Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

## Valentine Exchange

Video Overview

This lesson begins with students discussing the Valentine's Day card exchange from the previous day. Students are asked how many cards would be exchanged if two students were involved. The students make predictions, and exchanges are modeled with the teacher and two students and the teacher and four students. Students are given the problem that if all twenty-four of them exchange Valentine1s Day cards, how many cards would be needed? Students investigate a mathematical relationship of exchanges based on the number of people involved. Students can choose to investigate the problem with a group, a partner, or individually, and can choose the method and materials they want to use. As they work, students intuitively develop a sense or idea of a functional relationship as they look for regularity in the task. During their problem solving, students discover patterns and are asked to explain their strategies and reasoning. After students complete their work, they share their problem-solving strategies with the class.

Topics for Discussion

The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.

Using Genuine Problems

1. How could the task in this lesson, finding the number of valentines exchanged, be considered a genuine problem?

2. Identify the students1 understanding of the task presented in this lesson. How did the teacher facilitate this understanding? How might you have introduced the task if you were the teacher in this classroom?

3. How did the task, materials, and environment all facilitate problem solving in this lesson?

4. What strategies did students use to investigate the problem? Did any of their strategies surprise you? Why or why not?

5. How were patterns a part of the problem-solving task in this lesson? Why is the study of patterns important? How does it connect to the real world?

Developing Student Discourse

1. What tools did students use to reason as they investigated the valentine-exchange problem? What strategies did students use to understand and make sense of the problem?

2. Identify examples of students listening to, responding to, and questioning the teacher and one another during the lesson.

3. How did the teacher promote the students1 discourse throughout the lesson and elicit the students1 thinking without imposing her own ideas?

4. Describe ways in which students made conjectures regarding the problem situation, using both accurate and inaccurate reasoning.

5. How did students try to convince themselves and one another of the validity of particular representations, conjectures, and solutions?