Linear Growing Patterns - Representing


The Ontario Ministry of Education is not responsible for external content and resources.

Student Links


Math Gizmos

Library of Virtual Manipulatives - Algebra Strand
Links to a listing of activities related to the NCTM algebra standard

Guess the Function
Links to an activity in which x-values are used to generate ordered pairs; the objective is to guess the rule

Guess the Rule Used by the Machine
Links to an activity which allows the user to explore simple linear functions

Collect Gems by Choosing the Dragon's Flight Path
Links to an activity in which the user determines which linear relations would be the best flight path for the dragon


Teacher Links

Linear Growing Patterns CLIPS Content at a Glance CL004_CAG_May 7.pdf
List and description of Additional Resources available through CLIPS: CL004_Additional Resources.pdf
NCTM Illuminations Web Links - Algebra
Wired Math - Grades 7-9 - UW's links to fun resources

Barb Seaton has been using CLIPS in TVDSB. Feedback is welcome in the discussion posts.

Hi all - I've been using CLIPS as part of three part lessons to model for the teachers in my region how valuable they are and how they can be embedded into our lessons. Please find selection of patterning lessons - they include some ideas for extending the teaching, creating anchor charts etc. They all have a CLIP or 2! Viewers will need Smart Notebook to open the file.
Patterning lesson 1
Patterning Lesson 2
Patterning lesson 3
Patterning more ideas with CLIPS
I'd love to hear how they go!


Research Links

Beatty, Ruth and Bruce, Cathy, Assessing a Research/PD Model in Patterning and Algebra, http://tsg.icme11.org/document/get/170
In this study, researchers and teachers worked together to evaluate a series of lessons developed to foster student understanding of linear functions. To bridge the research-practice gap, we developed a Research/PD Model of professional development that included teachers as research participants. Our research questions were 1) will participation in the PD program increase teachers’ pedagogical content knowledge in patterning and algebra?; 2)will participation in the PD program influence teacher efficacy?; and, 3) what is the role of teacher enactment in theprofessional development of teachers?

Beatty, Ruth and Moss, Joan, MULTIPLE VS. NUMERIC APPROACHES TO DEVELOPING FUNCTIONAL UNDERSTANDING THROUGH PATTERNS – AFFORDANCES AND LIMITATIONS FOR GRADE 4 STUDENTS, http://www.pmena.org/2006/cd/ALGEBRAIC%20THINKING/ALGEBRAIC%20THINKING-0000.pdf , PME-NA 2006 Proceedings Vol.2, 87-94
In this paper we present different approaches and outcomes of two grade 4 students who were participants in an intervention study for the development of an understanding of functions through patterns. We contrast one student who used multiple representations (visual, narrative, graphic and numeric) to another who relied exclusively on numeric tables in order to reveal the affordances and limitations of these approaches.

Moss, Joan and Beatty, Ruth, Knowledge building in mathematics: Supporting collaborative learning in pattern problems, http://ijcscl.org/?go=contents&article=21 , International Journal of Computer-Supported Collaborative Learning, Vol.1(4), 441-465, December 2006
While it has been suggested that patterning activities support early algebra learning, it is widely acknowledged that the shift from perceiving patterns to understanding algebraic functions -- and correspondingly, from reporting empirical patterns to providing explanations -- is difficult. This paper reports on the collaborations of grade 4 students (n = 68) from three classrooms in diverse urban settings, connected through a knowledge-building environment (Knowledge Forum), when solving mathematical generalizing problems as part of an early algebra research project.

Rivera , Ferdinand, Visualizing as a Mathematical Way of Knowing: Understanding Figural Generalization, Mathematics Teacher 101(1), August 2007, 69-75
available online at http://www.math.sjsu.edu/~rivera/rivera.mt.pdf