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A new manipulative has emerged that appears to provide many students with a better understanding of early number concepts. The Rekenrek, arithmetic rack, or counting rack was developed at the Freudenthal Institute in the Netherlands by Adrian Treffers. Resembling an abacus, the Rekenrek typically consists of two rows of ten beads, with each row having five red beads and five white beads. The Rekenrek takes its place in the primary grades classroom alongside other popular models for developing early mathematics concepts, such as Unifix Cubes, base ten blocks, ten-frames and counters. The focus in using a Rekenrek is on fives and tens. Rekenreks are also available with four rows of beads or ten rows of beads to deal with numbers 21 through 100.Read More
Double, or dual, number lines are an ideal "visual model" for solving mathematical problems involving equivalences, ratios, proportions, and more. Though double number lines are not mentioned specifically in the CCSS until Grade 6 (6.RP.3), they are a viable tool for mathematical understanding beginning as early as first grade.Read More

"Would you rather have half of one chocolate bar or a quarter of a different chocolate bar? Most popular answer: It depends on the size of the chocolate bars! As teachers know, the relative size of fractions depends on how the whole is defined. Authors Jim Callahan and Marilynn Varricchio address these common problems with fractions in their new book Fractions Made Easy (Didax, 2016). Drawing on material from the book, we will focus on how visual models can be used to support a solid conceptual understanding of fractions in third grade.

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"With current math standards' emphasis on number lines as a visual math model, number lines are being used in nearly all primary grades classrooms for learning such things as counting and early operations. However, research has shown that number lines are conceptually too difficult for young children to understand and instead we should be using number paths, at least until second grade (Fuson, et. al., 2009). A number path is a visual model for counting, addition, subtraction and more. Experts say that the number path is superior to the number line as a visual model for early math learning. We caught up with Educator Margaret McGinty to learn why.

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According to the American Statistical Association, "Effective prediction is essential to improving medicine; monitoring climate; providing sufficient, safe food supplies; and much more." To make educated predictions as adults, children need to understand probability -- and start learning about it at an early age. Prediction is an adult skill used in many professional fields, including science, medicine, finance, and insurance. Underlying prediction is the notion of probability: whether a given event is certain to happen, likely, unlikely, or impossible.Read More
Success in school, the workplace, and society increasingly depends on our ability to comprehend informational text. Yet, despite current language arts standards, informational text often gets short shrift in primary grades classrooms. One study of 20 first-grade classrooms showed that nonfiction books constituted less than 10 percent of the classroom library and that students spent less than four minutes per day reading informational text. (Duke, 2000)Read More
From a very young age, children learn and develop using all their senses. As infants they are surrounded by the stimulation of shape, color, lines, numbers, patterns, and textures. By the time they reach preschool, they are engaged in stories and imaginative pursuits that build on these sensory explorations. Thanks to the materials they have explored in their first five years, children already have a strong foundation for mathematics when they start kindergarten.Read More
As an undergraduate education student, I was challenged to write my personal mission statement that would help me define myself as a teacher. I don't recall the entire statement, but I know that it included something along the lines of "helping students think critically about mathematics." Looking at this from an experienced perspective, I'm not convinced that I knew what critical thinking was, let alone how to help my students become critical thinkers. With time, I've come to understand that there is no one way to accomplish this task, but there are strategies we can implement that will help students develop these skills.Read More

When working with math teachers at any level, one of the complaints I've heard over and over begins with the phrase, "If they only knew their facts..." Fluency with basic facts, however, is only one part of a bigger picture, and I always encouraged teachers to think about the conceptual foundation they were building rather than how quickly students can rattle off some facts. As we consider the increased emphasis on rigor, we need to keep in the back of our minds what rigor is: a balance between conceptual understanding, application, and procedural fluency.

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One of the things I really enjoyed about my Geometry classes in college was that they were very hands-on. We used a variety of manipulatives to explore geometric concepts, and the lessons have stayed with me for a long time now. I carried many of these ideas into the classroom when I started teaching, using ideas as simple as nets and tools like marshmallows and toothpicks. While these models are adequate for teaching the general ideas, they lack the consistency and formality that Geofix shapes offer.Read More
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