## Drawing Bugs Game

### Michal Dunnivant

#### Description

Students explore probability by predicting the likelihood of rolling any one number on a fair die, graphing data, and analyzing the results of playing a drawing game.

#### Standards

Florida Sunshine State Standards
LA.B.2.2.1
The student writes notes, comments, and observations that reflect comprehension of content and experiences from a variety of media.

MA.E.1.2.1
The student solves problems by generating, collecting, organizing, displaying, and analyzing data using histograms, bar graphs, circle graphs, line graphs, pictographs, and charts.

MA.E.2.2.2
The student predicts the likelihood of simple events occurring.

Florida Process Standards
Effective Communicators
02 Florida students communicate in English and other languages using information, concepts, prose, symbols, reports, audio and video recordings, speeches, graphic displays, and computer-based programs.

Numeric Problem Solvers
03 Florida students use numeric operations and concepts to describe, analyze, communicate, synthesize numeric data, and to identify and solve problems.

#### Materials

- Graph Paper (see Attached File)
- Overhead transparency of Graph Paper
- Standard die (one per student or pair of students)
- Data Diary (one per student)
- Crayons or other marking pencils
- Overhead transparency grid for class graph or butcher paper
- Graph Criteria poster (see Attached File)
- Product Rubric (see Attached File)
- Drawing Bug Direction Sheet (see Attached File)
- Online student lessons (see Web Links)

#### Preparations

The teacher needs to:
1. Duplicate Graph Paper one per student or per pair of students from the master in the Attached File.
2. Make one transparency from the Graph Paper master.
3. Make one Data Diary (or journal) per student by stapling five sheets of folded 11 x 17 copy paper book-style together with a construction paper cover.
4. Preview the lessons listed in the Weblinks that reinforce the concepts taught in this lesson.
5. Prepare an overhead transparency or butcher paper to organize the data into a class graph.

#### Procedures

1. Review other simple events and experiments conducted with spinners and coins thus far in the unit. (see Extensions)

2. Ask students what they know about a die or dice and why they think people use dice (or number cubes).

3. Tell students that today we will explore probability by playing a drawing game with a die. Discuss the importance of understanding how likelihood works in probability for decision-making in life.

4. Ask: When you roll a die, what are the possible outcomes? Draw a tree diagram to illustrate each of the possible outcomes.

5. Ask: What is the likelihood of rolling any one number on the die? During this discussion, ask a number of questions and refer back to previous experiments.
-Is a standard die fair?
-Why do you say so?
-Will any one number be rolled more than another?
-What are the chances of rolling one number rather than another?

6. Ask students to predict which number will win? Chart their responses. Ask for clarification or justification based on their past experiences.

7. Tell students that today we will play the Drawing Bugs game to help us answer the question, What is the likelihood of rolling any one number on a die? Establish this as the problem.

8. Model one round of the game for the class and record the results on the Drawing Bug Directions Sheet overhead transparency.

9. Distribute the Drawing Bugs Direction Sheet. Ask the class: How many dice rolls will it take to make a complete bug? Will the bug have more or less of the body parts it needs to be complete? Discuss their predictions as they record in their Data Diary.

10. Check to make sure students understand how to play the game and distribute the materials: One die per student or pair of students, Drawing Bugs Direction Sheet, and Data Diaries or journal paper. Remind students to keep a tally of the each and every roll of the die as they complete their drawing. (This is very important to minimize confusion. Students record each roll of the die as a tally mark, but they are only allowed to draw a certain number of each body part.)

11. Allow time for students to conduct experiments and record data by tallying in the box at the bottom of the sheet. Then, they can draw the number of bug body parts that coincides with the number rolled.

12. During the round, pause and analyze the results.
-What is the data telling us?
-Would you like to change your prediction? Why?
-What true statements can you say about the data? (A true statement is a fact expressed by the data, i.e., six is rolled 10 times, two was rolled more times than three of the other numbers, etc.)
Emphasize the importance of recording the data accurately.

13. Ask students to make predictions for class results of the game, i.e., Which insect body part will have the most wins? Why?

14. After students complete their games, model the process of deciding how to organize the data so we can analyze the results. Ask,
-Do we know what the likelihood is for rolling any one number on a die from the results of the game?
-Why or why not?
-How can we easily determine this with the data we have?
Lead students to realize that the data needs to be organized first.

15. Tell students that they are going to create a graph to organize the results. Model how to create a graph. Graphs should include appropriate labels, scale, and title. As you create a graph on the overhead, review the components of a graph as shown on the Product Rubric written in student wording (see Associate File).

16. Allow students time for creating their graphs to display the results.

17. Encourage students to check their predictions with the data. Ask
-What do we know about the likelihood of rolling any one number on the die after conducting our experiments?
-How close were our predictions to the actual results of the experiment?
-Was any one number rolled more times than another? Why?
-Did everyone get the same results? Why or why not?

18. After the discussion, students then record what they know about probability based upon previous experiments in their Data Diary. Their entry should also explain their initial prediction and how close it was to the actual results. Here are some other questions to which students might respond.
-Did you change your prediction during the experiments? Why?
-What is the likelihood of rolling any one number on the die? How do you know?
-Is the die fair? How do you know?
Then show the students a non-standard die, i.e., maybe an eight-sided die or one with fewer than six sides, or maybe one with different markings. Ask: What is the likelihood of rolling any one number on this die?-

NOTE: The real-life bug with the same number of body parts is the honeybee.

#### Assessments

Assess the student-created graphs in this lesson as a product and the Data Diary (or journal) entry for understanding content.

Introduce the Product Rubric (for students) that is in the Attached File as you assist students with self-assessment. The purpose of this assessment is not for a grade, but to guide students to reach for higher quality products and understanding. If you need to take a grade at this point, equate a value to the levels of performance on the rubric, but allow students to improve their work through self-assessment before you actually score it. It is also helpful for students to score their own work. This will help them evaluate the quality of their work based upon the criteria and begin to see where they need to adjust to improve next time.

#### Extensions

In this lesson, students examine likelihood. This concept can be extended to express likelihood as ratios in fraction form as found in the lesson entitled Notes to a Mathematician.