Investigations: Cont"rolling" Variables
Dixon, Juli K., Adams, Thomasenia Lott, Hynes, Mary Ellen, Teaching Children Mathematics
The purpose of the "Investigations" department is to provide mathematically rich and inviting contexts in which children and their teachers solve problems, communicate, and reason. Investigations encourage students to make connections among mathematical ideas, as well as connections with contexts outside of mathematics. As students collaborate, experiment, explore, collect data, research various sources, and engage in activities during the investigation, they will have opportunities to represent their mathematical ideas in multiple ways.
Investigations are comprised of several tasks that collectively promote deep examination of a core topic and question. They are open-ended and often require more than one period to complete. The following investigation has been enriched by teaching suggestions that encourage reflection. These tasks are expected to mark a point of departure for students and teachers to embark on thoughtful, coherent mathematical explorations.
On the Move (Levels 1-3)
* measure distances using nonstandard units (e.g., string or long wooden rods) or standard units (e.g., customary or metric),
* compare distances,
* distinguish between what remains constant during the investigation (time and traveler) and what changes (the types of movements or number of repetitions during travel), and
* identify relationships between the types of movement and distances.
Each group will need--
* a timer or stopwatch that can measure seconds,
* a measuring stick or tape for standard units,
* string or long wooden rods for nonstandard units, and
* a copy of the reproducible page "On the Move."
Preparing for the investigation
In such games as red light--green light, Simon says, and red rover, children are challenged to cover given distances with different purposes and in different ways. This investigation focuses on the effects of changing the ways that students "walk" a distance and the number of "steps" that they take in a given amount of time. Students will measure the distance that they can travel using various types of movements in fifteen seconds. Remind students of games that involve walking, hopping, or other ways that children cover distances without the help of others. You might start the discussion by asking about games with which your students are familiar, such as Simon says.
Structuring the investigation
1. Ask students, "Which type of movement would you choose in playing red light--green light if you were trying to get through the light?" Ask students whether their answers would be different if they were playing the part of the traffic light and trying to keep people from getting through.
2. Have students brainstorm to identify how they move in different games, as well as other ways that they can move from one place to another. Be sure to include suggestions for children who are physically challenged, including children who are in wheelchairs or who use crutches or braces. List these suggestions for students to see.
3. Have students make conjectures about when and why different types of movement are better in each of the games. Guide students toward investigating and comparing different ways of moving during a set period of time.
4. Students should consider two questions:
* How far can a student travel in a given amount of time?
* How many paces or repetitions of movement can a student make in a given amount of time?
Students might suggest races using different types of movement to determine who can get to a destination first. At this point, you might choose students of various heights and ask them to take "giant" steps to ascertain who can get from point A to point B in the fewest number of steps. Lead your students to see that different people can use the same type of movement and end up with different results. …