As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

Mathematics teachers, are always making and remaking their curricula to better serve the needs of their students. Sometimes, these revisions happen while they are teaching a new task. At other times, as they grow in their thinking, they become aware that some of the tasks they've used for years--and might even name as favorites for their potential…

This activity engages students with the concept of mathematics identity to expand conceptions of what mathematics is and therefore what doing mathematics and being mathematical can mean. By mathematics identity, we refer both to ways a learner sees themselves and participates in mathematics, and the ways that others speak about or treat that…

There is a growing reliance on plastic, even though it is a synthetic material that does not decompose. This article presents a series of six mathematics activities that use plastics as the context to teach environmental education to seventh-grade students. The activities can increase students' awareness of the plastic problem while also serving…

Play allows young children to acquire and practice mathematics skills and concepts while engaging in meaningful and enjoyable activities (Bobis, 2010; Reed & Young, 2018). In particular, open-ended play provides children opportunities to discover materials, explore concepts, and solve problems (Rosli & Lin, 2018) and in the process,…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

The lesson described in this article was developed and taught by a team of mathematics educators and physical therapists, with the shared goal of broadening students' perception of how mathematics concepts are applied in the real world. This lesson gives students authentic experience with the Gait Speed Test as a physical therapist would…

Our bodies help us learn, and our bodies may know something before we can articulate it. Embodied explorations are body-based learning experiences where learners have opportunities to make sense of and convey ideas with their bodies. These embodied explorations were taught at a suburban public high school, in the southern United States, that…

A primary goal of ethnomodeling is to value, sustain, and in some instances introduce cultural practices and traditions that have often been lost or overshadowed because of an emphasis on modern methods (Orey & Rosa, 2010). Through an ethnomodeling task focusing on geometric transformations, the authors share a Model It! activity to engage…

The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…