# MA.7.DP.2.1

Determine the sample space for a simple experiment.

### Clarifications

Clarification 1: 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.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

• Event
• Sample Space

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students determine the sample space for a simple experiment, and in grade 8, they will find the sample space for a repeated experiment.
• For mastery of this benchmark, an experiment is an action that can have more than one outcome. Experiments tend to have randomness, or uncertainty, in their outcomes.
• For example, an experiment can be the action of tossing a coin. Possible outcomes would be whether the coin lands on heads or lands on tails.
• For mastery of this benchmark, simple experiments are restricted to those listed in Clarification 1.
• Tossing a coin
Coins are not limited to those with heads or tails.
• Rolling a die
Dice are not limited to 6-sided dice.
• Picking a card from a deck
Card decks are not limited to a standard 52-card deck.
• Picking a marble from a bag
Picking a marble from a bag is not limited to colors. Picking a tile, slip of paper or other objects from a bag are acceptable for this benchmark.
• Spinning a spinner
Spinning a spinner is not limited to colors.
• Students should experience experiments before discussing the theoretical concept of probability.
• Students should informally explore the idea of likelihood, fairness and chance while building the meaning of a probability value. In this benchmark, all experiments are fair, meaning that all of the individual outcomes are equally likely.
• For example, if the experiment is to draw a marble from a bag, then each marble is equally likely to be chosen.
• Have students practice making models to represent sample spaces to gain understanding on how probabilities are determined. Use familiar tools, including virtual manipulatives such as a coin, fair die, deck of cards and fair spinner (MTR.2.1).
• For simple experiments, a sample space will typically be represented by a list of outcomes, such as Heads, Tails or by a written description, such as “The sides of a 20sided die.” Providing opportunities for students to match situations and sample spaces will assist with building their ability to visualize the sample space for any given experiment.
• For example, the experiment of drawing a marble from a bag containing 2 red marbles and 1 blue marble has the sample space that can be written as {red, red, blue} or as {r, r, b}.

### Common Misconceptions or Errors

• Students may incorrectly list more outcomes than the experiment merits. To address this misconception, ensure students can explain the experiment in their own words to then verify what is listed in their sample space.

### Strategies to Support Tiered Instruction

• Teacher provides examples of situations and has students decide on the sample space necessary.
• Teacher co-creates a graphic organizer with different examples of sample spaces with the use of virtual manipulatives.
• Teacher co-creates a graphic organizer of a T-chart to list the experiment and the sample space necessary for the examples provided.
• Teacher co-creates models with students to represent sample spaces using a coin, fair die, fair spinner or deck of cards.
• Teacher ensures students can explain the experiment in their own words to then verify what is listed in their sample space.

List all of the possible outcomes for each experiment.

Compare your list with a partner and identify any differences. Allow each partner time to discuss their reasoning until an agreement is reached on the correct sample space.

### Instructional Items

Instructional Item 1
Letter cards for the word “probability” are placed into a bag. List the sample space for choosing a card from this bag.

Instructional Item 2
There are 10 blue, 5 green and 7 white marbles in a jar. List the sample space for the simple experiment of choosing a marble from the jar.

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

## Related Courses

This benchmark is part of these courses.
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.DP.2.AP.1: Use tree diagrams, frequency tables, organized lists, and/or simulations to collect data from a simple experiment.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Lesson Plans

What is the Likelihood?:

Students will develop an understanding of likelihood based on calculated probabilities and relate these concepts to being called for jury duty in this integrated lesson.

Type: Lesson Plan

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Casino Royale:

Students examine games of chance to determine the difference between dependent and independent conditional probability.

Type: Lesson Plan

Selecting a Sample Population:

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

Generating Multiple Samples to Gauge Variation:

Students explore variation in random samples and use random samples to make generalizations about the population.

Type: Lesson Plan

Chancy Candy:

In this lesson students will use candy to find the probability of independent compound events, determining the sample space from a tree diagram. They will then conduct an experiment to test the theoretical probability. Once the experiment is complete, the students will compare the theoretical and experimental probability.

Type: Lesson Plan

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.