Educators and parents hear a lot about developing number sense in children, but what exactly is number sense in mathematics? How does it affect students’ learning? What are some ways to build number sense routines in elementary students? Here, we’re defining number sense and sharing some teaching strategies, including movement-based activities and number sense games.

Number sense—or the ability to work proficiently with numbers—is a struggle for many elementary students since the subject of math, in general, is very new to them. Not having a strong number sense in elementary school can significantly impact a student’s academic success later in life.

Because of this, Math & Movement’s goal is to have all students feel confident in math. We’re sharing a variety of movement-based exercises designed to improve number sense abilities. By implementing these practices into their students’ routines, educators build the foundation for students to understand the meaning of math in the world – in a fun, engaging way!

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## What is Number Sense?

Number Sense Definition: *Number sense is the ability to work proficiently with numbers, understand their significance and relationships, and apply mathematical concepts in various circumstances.*

## How Some Educators Define Number Sense

Number sense is a person’s ability to work comfortably and effectively with numbers. According to educational experts like Gersten and Chard, it involves understanding the meaning of numbers, performing mental arithmetic, and making comparisons. This fluidity with numbers allows individuals to make sense of their numerical environment and apply mathematical concepts to real-life situations.

Additional educators, such as Jordan, Glutting, and Ramineni, say these skills appear to begin developing with little or no verbal instruction as early as infancy! Through observation and experience, a young child will start grasping number quantities and gradually exercise visualizing and estimating techniques. Eventually, children expand on this knowledge as they attend formal schooling, learn to count, and perform arithmetic operations.

#### Teaching Number Sense in Schools

When explaining number sense in schools, it is often described as the core of mathematical development. It includes various skills, such as understanding and using numbers in practical contexts. As a result, educators aim to strengthen students’ number sense routines by helping them practice mental calculations and applying their skills to solve problems. Number sense and operations go hand-in-hand.

#### How Does Number Sense Relate to Math

Number sense, as mentioned above, includes a range of abilities, such as:

**Counting**– Understanding the systematic assignment of place values and the relationships between numbers.**Quantity and estimation**– Comprehending amounts and making reasonable approximations.**Computing**– Performing mental arithmetic calculations.**Number fluency**– Increasing number sense fluency by grasping the symbols and vocabulary used in math and being aware of number patterns.**Real-world application**– Identifying connections between math equations and everyday life.

These skills provide the foundation for more complex mathematical learning.

##### Common Examples

Common examples of number sense activities include:

**Recognizing patterns**– Realizing that in the sequence, “3, 6, 9, 12,” the numbers are increasing by 3.**Mental math**– quickly solving 7 + 8 in your head to get 15.**Comparing quantities**– understanding that 10 is greater than 5.**Estimating**– guessing that a pile of objects has about 30 items.

## Why is Number Sense Important?

Math number sense is crucial because it builds the basis for all future mathematical learning. Strong number sense skills allow individuals to:

**Make informed decisions.**A person with thsese skills can understand under relationships and how they apply in different situations.**Understand patterns.**Being able to recognize trends in data and statistics is essential in many aspects of life.**Manage finances.**Individuals should be able to budget their money and comprehend things such as interest rates.**Solve problems.**Many people use approximation and quick calculations in everyday tasks.

## How to Teach Number Sense

To effectively build number sense routines in students, consider the following strategies:

**Build a foundation.**Begin by focusing on the fundamentals and basic concepts of math, such as place value and number operations.**Give clear instructions.**Teach numbers and new mathematical concepts in a logical sequence.**Provide practical experience.**Utilize interactive material and real-life examples to make abstract concepts more tangible.**Have regular review.**Reinforce number sense skills with consistent practice, especially to prepare students for more advanced math lessons.

### Movement-Based Number Sense Activities

Did you know that movement-based learning strategies increase student engagement AND boost test scores? It’s true! Young children never like to sit still for long periods of time. Math class can become particularly frustrating when a lesson is challenging and students have a lot of pent-up energy. By using kinesthetic learning strategies, educators can encourage students to move their bodies while effectively learning new math concepts.

Kinesthetic learning is a hands-on approach that uses physical activity to teach students new concepts. Physical activity increases blood flow and oxygen levels in the brain. As a result, the brain can function at optimal levels for learning. Additionally, proteins that the brain releases during exercise support the function and growth of neurons. Movement really works to boost learning comprehension!

But how can educators effectively incorporate movement into their lessons? Short active math movements or cross-body exercises are easy to add throughout the school day and into your number sense routines.

Math & Movement takes kinesthetic learning to the next level with large floor mats and stickers that students can walk across and jump on. Then, as they interact with these materials, students can “experience” new math lessons and be more engaged in their learning process through number sense games.

Math & Movement harnesses a child’s natural inclination for activity and turns it into enthusiasm for acquiring math skills. Our wide selection of math products can be used to build number sense routines in elementary students as well as to teach grade-level concepts in your school’s existing curriculum. Here are a few of our favorite activities to build number sense. Consider incorporating these movement-based number sense games into your lessons!

Our Number Line to 10 mat is a large, colorful number line that includes the numbers zero through ten in numerals, words, and symbols representing the quantity. Number sense activities can involve imagination! In the activity “Blast-Off”, preschoolers and kindergarteners can pretend that they are on a rocket that’s ready to take off.

Have one student start on the 10 block and hop down the mat as the whole class counts down to takeoff with them. “10, 9, 8, 7, …2, 1, blast-off!” Students can jump up and clap while saying, “Blast-off!”

The Skip Counting by 2s mat is a number line from 0 to 20, featuring each numeral, number word, and corresponding number of symbols. Each multiple of two is in a blue block. The “Matching Numbers” activity is a great way for Kindergarten and first grade students to match numerals to the same number of objects.

In order to participate, have students place one object on the number one on the mat, two on the number two, etc. Choose two of the same object – like two shoes, two books, two pencils, two blocks, etc. For bigger numbers like ten, try pennies, paperclips, or popsicle sticks. You can also have students stand on the mat as the “objects.”

Our Ten Frame Hop features two rows of five blocks, each including the numbers 1 through 10 in them. “Make the Number” is a number sense game that helps Kindergarten and first grade students practice counting and one-to-one correspondence.

First, create flashcards with numbers 1-10. Show a student a card and have them place the correct number of markers (or another small object) on the mat. Repeat several times with different numbers. Students can “check” their work by hopping on the numbers on the mat and counting aloud. For an additional challenge, after making the number, ask the student how many squares are empty.

The Count to Ten mat features numbers 0 to 10 in order, depicting each numeral, number word, and dots representing the corresponding quantity. Moreover, “The Number Walk from 0 to 10” activity helps preschoolers and kindergarteners master counting, cardinality, one-to-one correspondence, and number recognition.

To begin, have your student stand on “start”. Instruct them to walk up the mat and step on each number. As the student walks, encourage them to simultaneously say the number name aloud. If their counting gets ahead of their stepping, ask the student to go back to “start” and begin again. Be sure the student’s stepping is in sync with them saying the number!

Likewise, our Place Value Mats teach the fundamentals of multi-place number building and how to read large numbers aloud. The “Building Place Values” activity is suitable for students in Grades 1-5 and helps them understand base numerals.

First, create a number using the included number cards. Then, build the number in the allotted space below with popsicle sticks to show the value of each digit.

For example, put the number 9 card in the box at the top of the mat above the “ones”. Put 6 in the “tens” box, put 8 in the “hundreds” box, and put 7 in the “thousands” box. Place nine “ones” (single sticks) in the ones box. Next, arrange six “tens” (bundles of ten sticks) in the tens box. Then, place eight “hundreds” (bundles of one-hundred sticks or ten bundles of ten sticks) in the hundreds box. Finally, put seven “thousands” (ten bundles of one-hundred sticks) in the thousands box.

The Add/Subtract (1-100) is our large hundred number grid! It is one of our most popular and versatile materials, making dozens of number sense activities possible. The activity “Patterns” allows third and fourth graders to understand arithmetic patterns.

Ask your students to stand on any number on the mat. Make a pattern by adding or subtracting a number repeatedly. Explain that this repetition is a pattern.

For example, a student stands on 3. “Mark” every 4th number to 27 by placing a bean bag, pencil, or post-it note on the numbers. The pattern is 7, 11, 15, 19, 23, 17.

The Skip Counting by 3s mat is a large format number that has large blocks for each multiple of three. All of our skip counting mats work great for teaching multiplication to third and fourth graders!

Skip counting by 3s on the mat is easy. Ask your student to start at zero. Point to the pattern that the red boxes with the feet follow. These boxes are multiples of three. Have the student start jumping down the mat. Whisper each number then shout each time the student jumps on a multiple of three.

For example, jump on one and whisper “one.” Jump on two and whisper “two”. Jump on three and shout “three!” From there, continue with this pattern down the mat to thirty. Have the rest of the class stand by the mat and count along. Once the students are comfortable with multiples of three, skip count by threes by only jumping on the red boxes and not whispering the other numbers.

This activity can be adapted to different multiples on our other skip counting mats, making them a great addition to number sense routines!

This Fraction Walk mat features numbers one through five with corresponding equivalent fractions in halves and quarters on either side of the number line. Proper and improper fractions are shown with numerals and symbols. The “Bean Bag Addition and Subtraction” activity on this mat helps fourth and fifth graders practice adding and subtracting fractions and mixed numbers.

Start by tossing two bean bags onto the mat. Add or subtract the numbers that they land on. To make this activity easier with like denominators, toss the bean bags in the same column – only halves or only fourths. To make this activity more difficult, toss one bean bag on the halves column and one on the fourths column. Then, find the common denominator to solve. Encourage students to step on and walk around the mat as they solve.

### Number Sense Worksheets

Worksheets can also be incorporated into your number sense routines. Some particularly helpful worksheets include:

**Comparison problems.**For instance, circling the larger number between two given options.**Counting exercises.**These may consist of filling in the missing numbers of a sequence.**Estimation challenges.**These questions have students guess the total amount in a group of objects and check their accuracy.

Best of all, many of Math & Movement’s materials can be used to help students solve problems on worksheets! Students can hop on a mat related to their lesson to solve, then return to their worksheet to record their answer. This really breaks up sedentary times during the school day!

### Number Sense Games

Interactive games make also make learning number sense skills fun and engaging. Some examples might include:

**Number matching games.**Match number cards to groups of items.**Approximation contests.**Estimate the number of objects in a jar and see who is the closest.**Number puzzles.**Solve puzzles that include completing patterns or arranging numbers, like Sudoku.

## Number Sense Activities for Math Intervention

When teaching number sense to students who need extra support, some tricks might include:

**Using manipulatives.**Use blocks, cards, or other tools to demonstrate number relationships visually.**One-on-one instruction.**Provide individualized support to address specific number sense challenges.**Focused practice.**Target areas of difficulty with tailored exercises and feedback.

## Why is Number Sense Important in Education?

A strong number sense is fundamental for students’ mathematics success and ability to solve everyday problems effectively. Significantly, a solid grasp of number sense lays the groundwork for understanding complex mathematical concepts and applying them practically.

Teachers play a crucial role in this development by providing explicit instruction, engaging in hands-on activities, and fostering an environment where students can explore and manipulate numbers. Through targeted lessons, movement, creative number sense games, and consistent practice, educators can help their students build confidence in working with numbers. Particularly, teachers who prioritize number sense routines in the classroom will ensure students are well-prepared for future mathematical challenges and equipped with valuable problem-solving abilities.

Investing in teaching number sense today will enhance your students’ mathematical proficiency and support their overall cognitive growth and everyday decision-making!

## FAQs

###### What is number sense?

In general, number sense refers to a person’s intuitive understanding and ability to work flexibly with numbers. It involves recognizing numerical relationships, performing mental arithmetic, and applying mathematical concepts in practical and meaningful ways.

###### How do I build number sense?

Teaching number sense involves several strategies, including providing clear and explicit instruction, using hands-on activities and manipulatives, incorporating engaging games, and encouraging mental math. In other words, it’s important to build a solid foundation by focusing on number relationships and real-world applications, and to continuously review and reinforce these concepts.

###### Why is number sense important?

Teaching number sense is crucial because it underpins all mathematical learning and problem-solving. It helps students build confidence in their math skills, apply mathematical concepts to real-life situations, and develop a deeper understanding of more complex mathematical ideas. Strong number sense also supports everyday tasks such as budgeting, measuring, and interpreting data.

Feature Photo by Susan Holt Simpson on Unsplash