Pre-Algebra Unit 7: Probability

Unit Driving Question

How can we use graphs and other representations to gain knowledge of real-world situations? 

Essential Questions

1. How can probabilities be determined when actual probabilities are not known?

2. How can predictions be made on unknown probabilities?

3. How can you determine if the representation of a data population is fair?

4. How are conclusions about a data set drawn using sampling?

Big Ideas

1. Experimental probability can be calculated and the result can be expressed in multiple ways.
2. Experimental probability can be used to make predictions.
3. Samples are used to generalize a population. 

Technology Resources

• Pre-Algebra Technology Resources

Launch Task

1 Lesson 

Lottery (MARS): In this task, you must use math to decide whether a lottery idea will make money.

• Task

• Rubric

• Student Work Analysis

Big Ideas for Development Lessons

3-4 Weeks (approximately 1 week per big idea)

Big Idea 1:  Experimental probability can be calculated and the result can be expressed in multiple ways. 

Key Resources 

1. Simulating Multi-step Experiments (OpenUp): In this lesson, students see that multiple chance events can be completed in a row to simulate a compound event. In this case, it is important to communicate precisely what represents one outcome of the simulation.

2. Multi-Step Experiments (OpenUp): In this lesson, students continue writing out the sample spaces for compound events and also begin using those sample spaces to calculate the probability of certain outcomes.

    

Big Idea Probe

• Big Idea 1 Probe (Card Game) 

Evidence of Understanding 

Calculate experimental probabilities

• Represent experimental probability

• As a fraction

• As a percent

• As a decimal between 0 and 1 inclusive

Compare and contrast dependent and independent events

Big Idea 2:  Experimental probability can be used to make predictions.

Key Resources

1. Candy Populations (Georgia Department of Education): In this task, students will draw inferences about a population of M&Ms based upon random samples of M&Ms using proportional reasoning developed in 7th grade.

2. Predicting Populations (Georgia Department of Education): In this task, students will use populations, samples, and proportions in order to make predictions about total population size.

Big Idea Probe

• Unit 8: Big Idea 2 Probe (OpenUp) 

Evidence of Understanding 

Use experimental probability to make predictions when actual probabilities are unknown

Big Idea 3: Samples are used to generalize a population.

Key Resources 

1. Estimating Population Proportions (OpenUp): In this lesson students make predictions about proportions of the population. In statistics the term proportion is used to refer to a number from 0 to 1 that represents the fraction of the data that belongs to a given category.

2. Sampling in a Fair Way (OpenUp): In this lesson, students consider different methods of selecting a sample. Students begin by critiquing different sampling methods for their benefits and drawbacks. In particular, students notice that some sampling methods are more biased than others.

Big Idea Probe

• Big Idea 3 Probe (OpenUp) 

Evidence of Understanding 

Determine how different samples are chosen to draw conclusions and support the conclusion about generalizing a sample of a population

• Including:

• Random samples

• Limited samples

• Biased samples

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)

• Memory Test (OpenUp): This lesson gives students a chance to use the material they have learned in the unit with the final goal of comparing two populations.