Professional Books/Websites

Mastering the MathRack

The Complete Guide to Teaching with a MathRack!

This book is an instructional guide for use with MathRack products. The original MathRack 20 was designed around the arithmetic rack from the Netherlands. This tool had two rows of ten beads; each row having five red and five white beads. The arithmetic rack is used to develop number sense and encourage children to use strategies instead of counting one-by-one. Since building the first MathRack 20 the company has manufactured other products that build up to the MathRack 20 and ones that extend children’s understandings beyond the MathRack 20. This book gives mathematics instructors the information they need to effectively use these powerful tools to their utmost potential.

The optimal setting for these activities is in a whole class or small group settings. The activities can be done in one-on-one settings; however, children will not get the experience of learning from others and hearing how other children “saw” the mathematics. Whichever setting you choose, all of these lessons should be used in conjunction with your current curriculum as an additional representation of what the children are already learning. Each lesson can be done in a day, but should not be done and then forgotten. Many of the activities can become “mini-lessons” that can be done when you have 5-10 minutes of spare time, as “starter” activities that you do the first 5-10 minutes of math time, or as math center activities that children can do on their own or with you in small groups.

Why use MathRack tools?

The MathRack tools have a built-in structure that encourages children to use theirknowledge about numbers instead of counting one-by-one. “In the United States, the manipulatives most commonly used with young children are single objects that can be counted – Unifix cubes, bottle caps, chips, or buttons. While these manipulatives have great benefits in the very early stages of counting and modeling problems, they do little to support the development of the important strategies needed for automaticity. In fact at a certain point they begin to reinforce low-level counting strategies. For example, to solve 6 + 7 with Unifix cubes, children need to count out six, then seven, and then either ‘count on’ as they combine or (as is most common) count three times – first the two sets, then the total” (Fosnot & Dolk, 2001, p. 103). With the MathRack 20, children can model and solve the problem the same as they would with Unifix cubes, but the built-in structure of the MathRack allows children the flexibility to develop more advanced strategies as well.

Fluency through Flexibility


Fluency through Flexibility: How to Build Number Sense, Numbers 0-20

Written by Christina Tondevold

Fluency through Flexibility delves deeper into spatial relationships, one/two more or less, benchmarks of 5 and 10, and part-part-whole looking at how they affect a child’s ability to work flexibly with numbers and become computationally fluent. Fluency through Flexibility provides PreK-2nd grade teachers with 15 activities for each of the four relationships to build children’s number sense. An assessment for each relationship is included in the book and Blackline Masters are available online for all the print materials needed for each activity.