This lesson is a re-engagement lesson designed for learners to revisit a problem-solving task they have already experienced. My colleague Stacy Emory best describes re-engagement by comparing it to re-teaching. Re-teaching is a teacher-directed activity where we plan a different lesson to address something that is perceived to be a misconception with our students. Re-engagement is a learner-centered activity wherein the original task is posed in such a way that we may expose learners to different strategies, alternate solutions, or even misconceptions. Think of the original task as a formative assessment that helps you shape the lessons that follow.
As learners enter the 6th grade, they have had many experiences with modeling and describing numeric patterns. The "Buttons" task comes from the 2003 MARS test for grade 5. Within this task learners are asked to investigate a numeric pattern and to generalize what they see happening as the pattern grows. Counting on strategies will work, but there is a clear emphasis and interest on our part as educators on moving learners towards multiplicative thinking in this task. This increase in cognitive demand needs to be further explored to ensure the learners are making connections between the numeric pattern and a generalized “rule” or function. There are five representations that learners should be exploring as they puzzle with numeric patterns/algebraic thinking: pictorial, numerical, verbal, graphical, and algebraic representations.
Main Goals of the Lesson
Make connections between the different representations to more critically compare the two interpretations
Algebra and Functions 1.0
This lesson also touches on all of the NCTM Process Standards: Problem Solving, Reasoning and Proof, Communication, Connections, and Representations
Challenges for Students with this Content
Experience with using one or more of the representations will vary from learner to learner
Taught by: Fran Dickinson, San Carlos Charter Learning Center, San Carlos School District, San Carlos, California
- Operations & Algebraic Thinking