# Number Sense

## (Quantity & Relationships)

For students in elementary, number sense is an important and expansive topic in their learning progression. In grades 4 to 9, students extend their understanding of whole numbers to rational numbers and are introduced to irrational numbers.

Having a solid foundation of number sense in the elementary years can set a student up for success in their future studies. If an emphasis on numbers is introduced to a child during their time in elementary, it will reflect on their understanding of comparison of quantities, generating equivalent representations of numbers, understanding rates, ratios, proportional relations, and computations of whole numbers, decimals, fractions and integers.

## Understanding Number Sense

Having number sense is primarily understood as understanding the quantity represented by a number. Primary students start out by exploring the quantities of numbers less than 10 and later learn how to relate quantities to more significant numbers such as 10 and 100. By the end of a student’s primary grades, they should understand quantities associated with two and three-digit whole numbers. During their junior grades, students can develop a sense of multidigit whole numbers, fractions, decimal numbers, and percentages.

At Dropkick Math, we understand where a student’s understanding of number sense should be. Using concrete and pictorial models and interactive guides, we can help students understand the “howmuchness” of various numbers. We will also work with a student and parent through experiences that allow them to interpret symbolic representations of numbers.

## Quantity Comprehension

In junior grades, there is a tendency in education to focus on student’s understanding of computational procedures and to pay less attention to their development of quantity comprehension. But we understand that it is crucial to help students make sense of numbers through meaningful context that relates specifically to them.

## The Importance of Fractions

Research has shown that students build on their sense of numbers throughout their elementary schooling through connections among whole numbers, fractions, percentages, and decimals which ultimately deepen their understanding of ratio and proportionality.

An extensive study from The College Student Achievement Project found that understanding fractions is one of the most critical skills needed for college mathematics in both technology and business. It was also noted that fractions are one of the main areas in which many students lacked the necessary understanding, which is why it is vital for greater involvement from parents to help guide their child’s studies. With Dropkick Math, we make it accessible and easy for both parent and child to learn together, fostering a learning relationship.

By providing a solid understanding of fractional quantity, we help students gain the knowledge they require in later grades and can assist them in avoiding errors that are often caused by poor number sense.

## Student Learning

Students who have a strong understanding of number sense can represent quantities using diagrams and materials explaining how they show the quantity of numbers. These students also understand the base ten relationships in the number system and can compare whole numbers with decimal numbers considering the value of the numbers.

Understanding fractions and explaining the quantity relationship between the denominator of a fraction and the size of the fractional parts also shows a strong understanding of number sense.

With various other reference points, we can determine a child’s overall understanding of number sense and bridge the gap to any areas they may be struggling. With Dropkick Math, we make learning fun as we know that creativity is at the core of what mathematicians do.

Relationships are an essential part of understanding operations. When students understand these relationships, they are able to use alternative ways of computing with numbers. For example, addition and subtraction are related as inverse operations, which students can learn to help compute problems.

When students understand the relationships between operations, they learn how numbers can be composed or decomposed. Understanding that a whole number can be broken into parts helps students develop their own strategies for addition and subtraction.

Students who have a strong understanding of relationships understand base ten relationships in our number system and can use this in the number system to think about size, perform calculations, and compare numbers. They can also apply ways of comparing and ordering whole and decimal numbers, considering their place in value.

## FAQ

Number sense is the ability to understand the quantity represented by a number. This includes understanding the value of numbers, their relationships to each other, and their order. It is an important math skill because it allows students to understand and work with mathematical concepts. Number sense also helps students develop a foundation for future math learning.

Number sense is essential for children because it helps them develop a strong foundation in mathematics. Without a good understanding of quantities and number relationships, children can struggle with more complex mathematical concepts later on. Number sense also helps children to become better problem-solvers and to think more logically.

One way to improve number sense in children is to provide them with opportunities to practice representing, comparing, ordering, counting and identifying numbers. Additionally, parents and teachers can help children understand basic mathematical concepts, such as addition and subtraction. Providing fun and interactive learning activities focusing on math can also help improve number sense.

Number sense strategies are various methods that can help students develop their understanding of quantities represented by numbers. Some common strategies include using manipulatives, drawing pictures, and counting out loud.

#### Student Learning

Students who have a strong understanding of number sense can represent quantities using diagrams and materials explaining how they show the quantity of numbers. These students also understand the base ten relationships in the number system and can compare whole numbers with decimal numbers considering the value of the numbers.

Understanding fractions and explaining the quantity relationship between the denominator of a fraction and the size of the fractional parts also shows a strong understanding of number sense.

With various other reference points, we can determine a child’s overall understanding of number sense and bridge the gap to any areas they may be struggling. With Dropkick Math, we make learning fun as we know that creativity is at the core of what mathematicians do.

#### Relationships in Performing Computations

Relationships are an essential part of understanding operations. When students understand these relationships, they are able to use alternative ways of computing with numbers. For example, addition and subtraction are related as inverse operations, which students can learn to help compute problems. When students understand the relationships between operations, they learn how numbers can be composed or decomposed. Understanding that a whole number can be broken into parts helps students develop their own strategies for addition and subtraction. Students who have a strong understanding of relationships understand base ten relationships in our number system and can use this in the number system to think about size, perform calculations, and compare numbers. They can also apply ways of comparing and ordering whole and decimal numbers, considering their place in value.