This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

Inspired by the promise of new 3D technologies and the proposition that new tools make innovation possible, this article provides a case study of how a tool called Thirty6 was designed and used in classrooms by mathematics teachers in their own varied and invented ways. Unlike established manipulatives that are designed to support the learning of…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

To help middle school students make better sense of decimals and fraction, the author and an eighth-grade math teacher worked on a 90-minute lesson that focused on representing repeating decimals as fractions. They embedded experimentations and explorations using technology and calculators to help promote students' intuitive and conceptual…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

Discusses problems related to teaching decimals and fractions and converting between these two representations. Provides problems and activities that teachers can use in their classrooms to overcome student difficulties related to these subjects. (ASK)

Describes "fraction flags", an activity through which fraction concepts can be explored. The activity was invented by 2 12-year-old students and this article is presented with emphasis on the students' viewpoint. It begins with an overview of the fractions unit and presents vignettes of students exploring the fraction flags. (AIM)

Presents a game along with several variations involving three players using three-digit numbers to help students improve their number sense on decimal numbers and fractions. (ASK)

Describes the construction and use of the "fraction computer," a simple manipulative that helps pupils understand how to add and subtract unlike, unrelated fractions. (YDS)

Discusses the language used in mathematics classrooms and states that appropriate language is based not only on the words we say but also on how those words are being perceived. Indicates that teachers should give students time to develop the meaning of numbers, operations, or problems. (ASK)