Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

## Products and Sums

Video Overview

Students in this lesson explore relationships between addition and multiplication. Throughout the lesson they search for mathematical language to describe the patterns and relationships to their peers, to the teacher, and in writing. They are first asked to find a relationship between a number (4), the sum of the number added to itself (4 + 4 = 8), and the product of the number multiplied by itself (4 x 4 = 16). Symbolic and geometric examples are modeled on the chalkboard. Each group of four students is given a number to explore. After groups have represented numbers, sums, and products with symbols and identified geometric relationships with patterns on grid paper, they post their results on the front board for viewing and discussion. Each group then receives a chart showing the numbers, sums, and products all the groups recorded. Groups look for and record numerical relationships and geometric patterns in the chart. These observations are discussed by the whole class. The lesson closes with students writing what they like or dislike about looking for patterns and relationships.

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.

Investigating Patterns and Relationships

1. Students are investigating sums and products in the lesson. What mathematical ideas are being developed through this activity?

2. Ms. Doolittle gave students an organized arrangement of the sums and products. How did this arrangement affect the students1 discoveries of patterns?

3. List the patterns and relationships that students discovered.

4. How is mathematical understanding revealed in the patterns the students discovered? What is the value of devoting an entire lesson to searching for patterns and relationships among numbers?

5. What is the role of patterns and relationships in the study of mathematics?

Developing Classroom Discourse

1. Ms. Doolittle was a facilitator of classroom discourse. What kinds of questions and responses did she use to promote discourse? What other questions might you have asked?

2. Identify ways in which writing was used to enhance understanding and discourse in this lesson.

3. Students worked in small groups during the lesson. How did small-group work foster discourse?

4. The students and teacher talked about models. What is a model? How does using models promote discourse?

5. Why did Ms. Doolittle say 3Write down anything you see2 before the groups began their work?

6. Identify instances of the teacher1s nonjudgmental manner and her acceptance of all responses by students. How did she probe students to get them to clarify their patterns and relationships?

Extension

Number Patterns

Create a list of additional number patterns that could be explored, such as odd and even numbers, triangular numbers, square numbers, Pascal1s triangle, or the relationship between the number of folds you can make on a sheet of paper and the number of parts created by the folds. Select one pattern and develop an investigation for its use with elementary students.