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Watching my children and students work with manipulatives, I can see how hands-on experiences with math concepts help build a solid foundation for future learning. Often, teachers and students struggle with the transition from concrete manipulatives to a representation of the concept. Web- or app-based “virtual” manipulatives help to make this transition easier, although many teachers struggle to find a place for these tools in the classroom. Hands-on manipulatives are an excellent tool on their own, and they are even more powerful when coupled with virtual manipulatives. To support the use of these virtual tools, Didax has developed more than a dozen free virtual resources, available on our website. If you need some help getting started, read on for some ideas!

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As a middle grades math teacher, instructional coach, and tutor who works with students across all grades, I witness the struggle with fractions at every level. There are two primary sources of difficulty with fraction operations: The first is recognizing factors hidden in numerators and denominators; the second is choosing the correct rule and applying it properly. "Fractions with Prime Factor Tiles" is a revolutionary tool for teaching fraction operations that corrects both of these deficiencies through hands-on activities. Numerators and denominators are expressed as products of prime factors with color-coded tiles that make the common and non-common factors of numbers visually obvious. Rules for operations are taught and reinforced through physical manipulation of the tiles in a manner that is logical and intuitive.

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Posted in Math, Middle School by David A. Bernasconi
Mathematics educators have recently highlighted the need for “low floor, high ceiling” tasks that lead students into rich areas of inquiry. The “Four 4’s” problem is a fairly well-known example cited by Jo Boaler and others, but such challenges are hard to develop. It is often difficult to find an exercise, game, or a puzzle that is instantly accessible at a basic level, yet also leads to the exploration of higher-order thinking and deeper mathematical insights. The PEMDice game is designed to scratch this itch. Very simple in concept and, when played in its elementary form, it is ultimately as complex and as challenging as anyone cares to make it.Read More
Every spring, millions of people turn their attention to what is, mathematically speaking, a tree diagram. Some think about it only when their favorite team is playing, while others are completely immersed in the annual College Basketball tradition known as “March Madness.” This frenzied tournament provides multiple opportunities to engage students in math, although we sometimes focus so narrowly on probability and statistics that students miss out on other opportunities to learn. In the spirit of the season, we’d like to share some ideas for teachers of all levels to bring March Mathness to the classroom. You can use the link below to access the activity sheets to use in your classroom. A printable tournament bracket is available here.Read More

It’s hard to believe that 2018 is here, and we’re quickly approaching the 100th day of school. When I first started working with elementary school teachers, the concept of a 100 days celebration was foreign to me—it wasn’t something that we did in high school. Over time, I’ve come to appreciate this tradition and the mathematical opportunities it brings. In honor of 100 days of learning this school year, here are a few ideas for your 100th day activities. Try them out and let us know what you think!

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Posted in Math, Elementary, Middle School by Matt Christiansen

When I was teaching in the high school, we taught a unit on rational expressions and equations. In simple terms a rational expression is a fraction that has numbers and variables in the numerator, denominator, or both. Because rational expressions behave a lot like fractions, I usually started this unit with a day or two of review of fractions to help students build confidence with this foundational concept. Every year, I was surprised how many students struggled with fraction concepts, and it was clear to me that we needed to do more to build their conceptual understanding in the early grades. Generally, we are doing better with this, using more and different models to help students really understand the relationships between the part and the whole and also between fractions. Number lines help build conceptual understanding of fraction relationships and area models are useful tools for both relationships and operations. Another tool that helps students build an understanding of both fraction relationships and operations are interlocking fraction circles. The short video below explains how these circles support students’ understanding of fractions.

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Posted in Math, Elementary, Middle School by Matt Christiansen

Every year around this time, my family is getting ready for back-to-school night. Now that I have children in high school, junior high, and elementary school, it’s always fun to see how this event is handled at the different levels. When I was teaching high school, we were very structured, with parents moving from class to class as though on a regular schedule; I think we had each group for ten minutes, just long enough to quickly review the syllabus and policies and send them off to the next class. Regardless of the structure of back-to-school night at your school, there are a few things you can do to make the evening more engaging for students and their parents. A good place to start is having some manipulatives you’ll be using during the year out for parents to handle. Things like Unifix Cubes, Pattern Blocks, Ten-Frame Floor Mats and Fraction Tiles are always good choices.

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I taught an Algebra 1 or Algebra 2 class every year I was teaching, and I was always looking for ways to make the content engaging for the students. I firmly subscribe to John Van de Walle’s notion that drill and practice are two very different things, and sought opportunities for the students to have meaningful practice with the concepts they were learning. As a result, I avoided the lengthy problem sets and worksheets that are prolific in high school math classes, opting instead for problems, explorations, and games that encouraged thinking and discussion.Read More
Posted in Math, Middle School by Matt Christiansen
As a teacher for over 15 years, I recognize that the kinds of experiences that teachers offer their students play a major role in determining the extent and quality of students’ learning. For example, rich problem-solving activities help students build understanding by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Playing math games affords students the opportunity to build understanding while encouraging strategic thinking as students will have different approaches for solving problems. Using classroom activities and games is also a great way to check in on their progress as well as to provide reinforcement of key concepts. I like problem-solving activities that are easy to put together, fun, and require all students to participate.Read More
Posted in Math, Middle School by Camille Mattson
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
Posted in Math, Elementary, Middle School by Matt Christiansen
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