# Introduction

Developing number sense is critical to ensuring success in mathematics. Many learners lack a deep understanding of number concepts. Often numbers remain vague for learners, resulting in gaps in the procedural knowledge needed to progress to higher levels of mathematics. It is important to develop the concepts of numbers as well as to develop fluency in number skills.

The Number Nudget is a tool designed to assist learners in developing number concepts and making connections to the abstract symbols. The tool can be made using the detailed instructions included at the end of this guidebook, or a modified version can be created using a simple number strip and checkers.

This guidebook provides sequenced activities to develop a variety of numerical concepts and to connect those concepts to number symbols using the Number Nudget tool. The aim to stress not only procedural skill but also conceptual understanding. The standards in the early grades (K-3) focus on number concepts and developing number skills. The domains of Counting & Cardinality, Operations & Algebraic Thinking, as well as Number & Operations in Base Ten can all be developed using the Number Nudget.

The Number Nudget reflects a number of key mathematical principles that makes this an effective tool. Notice the movement of the checkers reflects the directional principles of the number line. As checkers or disks are “nudged” or moved from right to left, the numbers increase. As checkers are nudged from left to right, the numbers decrease. This principle of the number line, i.e., numbers increase as you move right, and decrease as you move left, is reinforced with the tool. Similarly, the principles of a vertical axis are seen in a Nudget bar that is oriented vertically. A vertical Number Nudget represents increasing numbers as counting progresses upwards.

Number composition principles, specifically how numbers are composed using the digits 0 to 9 is easily developed using the Number Nudget. One bar of the Nudget delineates the numbers 0 through 9. Once the tenth checker moves left, something must happen in order to keep counting. The process of counting numbers larger than 9 requires notation of a 10, which provides opportunity to develop place value understanding. Using additional Nudget bars assists learners in developing place value concepts, skills, and fluency.

It is important to allow time for learners to develop numerical concepts concretely and to make connections to abstract notation. It takes time to save time. When learners conceptually understand number concepts and understand how to represent them abstractly, developing new operations and complex mathematical skills takes less time. The Number Nudget is designed with this methodology in mind.

May your learners gain important concepts about numbers and develop genuine mathematical understanding!

~ Kim Chappell