## Learning Math: Patterns, Functions, and Algebra

# Classroom Case Studies, Grades 6-8

## Explore how the concepts developed in Patterns, Functions, and Algebra can be applied at different grade levels. Using video case studies, observe what teachers do to develop students' algebraic thinking and investigate ways to incorporate algebra into K-8 mathematics curricula. This video is for the 6-8 grade band.

**In This Grade Band:**

- Part A: Classroom Video
- Part B: An Example for Developing Algebraic Thinking
- Part C: Patterns That Illustrate Algebraic Thinking
- Part D: More Problems That Illustrate Algebraic Thinking
- Part E: Critiquing Student Lessons
- Homework

This is the final session of the *Patterns, Functions, and Algebra* course! In this session, we will examine how the types of mathematical tasks involving algebraic thinking from the previous nine sessions might look when applied to students in your own classrooms. This session is customized for three grade levels. Select the grade level most relevant to your teaching.

In the previous sessions, we explored the components of algebraic thinking: fundamental algebraic ideas (content) and mathematical thinking tools (process). You were asked to put yourself in the position of a mathematics learner, both to analyze your individual approach to solving problems and to get some insights into your own conception of algebraic thinking. It may have been difficult for you to separate yourself as a mathematics learner from yourself as a mathematics teacher. Not surprisingly, this is often the case! In this session, however, we will shift the focus to your classroom and to the approaches your students might take to mathematical tasks involving algebraic thinking. **Note 1**

**Learning Objectives**

In this session, we will focus on your experiences as a classroom teacher, as you:

- Explore how algebraic thinking is developed at your grade level
- Examine problems for their algebraic content
- Analyze mathematical tasks and their connection to mathematical themes in the course
- Critique lessons at your grade level for algebraic thinking

### Key Terms

### Notes

**Note 1**

This session focuses on developing algebraic thinking in the K-2 classroom. We’ll consider the mathematics content of the previous sessions and the relation of that content to the mathematics you teach in your own classrooms. We’ll explore how algebraic thinking develops at your grade level by analyzing mathematical tasks appropriate for the K-2 classroom. We’ll also look at lessons from existing curriculum materials and critique them in relation to how students are asked to demonstrate their thinking and to how the mathematics reveals algebraic thinking.

**Review**

Begin the session by reviewing the mathematics content in the previous nine sessions: patterns, functions, linearity, proportional reasoning, nonlinear functions, and algebraic structure. You may want to think about one big idea in each of these topics.

**Homework Review**

**Groups:** Discuss any questions about the homework.