## Leap Frog Experiment

### Michaél Dunnivant

#### Description

As an introduction to problem solving, students ask questions and design an experiment to explore different spinners in -The Leap Frog- board game. As students conduct their experiment, they collect information and interpret the results using a graph.

#### Objectives

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

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

-Leap Frog Experiment Sheet and game board (download masters from Associated File)
-Card stock (for spinners and game boards)
-Paper fasteners, such as brads (one per spinner )
-Class graph on which to compile data (butcher paper, poster, or chalk board)
-Overhead markers in green, yellow, and orange
-A list of the steps for conducting an experiment as explained in the lesson procedures
-Online student lesson -It's a Froggy Experiment- (click on Weblinks)

#### Preparations

The teacher needs to:
1. Make copies of -Leap Frog Experiment- and -Think Space- sheet for each student after downloading them from the Associated File.
2. Copy the Leap Frog game board and Spinner Sheet with spinners onto card stock or heavy weight paper. Cut the frogs from the Spinner Sheet. Color one each orange, green, and yellow or have students do this.
3. Make spinners so there are enough for each pair of students to have one of each spinner (about 10 of each). Use a paper fastener to attach the colored card-stock spinner to a card stock square. Make sure the hole is round before you insert the paper fastener. If you have the holes punched, the students can make their own spinners.
4. Make overhead transparencies of the -Leap Frog Experiment- sheet, -Spinner- sheet, -Leap Frog Game Board,- and -Think Space- sheet.
5. Set up the overhead projector and have orange, green, and yellow transparency markers ready. Color the spinners according to the labels (O = orange, G = green, Y= yellow).
6. Prepare the class graphs (three total) on butcher paper. Be sure to label the axes of the graphs and title them as -Spinner 1 Graph-, -Spinner 2 Graph-, -Spinner 3 Graph.- It also works well to put a picture of each spinner on their respective graphs. This graph is just a simple bar graph.
7. Put crayons yellow, green, and orange near the class graph so students can record their results.
8. Preview the Beacon Learning Center online student lesson -It's a Froggy Experiment.-

#### Procedures

1. Ask students what they know about experiments. As students brainstorm, chart their responses on the board. Draw upon students' experiences as listed on the chart throughout the lesson as appropriate. If students have experiences with experiments in science, draw parallels to mathematics.

2. Tell students that today we are going to learn how to design experiments in math while solving a problem. Elicit from students how they think experiments are designed in mathematics.

3. By referring to what the students suggest, introduce the problem-solving steps as they design an experiment during this lesson. (The problem-solving steps are: understand the problem, decide on a plan, carry out the plan, look back and review.)

4. Tell students you've got a new game called Leap Frog. The object of the game is to spin the spinner in order to -leap- your frog across the pond. Each frog -leaps- when its color is spun on the spinner. The first frog to reach the other side of the pond is the winner. The game comes with three different spinners. The problem is: Which spinner is fair? Ask students what they think fair means.

5. Show students the three different spinners on the overhead. Ask students for their observations about each spinner. Chart their responses on the -Think Space- overhead transparency (a tree diagram of sorts used as a graphic organizer) next to each respective spinner so you can refer back to their comments.

6. Ask, -Do we understand the problem?- Get clarification by asking students to restate the problem as the class comes to consensus. State that this is the first step to designing an experiment. In pairs, have students record the problem in their own words on the -Leap Frog Experiment- sheet.

7. Next, each pair of students choose the spinner they would like to test for fairness. Ask why they selected a particular spinner.

8. Model how to decide on a plan for the experiment by -thinking out loud- the strategy you would use. Make sure to make a prediction about what you think will happen in your experiment. Show them how to play the game using the game board and how to record their data using the Spinner Sheet. Students might choose to record the data in their own way, like tallying on a chart, etc.

9. Ask students what they will do to test their spinner. Tell students that this is the second step to designing an experiment, -Deciding on a plan.- Instruct students to -think out loud- about what they will do and record these thoughts in the Think Space provided on the -Leap Frog Experiment- sheet. (You may also want students to use the -Think Space- sheet if they need more direction in critical thinking.) Students select one of the strategies listed on the sheet as part of their plan for the experiment. Give examples and non-examples of each as necessary.

10. As pairs of students decide on their plan, which should include making predictions, they will need to check with the teacher before preceeding with their experiment. (I had students pair up with the person sitting next to them. As students cut and colored their frog pieces, they discussed what their plans were. I circulated and asked them about their experiment plans during this time.)

11. If the plan seems plausible, give students time to conduct experiments and record data. If the plan is not plausible, work with students as they revise their plan. Tell students that this is the third step, -Carrying out the Plan.- Assist pairs with collecting information accurately and ask questions about their experiments. This is also a good time to assess students' understandings, misconceptions, and problem-solving strategies while you observe.

12. About half way through one round of experiments, ask students to pause and share the results.

13. As students finish a few rounds of their experiments, have them reflect upon their predictions, summarize in writing what they did to conduct their experiments, and begin to interpret their experiment findings on the -Leap Frog Experiment- sheet. You will need to model this.

14. Instruct students to record their data on the class graph labeled with the spinner number and spinner that they used. (For example, if a pair of students used spinner number three to conduct their experiment, they would record the number of wins for a particular color frog on the class graph labeled Spinner Three.)

15. Emphasize how important it is to record data correctly so we can answer our question, -Which spinner is fair?- In experiments, accuracy is very important and part of what it means to be a mathematician. Give examples and non-examples of what happens when data is recorded correctly or incorrectly.

16. As students finish recording the number of wins for each frog on the class graph, bring students back together for a review and interpretation of class results. Tell students that the final step to conducting an experiment is to -Look back at what they did.- Ask the students if we answered our question, -Which spinner is fair?- with our experiments. Ask students to justify their conclusions based upon the collected data. 17. Conclude the lesson with a review of how to conduct an experiment using the chart that lists the steps.

18. Follow up this lesson with the Beacon Learning Center online student lesson, -It's a Froggy Experiment.-

#### Assessments

During the lesson, the Beacon Learning Center online student lesson, and the student-led experiment, use the following formative assessment criteria:
Pairs of students design an experiment that follows these steps.
-State the problem in the form of a question
-Use one of the strategies as listed, which should include making a prediction as to the outcome and selecting the spinner as a model
-Conduct the experiment
-Record data accurately
-Interpret the results in graph form based on the data collected

Based upon the information you collect during this formative assessment, you should plan the next lesson to address particular weaknesses. The information is to inform you about where the students are in their understanding of how to design an experiment and collect data to answer personal or class questions.