Common core State Standards

  • Math:  Math
  • 7:  Grade 7
  • SP:  Statistics & Probability
  • C:  Investigate chance processes and develop, use, and evaluate probability models
  • 8a: 
    Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

    a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

    b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \"rolling double sixes\"), identify the outcomes in the sample space which compose the event.

    c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Download Common Core State Standards (PDF 1.2 MB)

Probability of Dependent and Independent Events
Lesson Objective: Identify and create examples of independent and dependent events
Grade 6 / Math / Probability

Thought starters

  1. How does Ms. Posada prepare students before they begin to write their own events?
  2. How do the manipulatives affect student engagement?
  3. What elements of the student presentations help to further reinforce student learning?

Thank you very much ma'am Posada for sharing your materials and strategies, I wish you will continue sharing us your expertise in teaching mathematics. God bless.

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Thanks for sharing supporting materials.
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I really like how she developed the math vocabulary and how she had the students express math concepts.
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Thanks for the lesson. I especially like how you provide a variety of examples & have students create their own to share.
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I really liked how she had the students involed and engaged
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  • Great Lesson Ideas: Probability of Dependent and Independent Events with Anna Posada

    Posada: [00:00:08] Hello. My name is Anna Posada. I

    Great Lesson Ideas: Probability of Dependent and Independent Events with Anna Posada

    Posada: [00:00:08] Hello. My name is Anna Posada. I teach sixth grade math at Middle Springs Middle School, Winston Salem, North Carolina. [00:00:14]

    [00:00:19] This lesson is called probability of dependent and independent events. All right, we were talking about how do you recognize that an event is dependent or independent? [00:00:31]

    [00:00:31] It is important that the students understand the concept of independent and dependent events as a part of the probability unit which is a very big unit. [00:00:41]

    [00:00:41] What is the probability of drawing a green marble, then a purple marble if you replace the marble after the first draw? [00:00:49]

    [00:00:49] This lesson begins by identifying the key words that are going to help the students realize that if the events we’re talking about are dependent or independent. [00:00:58]

    [00:00:58] What are the key words that are going to help you know whether it’s dependent or independent? Louise? [00:01:03]

    Child: [00:01:03] Replace. [00:01:03]

    Posada: [00:01:04] Replace what does that mean to replace? [00:01:06]

    Child: [00:01:06] Put it back. [00:01:07]

    Posada: [00:01:07] To put it right back in. Okay. Key word right there. I’m going ahead and highlight it so that we make sure we don’t forget it. Replace the marble. [00:01:16]

    [00:01:16] We went over a few examples. I did a problem. I took a bag and pulled some cubes out of the bag, and they decided what the probability was. Then I gave them some examples where they had to decide according to the vocabulary involved whether it was dependent or independent. [00:01:35]

    Child: [00:01:36] Well right, number one it says a quarter, a nickel and a dime are in a bank. What is the probability that the quarter falls out first when the nickel falls out second? Basically it’s dependent because he didn’t place it. He just left it out, so that’s the dependent question. [00:01:56]

    Posada: [00:01:56] Once that was clear, I asked the children to develop their own examples using their own manipulatives. [00:02:03]

    [00:02:03] Now that you—I gave you the events, and you identified them as dependent or independent, now you’re going to make up your own. I’m going to give you—[00:02:13]

    [00:02:13] The manipulatives I gave the students were color chips, dice, coins and spinners. [00:02:19]

    [00:02:20] You’re going to make up a problem. You’re going to make up an event; one that is independent and one that is dependent. So remember the key words. [00:02:28]

    [00:02:29] And what are the key words you need to write in your problem? [00:02:31]

    Child: [00:02:31] The key words that we do not replace it.

    Posada: [00:02:33] You do not replace it. So very good. So say it again. What is the probability—[00:02:38]

    Child: [00:02:39] What’s the probability that you will pull out a purple the first time and a green a second time? Independent or dependent? [00:02:47]

    Posada: [00:02:47] Without replacing. That’s what you want—[00:02:49]

    Child: [00:02:49] Yeah without replacing. [00:02:50]

    Posada: [00:02:51] You got to include those words. [00:02:51]

    [Showing children working 00:02:51 – [00:02:59]

    Posada: [00:02:59] What is the probability of rolling your five and spinning. [00:03:03]

    Child: [00:03:03] The purple. [00:03:04]

    Child: [00:03:04] Well it’s 12. So if I pick out a green one, it will be four 12s. Be four 12s and the super finite will be one-third. [00:03:18]

    Posada: [00:03:18] They created one dependent example and one independent example, and then they were able to share with the class and explain why each example was either independent or dependent. [00:03:29]

    [00:03:29] So what makes this an independent event? [00:03:34]

    Child: [00:03:36] You spin it twice and then you can spin it almost one and it could still be the same. [00:03:42]

    Posada: [00:03:42] All right you still have the same number of possible outcomes? [00:03:46]

    Child: [00:03:46] Yeah. [00:03:47]

    Posada: [00:03:47] Okay. Spinning a spinner twice is a perfect example of independent events. All right. Very good. [00:03:54]

    [00:03:55] I firmly believe that if they can hold it in their hands, they can hold it in their mind. If they can explain it to the rest of the class or a partner or a person in their group, that means they understood. [00:04:05]

    [00:04:06] All right it helped doing the problem itself, the hands-on part? [00:04:00]

    Child: [00:04:09] Yes. [00:04:10]

    Posada: [00:04:10] That help you do it better? Understand it better? All right good job. [00:04:14]

    [00:04:14] You should try this lesson. It is a really cool lesson. The kids get it. The kids get into it. It’s not another worksheet, it’s not another paper and pencil activity. And everything that seems to them like a game, hands-on things, is a lot of fun for them. I would be happy to share my lesson plan, the worksheet with the different kind of events for the students to identify as dependent or independent, and obviously a list of the materials or manipulatives that I put in the little baggies for them to develop their own events. [00:04:45]

School Details

Mineral Springs Middle
4559 Ogburn Ave
Winston Salem NC 27105
Population: 393

Data Provided By:



Ana Posada
Math / 6 7 8 / Coach


Teaching Practice

All Grades / All Subjects / Collaboration

Teaching Practice

All Grades / All Subjects / Planning

Teaching Practice

All Grades / All Subjects / Engagement

Lesson Idea

Grades 9-12 / ELA / Tch DIY