Finally, something exists for the quirky math student who can’t help but ask, “what does it all mean?” Long before third graders take their first time tests, their relationship with numbers begins. Number sense goes beyond what numbers are, to what they mean, especially in relation to each other. Specifically, number sense describes a child’s fluidity and flexibility with numbers.

**What number sense looks like **

Children demonstrate number sense when they’re able to understand and connect numbers. Children with good number sense realize that you can get to 8 by adding 6 + 2, or 3 + 5 and so on. They can use mental math to solve problems without paper and pencil. They can understand math’s application in everyday life, calculating that if their allowance is $5 a week, it’ll take them two weeks to save up for a movie ticket.

Number sense involves the following skills:

- Following numbers in a list: First through fifth, etc.
- Understanding comparisons like bigger vs. smaller, or more vs. less
- Registering quantities and how individual items make up one group
- Recognizing numerical symbols: Five is the same as 5
- Understanding how numbers relate: 6 is made up of two 3’s, or 6 is greater than 3
- Competence in arithmetic and the ability to do mental math

**Why number sense is critical **

In her book *About Teaching Mathematics, *educator Marilyn Burns states that through number sense, “students come to understand that numbers are meaningful and outcomes are sensible and expected.” In other words, number sense is to literacy what equations are to sentences. Number sense clues children in on the predictable relationship between numbers and outcomes. Numbers become part of a coherent concept in the way words come together to form a sentence.

Number sense gives young students confidence to solve problems in arithmetic and all math that follows. To struggle with number sense is to struggle with essential building blocks. This means a student with poor number sense will have difficulties initially with addition and subtraction, then have further difficulties with multiplication and division. For example, when presented with 2 groups of 4, a child with good number sense would multiply 4 by 2 to get 8. A child with poor number sense would only get to 8 by counting 1, 2, 3, 4…8.

A 2013 University of Missouri study is a testament to how essential developing a core number sense is early in education. After studying 180 seventh-graders, researchers found those who had the least number sense fluency in first grade were the same students who lagged behind their peers in a test of core math skills necessary to function as adults. Psychologist Dr. David Geary, who led the study, put it simply: “The gap they started with, they don’t close it.” You can’t build a sturdy house on a shaky foundation.

In fact developing a fluent number sense is so critical that Dr. Geary is now studying how to instill better number sense in preschool to set children up for success later in life, both academic and otherwise.

**The relationship between mental math and number sense **

One of the signs of good number sense is the ability to do mental math. And one of the best ways to improve number sense is to do mental math. When you think about it, this chicken and egg relationship makes a lot of sense.

Strong mental math and number sense skills demonstrate the same key principle – a conceptual understanding of math. Understanding the connections between numbers means understanding the “why.” And understanding the “why” means being able to rely on strategy rather than memorization when confronted with new problems. A fluent number sense gives students confidence to tackle problems that extend even beyond the classroom.

**How to improve number sense in children **

**Explore different problem-solving strategies **

Thinking there’s only one way to solve a math problem is an all too common mistake. Exploring different ways to get the same answer helps students find the way that makes the most sense to them. It also teaches them that strategy, not memorization, is their best bet for solving future problems. Discussing different mental math strategies is especially helpful in this regard.

**Communicate with classmates **

Whether this happens at school, in a study group or around the kitchen table, have students talk about the strategies they’ve used to solve problems. This takes our first tip a bit further, asking students to evaluate the merits and shortcomings of various approaches to hone in on the most efficient method.

This also should involve judgement-free chats about where they went wrong when an answer is incorrect. Instead of a simple “nice try” in response to an error, understanding why they’re wrong helps students adapt and maintain confidence in their next attempts.

**Encourage estimation – it’s a life skill **

When we use math in our everyday lives, we rely on estimation far more than precise numerical answers. If an appetizer serves four, how many does my family need? How long will it take to drive to work? Will my SUV fit in this spot? These seemingly simple questions become more complicated for someone with poor number sense. Encouraging children to estimate, a skill not taught in math class, at a young age improves their number sense.

No matter how you make it fun, the key is to forsake memorizing formulas in favor of choose-your-own-adventure style math problems. There may be one right answer, but the way you choose to get there makes all the difference. And that’s a lesson too big to stay trapped in a math book.