#### What Is Delta in Math? Here’s Everything You Need to Know

Welcome to our beginner-friendly guide to the delta symbol (Δ) in math! Learn about its background, how it’s used in various math subjects, and take a short quiz to test your knowledge.

Jul 28, 2021 | Bountiful

Unlike many academic subjects, math builds upon itself level by level, so it’s important to start with a strong foundation. The proven Mathnasium Method^{TM} forms the foundation for math mastery through deep understanding, with carefully selected topics that lay the groundwork for Number Sense and other concepts encountered later in school. As students increase comprehension and build math skills, their excitement and confidence grow, and they strengthen their natural love of learning.

*Dependent Skills: A child must understand counting, then grouping, in order to be able to work with fractions and more advanced concepts. Introducing concepts out of order puts the student’s mathematical foundation at risk.*

*Independent Skills: As a child advances through each dependent skill, they also use independent skills. For example, when a student works on grouping, they can also solve word problems, identify even and odd numbers, name basic geometric shapes and more.*

One of Mathnasium’s strengths is that we are able to assess where a child is in their math development – at any age – and fill in the gaps. When we give assessments to children in our math learning centers, we see that a high proportion of their knowledge gaps stems from a lack of Number Sense, or “the ability to appreciate the size and scale of numbers in the context of the question at hand.” In essence, it’s the understanding of what numbers mean, how they work together, and how they connect to real life.

It’s critical that children have a firm grasp of Number Sense, because it underlies all mathematical comprehension and ability. However, it’s never too late to learn.

We break down number sense into three basics:

**Counting**. A child who fully understands counting can count FROM any number, TO any number, BY any number, both forward and backward. And they can do this in their head.

**Wholes and Parts**. We teach the principle “the whole equals the sum of its parts or, any part is equal to the whole minus the rest of the parts.” A full comprehension of this principle leads to success with problem-solving and fractions – the nemesis of many children (and many adults, too).

**Proportional Thinking**. Proportional thinking is thinking “according to amount.” It’s a sense of scale. It helps children to understand problems such as: Five is what part of 15? If you can buy 3 candies with $2, how many candies can you buy with $10? Children who have learned proportional thinking can answer these questions quickly and easily.

The following principles are also important to fully possess number sense:

**Quantity and Denomination**. The quantity is the amount of something – the number of things. The denomination is the name-value of that thing. In order to solve math problems, you need to know both.

**The Law of Sameness**. Mathnasium’s “Law of SAMEness” says that we can add and subtract only things that have the same name (same denomination). Here’s the classic Mathnasium example: When you add two bananas and three apples, do you get five banapples? Of course not. You can, however, get five fruits. “Fruit” is the denomination (name) that both apples and bananas share.

**Numerical-Computational Fluency**. Numerical fluency is the ability to effortlessly recall – to know by heart. While memorization is the way that many of us learned, it does not teach the mathematical thinking that is needed to build higher-order math skills. A student may memorize their multiplication tables, but a numerically fluent student uses efficient, scalable, reliable strategies to quickly answer questions far beyond that. For example, a student with numerical fluency can solve problems like 18 x 12 = ? without the need for pencil and paper. We like to say: “It is fairly easy to forget that which you have memorized, and it’s nearly impossible to forget that which you have learned.”

Mathnasium places enormous emphasis on number sense because it truly is the key to mathematical understanding. When children learn number sense, they are on the path to math mastery and to a love and appreciation of math that will positively impact their entire lives.

When children start learning math correctly, and at a young age, they are able to get the basic concepts and build upon them. However, many children have gaps in their math foundation that prevent them from reaching their potential. Mathnasium can address these gaps in children of any age and keep them from falling behind in the future.

Our proprietary curriculum ensures that students master math concepts before moving on, giving them the rock-solid foundation needed to succeed at more advanced levels. Mathnasium builds math comprehension and skills from the ground up, balancing the short-term goal of raising school grades with the long-term goal of math mastery.

We invite you to stop by your local center to learn more and schedule a free assessment.