## Problem-Solving Tasks

## Text Resource

## Tutorials

## MFAS Formative Assessments

Students are asked to estimate the frequency of an event given its probability and explain why an expected frequency might differ from an observed frequency.

Students are given a scenario and asked to determine the probability of two different events.

## Student Resources

## Problem-Solving Tasks

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Type: Problem-Solving Task

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Type: Problem-Solving Task

## Tutorials

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Type: Problem-Solving Task

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Type: Problem-Solving Task