Utah State Core Standard 7

Our team focused on the following standards for our learning cycle:

Utah State Core Standard 7.SP.8.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.

Our goal statement is:

Students will be able to represent sample spaces for compound events using a variety of methods and identify the outcomes.

Our Developing Understanding task is to take a variety of situations and list the outcomes using various representations.

Our Developing Understanding task goal is to have students identify outcomes through various representations.

Possible Questions asked by students:

How should we do this? How do we show our work? (Response – What do you think would work?) Could we use manipulatives to model the situation? (Response – What would you like to use? Could you find something in the cupboard that would be valuable to you?) Does order matter? (Does it matter if you put on your shirt first and then your pants or your pants first and then your shirt?) Do the clothes have to match? (No) Does Neapolitan ice cream count as 3 flavors? (Does it come in one carton?) Does it matter which coin we use? What would the difference be if you used difference coins?

Launch:

Bring some clothes to class and visit with the class about how you wish you had more outfits when trying to decide what to wear. How would you determine how many outfits you would have? In our task today that is what we are doing. You need to use various representations such as tables, diagrams, pictures, models, etc. to complete your task.

Have students work on problems 1-4 individually for approximately 15 minutes and then work in groups to complete the task. Monitor the groups and plan how to have groups present to make the connections.

Task 1:

Find all possible choices in the following situations. Show all work using various representations.

1. How many different outfits could you make with 3 shirts and 3 pants?

2. How many different ice cream sundaes could you create if you had 3 ice cream choices and 5 topping choices? You can only use one ice cream and one topping on each sundae.

3. How many outcomes are there if you roll a six-sided number cube with a different number on each side and flip a coin?

4. Analyze your answers for 1, 2, and 3 looking for connections or patterns. Explain how you would find the number of different outcomes if you had 25 shirts, 10 pants, and 5 hats. Task 2:

The solidify task we chose was “Door to Door.”

The solidify goal is for students to be able to identify the possible outcomes for entering and exiting the building.

1. Directions: You must enter through one of the three outside entrance doors, you must pass through one of the two interior doors, in order to exit through one of the three exit doors. Find all possible pathways through the building.

ENTRANCE

______DOOR #1 DOOR #2 DOOR #3

INTERIOR ______DOOR # 4 DOOR #5

______DOOR #6 DOOR #7 DOOR #8

2. How many pathways through the building include going through Door 5?

3. How many pathways through the building include going through Door 8?

4. How many pathways through the building include going through Doors 5 & 8?

5. How are the answers for 1, 2, 3 & 4 related? The Practice Task we choose is an online, interactive review of compound events.

Our Practice Task goal is that students will be able to identify the compound events in a variety of situations. http://www.ixl.com/math/grade-6/compound-events-find-the-number-of-outcomes-by- counting

The following questions are examples of the 30 questions you will find at this site. They are interactive and give explanations with each question that is answered incorrectly.

Practice Task #3 1.

10. Additional resources and extensions:

www. youtube.com /watch?v=jtfbQ02Qryw If you've ever been at a restaurant and seen choices for an appetizer, main dish and dessert, have you ever wondered what could the outcomes be if you had to pick one of each from the choices you had? In this video, Mr. Almeida shows you how to list the possible outcomes of compound events.

This is not asking how many combinations are possible, but rather it is a lesson in WHAT the outcomes are.

http://www.studyzone.org/mtestprep/math8/e/treediagram6p.cfm

This site has interactive questions about possible outcomes and tree diagrams with detailed explanations if students need a review.

A tree diagram is a diagram showing all possible outcomes of an event. This type of diagram shows one branch for each possible outcome.

It is often easy to list the outcomes for a single experiment. It can be more complicated to list the outcomes for a series of experiments.

When trying to determine the possible outcomes from an experiment, it is often helpful to draw a diagram which illustrates how to arrive at the answer. http://illuminations.nctm.org/LessonDetail.aspx?ID=L248

In this lesson, students practice decision-making skills leading to a better understanding of choice versus chance and building the foundation of mathematical probability. This lesson is adapted from an article by Dan Brutlag, "Choice and Chance in Life: The Game of SKUNK," which appeared in Mathematics Teaching in the Middle School , Vol. 1, No. 1 (April 1994), pp. 28-33.