- Subject:
- Statistics and Probability
- Material Type:
- Lesson Plan
- Level:
- Middle School
- Grade:
- 7
- Provider:
- Pearson
- Tags:

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Text/HTML

# Project Rubric: Samples and Probability

# Collecting & Analyzing Data

## Overview

Students collect and analyze data for their unit project.

Students are given class time to work on their project. Some students may choose to use the time to collect data (if their project is an experiment based on experimental probability), while others will use the tools (spinners, coin toss, number cube, etc.) to collect their data. Students should use the time to analyze their data, finding the theoretical (if possible) probability and comparing it to the experimental results.

# Key Concepts

Students will apply what they have learned about probability to work on their project, including likelihood of events, determining theoretical and experimental probability, comparing results to calculations, and using simulations to establish probability.

Students may also use data analysis tools to discuss their results.

# Goals and Learning Objectives

- Complete the project, or progress far enough to complete it outside of class.
- Review concepts of probability (simple probability, compound events, experimental vs. theoretical probability, simulations).

# Review the Project Rubric

# Lesson Guide

Have students look at the rubric and talk with a partner to describe it as completely as possible in their own words.

Tell students they will have today to collect and analyze data and prepare for the project presentations. If they do not finish today, they will need to work on it outside of class.

SWD: Make sure that all students have access to and can comprehend the information in the rubric so that they can accurately interpret your assessment of their work.

Students with disabilities may benefit from support in understanding the expectations. Allow multiple means of representing the information in the rubric (visual presentation of text, Text to speech, visual supports, etc.).

Create and provide an enhanced version of the rubric with embedded text structures (labels, highlights, words in bold) to cue students to pay closer attention to particular terms.

## Opening

# Review the Project Rubric

Work with a partner to examine the project rubric.

- First, take a few minutes to study the rubric by yourself.
- Second, without looking at the rubric, take 1 minute to describe the rubric as completely as possible to your partner (who can look at the rubric). Your partner should listen carefully to your description.
- Third, briefly look at the rubric again. Your partner should now take 30 seconds to add to your description of the rubric—without repeating any of your description and without looking at the rubric.

HANDOUT: Project Rubric: Samples and Probability

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will determine how to collect and analyze data.

## Opening

Determine how to collect and analyze data.

# Questions

# Lesson Guide

Students will work in their project groups. Explain that they need to be clear about what is left to do on their project by the end of Work Time. Check with students as they work.

ELL: Consider writing your expectations and how the project fits into the grading scheme to be sure ELLs have clarity around these topics.

# Mathematics

Make sure students understand how to collect their data for their experiment, such as using one or more of the interactives, or having a clear procedure to collect experimental results (e.g., how to drop a cup the same way each time).

Some questions to ask as students are working:

- How many trials did you conduct for each set of data?
- Do you think that there is enough information to make conclusions?
- Did you find the theoretical and experimental probability?

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

Students must make sense of their question and the data they have collected or the trials conducted to help them answer it.

# Possible Answers

Answers will vary. Good things to think about may be the total possible number of outcomes of the trial and how the experimental probability may change by performing one more trial.

For example, if an experiment has 20 possible outcomes, it would be impossible to see them all (let alone measure accurate probabilities for them) with fewer than 20 trials. Think of a 20-sided die with the numbers 1 through 20 on the faces (and an even chance, 5%, of rolling any number on the die). If you only did 19 trials and had every number except 20 come up, you would think that the probability of rolling 20 is 0!

Then, you can think about what would happen if you wanted to perform one more trial after you performed 20 trials and had each number come up once. The next (21st) trial would necessarily repeat one of the numbers. Whichever number was repeated would then appear to have twice the chance of being rolled as any other.

- Answers will vary. Students should base answers on their reasoning in the previous question.
- Results can be compared by using a ratio of the expected and experimental probabilities (this can also be expressed as a percent) or by applying them to a specific scenario. For example, if flipping a coin 100 times, expected results are 50 heads and 50 tails, but experimental results may be 60 head 40 tails. In this case, the experimental probability of flipping heads ends up being 20% higher than the expected probability: $\frac{60}{50}$ = 1.2, or 120%.

## Work Time

# Questions

Today you will perform the trials for your experiment or gather your data. As you work on your project, consider these questions:

- How much data do you need to collect to be confident that the experimental probability or calculated probability is accurate?
- What size should each set of trials or set of data be?
- How can you compare the expected results to the experimental results?

# Project Work

# Mathematics

Some questions to ask as students are working:

- How will you display your results?
- How does your work align with the project rubric?

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

Students must determine the best way to organize the data and determine the measures that best summarize and describe what the data show.

**Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.**

Students must construct viable arguments to justify their conclusions based on the data collected and the statistical measures they have calculated.

**Mathematical Practice 5: Use appropriate tools strategically.**

Students must choose the most appropriate measures and displays for their data. Students might also use spreadsheet and plotting tools to explore various data displays and help them choose the best one.

**Mathematical Practice 6: Attend to precision.**

Students must communicate their conclusions and reasoning precisely in their project summaries.

SWD: Some students with disabilities may struggle with self assessment; use your knowledge of student strengths and vulnerabilities to inform and create interventions you will put into place for this period of class time. Meet with student groups to ensure they are clear about their “to do list” for their in class time.

## Work Time

# Project Work

Your completed project should include:

- A description of the project: Does it involve one event or compound events? Independent or dependent events? Equally likely or unequally likely outcomes? An experiment, simulation, or data collection?
- The theoretical probability of the event (or your guess if there is no theoretical probability)
- If you conduct an experiment, the expected results for three sets of increasingly larger trials (if there is no theoretical probability, or you are conducting a simulation, predict the results of the last two sets of trials based on the probabilities from the first set of trials).
- If you are collecting data, a description of what your
*samples represent*, and the probabilities for each set of data you collect - An analysis of all your data

As you work, use the project rubric to evaluate your progress and make sure you are on the right track.

# Make Connections

# Lesson Guide

Have students share their thoughts about the project and discuss possible additions to the rubric.

SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their Self Check. Teach your students how to review the rubric. Model for students how to plan for revisions based upon the assessment of the rubric.

## Performance Task

# Make Connections

Look at the rubric again.

- Notice the blank column with the heading “Specific to This Project.” Is there anything that you think should be added to this column?
- Next, look at the bottom row that is blank. Is there any scoring criterion for the project that you think should be added here?
- Take a few minutes to discuss these questions with a partner. Write down any ideas you have.
- Now discuss your ideas as a class. When you propose an idea, make sure to explain why you think it is important. After all ideas are discussed, the class will decide as a group whether to adopt any of the suggestions.

HANDOUT: Project Rubric: Making Connections

# Reflect on Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to find out how far project groups have progressed and what remains to be finished.

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful. Then share your reflections with your group.

**Today my group accomplished…
Our next steps are…**