## Cars on the Curve

### Michaél Dunnivant

#### Description

Students predict which car will -win- and then play a car-race game to test their predictions. Their results are analyzed to recognize patterns of central tendency.

#### Objectives

The student writes notes, comments, and observations that reflect comprehension of content and experiences from a variety of media.

The student analyzes real-world data to recognize patterns and relationships of the measures of central tendency using tables, charts, histograms, bar graphs, line graphs, pictographs, and circle graphs generated by appropriate technology, including calculators and computers.

The student predicts the likelihood of simple events occurring.

The student designs experiments to answer class or personal questions, collects information, and interprets the results using statistics (range, mean, median, and mode) and pictographs, charts, bar graphs, circle graphs, and line graphs.

#### Materials

-One Car Race gameboard per pair of students (see Associated File)
-Dice (two per pair of students)
-Transparency of Graph Paper for class graph or butcher paper
-Beans or other game markers (12 per pair of students)
-Crayons or marking pencils
-Data Diary (one per student) or paper for written comments

#### Preparations

The teacher needs to:
1. Make one Data Diary per student by simply stapling five sheets of folded 11 x 17 inch copy paper book-style with a construction paper cover. You could also use noteboook paper.
2. Preview the online student lesson that reinforces the concepts introduced in this lesson (see Weblinks)
3. Prepare a class graph on butcher paper or an overhead transparency to record class results.
4. Prepare an overhead and pens to use when recording data. If you use a chart for the class graph, markers are easier to see than crayons.
5. Download the Cars on the Curve gameboard from the Associated File and make one copy for each pair of students on 8 ½ x 14-inch heavy card stock.
6. Make copies of the Product Rubric (student wording) to use when assessing each student's content writing. Print one Product Rubric (teacher wording) for your reference.
6. Gather two standard dice or number cubes for each pair of students. You will also need 12 beans or markers per pair of students. The beans are the markers for the -cars- in the game.

#### Procedures

Session 1
Students should have experiences with conducting simple experiments, such as coin tosses, spinner games, and standard dice games before this lesson. (see Extensions)

1. Ask students if they have ever been to a race. Ask what they remember about the race. As students share their experiences, ask if they thought the race was fair. Discuss what fair means in mathematics.

2. State that today we are going to play a car race game using two dice called -Cars on the Curve- using two standard dice. Display the -Cars on the Curve- gameboard on the overhead. Explain how to play the game.

Directions for -Cars on the Curve- game are as follows:
-Predict which car will -win- the game and record it in the Data Diary. Students justify why they think so.

-Roll two dice.

-Add the numbers shown on the dice to determine which car moves one space toward the finish line.

-Move that car (represented by a bean) one space on the -Cars on the Curve- gameboard.

3. Ask students if they think the game will be -fair.- Discuss why or why not. Ask, -If we use two dice to play the game, which car do you think will win?- Chart all different responses. Students justify their predictions.

4. Model how to play the game by playing one round as a class. Place one bean for each car on the gameboard. Roll both dice. Total the numbers shown on the dice. Move the car with that number one space. For example, if a student rolls a six and a four, car 10 gets to move ahead one space. Pass the dice to a different student for each roll of the dice. Continue the game until one car wins.

5. Take frequent -pit stops- to look at the results. Ask students if they see any patterns emerging. Ask if they would like to change their predictions and why. Some possible questions are -Why are some cars not moving? Why are some cars moving more than others?-

6. Record the results of the first race on either an overhead or butcher paper class graph. For example, if car number six wins the game, color in one box on the class graph for the six car.

7. Distribute materials for students to play the game in pairs, -Cars on the Curve- gameboard, two dice, and 12 beans (one marker for each car).

8. Check to make sure students know the procedures by having them repeat the directions. Remind students to record their data accurately.

9. Students play one round of the game with their partner and then record the results on the class graph.

10. Discuss the results of the races as shown on the class graph. Ask, -What are true statements we can make about the data?- -How did the results of this car race compare to our predictions?- -Which car do you predict to win next time?-

11. Make time either during this class session or in other class sessions for the students to play the game again and again. This will provide data to analyze and to see patterns of central tendency (a curve). This is also an opportunity for students to practice designing their own experiments, predicting outcomes, and interpreting results. During these sessions, students should record their predictions in their Data Diary or journal to see their progress in making predictions and predicting outcomes. They should also write true statements or observations about the results of each game.

12. Once you have enough data on the class graph so students can recognize that the data is clumped in the middle (a pattern of central tendency), then you may proceed with Session 2.

Session 2
1. Review the results with the class. Ask, -What do you notice about the data displayed on our class graph?- If students recognize that there were more wins near the middle of the graph, ask them why they think so. After some discussion, tell them the game is called -Cars on the Curve- because the data clumps in a type of curve. Draw a line to emphasize the pattern of central tendency. Mathematicians call this a pattern of central tendency. Ask, -Why do you think they call it that?- Discuss student observations and assumptions and then clarify.

2. Proceed with the assessment.

#### Assessments

Assess student content writing in their journal or Data Diaries as they explain if the -Cars on the Curve- game is a fair one. Use the Product Rubric (see Associated File) to assess their explanation for;
-recognizing the pattern of central tendency in the game as shown by the data;
-several examples of why they think the game is fair or not based on the data;

Give students the opportunity to conduct other experiments that will result in patterns of central tendency, for example-classmate's height, shoe size, other dice games with standard or non-standard dice, or the price of food items. Students pose a question, predict the possible outcomes, gather the data on a graph, and analyze the data to recognize patterns of central tendency.

Assess student experiments using the following criteria with the Product Rubric (see Associated File)
-pose a question;
-predict the possible outcomes;
-gather the data on a graph;
-analyze the data to recognize patterns of central tendency.

#### Extensions

This lesson could be extended to introduce statistics, such as range, mean, median, and mode.