Reasoning & Explaining
Reasoning and Explaining, K-5
Classroom artifacts are used in this module to explore strategies that support students’ early development of reasoning and explaining. Participants experience a way in which properties of operations can serve as a vehicle to help students learn to look for regularities and construct viable arguments.
Module Resources
K-5 Properties of Operations – Presentation
K-5 Properties of Operations – Resources
Module Video
Reasoning and Explaining, 6-12
Participants will unpack the connection between similarity, slope, and the graphs of linear functions by doing mathematical tasks, analyzing student thinking, and exploring a computer-based applet. Together, these activities serve as the context for participants to consider strategies to support students to reason mathematically and learn to use precise language in their explanations.
Module Resources
Similarity Slope Graphs of Linear Functions – Presentation
Similarity Slope Graphs of Linear Function – Resources
Similarity Slope Graphs of Linear Function – Resources 2
Similarity Slope Graphs of Linear Function – Resources 3
Module Video
Reasoning and Explaining, 6-12
This module prompts participants to examine the meaning of defining congruence and similarity through transformations as articulated in the Common Core State Standards. To do this, participants are asked to compare and contrast static definitions of congruence and similarity with dynamic definitions of congruence and similarity. They are also prompted to consider implications for instruction that the dynamic definitions have on teaching and learning mathematics.
Module Resources
Congruence and Similarity – Presentation
Congruence and Similarity – Resources
Congruence and Similarity – Resources 2
Congruence and Similarity – Resources 3
Congruence and Similarity – Resources 4
Congruence and Similarity – Resources Lesson Graph
Module Video
Reasoning and Explaining, 3-8
The teacher engages students with the Button Pattern task over the course of two class periods. During students’ second experience, the teacher uses a powerful formative assessment strategy called “reengagement” to prompt advances in students’ mathematical thinking and reasoning. The teacher focuses the class on work samples strategically selected from the previous period.
Module Resources
3-8 Button Task – Presentation
3-8 Button Task – Resources