Q&A #20729

Difference between ordered lists, and a tree diagram

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From: Gail (for Teacher2Teacher Service)
Date: Apr 18, 2010 at 08:21:21
Subject: Re: Difference between ordered lists, and a tree diagram

Hi Teresa, I think it would be great for your students to see the relationship between the two. In the end, you probably want them to realize that if they can create a tree, they don't need to do the ordered list. An ordered list gives them all the possible outcomes, and from it they can determine the probability of a certain type of outcome occurring. They can really do the same thing with a tree. For example, if you are looking at the different sundaes that can be made from three types of ice cream, two types of sauce and two types of sprinkles, you could start your lists with one of those categories and then keep listing until you had them all: Chocolate - hot fudge - nuts Chocolate - hot fudge - coconut Chocolate - butterscotch- nuts Chocolate - butterscotch- coconut Vanilla - hot fudge - nuts Vanilla - hot fudge - coconut Vanilla - butterscotch- nuts Vanilla - butterscotch- coconut Strawberry - hot fudge - nuts Strawberry - hot fudge - coconut Strawberry - butterscotch- nuts Strawberry - butterscotch- coconut Or you could make the tree (I can't figure out how to make the connecting lines, here... - nuts - hot fudge - coconut Chocolate - nuts - butterscotch - coconut - nuts - hot fudge - coconut vanilla - nuts - butterscotch - coconut - nuts - hot fudge - coconut strawberry - nuts - butterscotch - coconut If you wanted to know what the chance was of getting a sundae with butterscotch topping if you just ordered randomly, you just count the times it shows up on the ordered list: 6 times out of 12 (or half the time, 50% chance) To do that with the tree, your students should notice that you end up with the same number of outcomes (12), and there are three branches out of 6 naming butterscotch as the topping. This could be a great way to point out how useful it is that they know about equivalent fractions, too! One thing I would be sure to do is to have them find the outcomes of the ordered list "hidden" in the tree. For example, if they are looking for "Vanilla - butterscotch- nuts" in the tree, they start with Vanilla, then take the bottom branch to butterscotch, and the top branch that comes next for nuts. They won't readily see this, unless you guide them to "discover" it. One thing I have done is bring in little vanilla wafers, oatmeal and chocolate cookies, some different types of frosting, and some different sprinkles. First we determined all the possible ways we could decorate the cookies, and then had a cookie decorating session. Eventually you will want your students to figure out that they can find the total number of outcomes by multiplying, but if they are actually looking for certain outcomes, knowing that won't get them the answer they are looking for. A tree or ordered list is a necessary skill, especially when they begin looking at dependent and independent events in probability later on. Can you tell I love desserts? Often this is done with outfits, or sandwiches. I hope I have given you something to start with. -Gail, for the T2T service

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