Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…

Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

Making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way. Math Teachers' Circles were developed with the aim of establishing a "culture of problem solving" among middle school mathematics teachers. This culture could then be carried back into…

Division of fractions is often considered the most mechanical and least understood topic in elementary school. Enacting fraction division tasks in meaningful ways requires that teachers know not only "how" fraction division works but also "why" it works. The authors have created materials to help preservice teachers develop that knowledge. To…

Storytelling can provide unique teachable moments. Mathematics content found in a good story can be seamlessly woven throughout a lesson. The technical vocabulary used in some stories occurs in a natural way, outside a textbook setting. A great story can also motivate students to actively engage in meaningful mathematics. With a wide range of…

This article describes a particular activity, the Motorized Toy unit, which supports science, technology, engineering, and mathematics (STEM) goals and teaches students the basic concept of ratio. The unit addresses both mathematics and science standards and is part of a team-teaching activity. The unit comes from a curriculum titled A World In…

Implementing Universal Design for Learning (UDL) principles can provide solutions for general educators in inclusive mathematics environments. Any lesson can be planned to provide learning experiences appropriate for meeting diverse learning needs. This article explores an example of both how to approach a topic in middle school mathematics and…

Assigning activities based on current or past events allows students to explore mathematics in a social context. Using social justice events in the mathematics classroom is a way for teachers to provide contextual problems that will reach all students and promote equity. Learning mathematics in an environment in which social issues are explored…

Providing student choice and opportunities for independent study are recognized as viable differentiation techniques. Daily homework sets that contain more demanding problems even though not required allow the teacher to provide challenge without incurring undue stress. The modest incentive of some homework bonus points is enough to whet the…

Posing mathematics problems in different ways will raise students' level of cognitive demand because it will push them to think more deeply about mathematics. By engaging students in a task that requires them to determine their own solution strategies, students will gain a deeper understanding of the mathematical concept explored through the task.…

Children learn from a very early age what it means to get their "fair share." Whether it is candy or birthday cake, many children successfully create equal-size groups or parts of a collection or whole but later struggle to create fair shares of multiple wholes, such as fairly sharing four pies among a family of seven. Recent research suggests…

With the ever-changing dynamics of society, teachers are often faced with a classroom of students who have diverse linguistic and academic needs. Research has shown that schools are becoming more linguistically diverse throughout the United States and that English language learners (ELLs) are posing their own sets of challenges for teachers.…

Roughly one-fifth of America's public school students attend rural schools. Low mathematics achievement scores in these communities suggest that math instruction needs to focus on the skills and content necessary for twenty-first-century jobs in contexts that are meaningful to these populations. This article describes how one rural school worked…

Proportional reasoning pops up in math class in a variety of places, such as while making scaled drawings; finding equivalent fractions; converting units of measurement; comparing speeds, prices, and rates; and comparing lengths, areas, and volume. Students need to be exposed to a variety of representations to develop a sound understanding of this…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…