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Many years ago, I was introduced to the elements of early Reading instruction. With my background in math, I had a lot of learning to do, but I immediately saw the value in helping students build an understanding of phonics and phonemic awareness. Using hands-on tools like Unifix® CVC and Blends cubes can accelerate students’ understanding of these critical early reading skills. Together with the new Early Phonics and Phonics activity books, these resources allow students to make concrete connections to the words around them. I’ve selected just a couple of the 211 activities available in these two books to get you started with this resource. All these activities are designed to support small-group phonics instruction using the Unifix phonics cubes and Word-Building Cards.

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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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As a part of my undergraduate education, I took a class called Mathematical Problem Solving. The professor presented us with a list of problems from which we chose at least five to solve and demonstrate to the class over the course of the semester. As a part of our solution, we had to choose and identify a problem-solving strategy (from George Polya’s list of strategies) that we would then apply to the problem. This was both a good introduction to a wide range of problem-solving strategies and a powerful example of how different students see and solve problems in different ways. When I started teaching, I sometimes tried to incorporate the strategies into my instruction. The challenge was providing a variety of problems that spanned both the standards and the strategies, giving students the opportunity to practice both in a meaningful way. To help teachers address this challenge, Didax now offers Problem Solving Practice Cards for grades 3 through 5 that provide both a problem and a suggested problem-solving strategy.Read More
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
Early in my publishing career, I was working with an author on an updated book series. In the course of our discussion, he mentioned the Rekenrek, a tool for building early numeracy. This was, at the time, a very new tool in the United States even though its use could be tracked back for many years in the Netherlands. I was intrigued, but not quite sure what we could do with this tool that would help teachers enhance their instructional practice. Fast forward several years, and the Rekenrek is far more familiar. Many educators are embracing this tool with varying degrees of success. To make this implementation a little easier, Don Balka has developed two activity books for the Rekenrek: Working with the Rekenrek (with Ruth Harbin Miles) and Working with the 100-Bead Rekenrek. These books provide both teacher support and engaging student activities to help us all use the Rekenrek more effectively. If you’re looking for some ideas to get started with the Rekenrek, here are two new ideas based on these resources.Read More
Here is a simple story problem. Rose has 5 pennies. Eva has 9 pennies. How many more pennies does Eva have than Rose? I have posed this problem to many, many children. More than a few of them have answered, “Eva has 9. You just told me that.” Those children didn’t understand the question. It is not simply that they got the wrong answer. It is not simply that they made a minor mistake. Those children really didn’t understand what I was asking. Here is another problem. Trixie has 3 baskets. There are 4 cherries in each basket. How many cherries does Trixie have altogether? I often ask children to draw pictures to represent story problems. For this problem, I have seen children draw 3 baskets, draw 4 cherries in each basket, and then miscount the cherries – maybe they count 11, or maybe 13. Of course, 11 is not right. And 13 is not right. But compare those children who miscount with those children who start out by drawing 4 cherries and 3 baskets. Miscounting is one thing – everyone makes minor mistakes. But children who draw 4 cherries and 3 baskets don’t understand the question. Those children need help.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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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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