Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

Much like one's experiences with the wonders of the world, concrete and multiperspective representations of mathematical concepts are key to understanding. Ideally, "learning environments should give students the opportunity to get to know different representations of a mathematical object in order for them to develop an appropriate…

This article describes a modeling project the author did with his algebra, geometry, and applications students in grades 9, 10, and 11 as an enrichment and exploration of an extremely relevant real-world phenomenon and introduction to the adult profession of epidemiologist. With discussion and exploration, this project consumed two periods of 88…