The Building Blocks of Number Sense in Kindergarten and Elementary

Want to set kids up for math success? Start with number sense.

Number sense is the ability to understand, relate, and work flexibly with numbers. It’s not just about counting - it’s about grasping how numbers connect, spotting patterns, and solving problems in creative ways. Educators’ practice shows that kids with strong number sense are more likely to excel in math later on, while those without it often struggle.

Here’s how to help children build number sense skills:

• Counting & Subitizing: Use hands-on tools like dice or dot cards to help kids recognize small groups of numbers instantly.

• Understanding Number Relationships: Teach kids how numbers break apart (e.g., 8 = 5 + 3) and connect them to operations like addition and subtraction.

• Flexible Thinking: Encourage multiple ways to represent numbers (e.g., 15 as 10 + 5, a numeral, or objects).

Activities like bead strings, hopscotch math, and cooking measurements make learning fun. Plus, educational apps can personalize math learning with interactive lessons.

Number Sense Routines for Kindergarten, 1st, and 2nd Grade

What Makes Up Number Sense

Number sense is a collection of skills that lay the groundwork for understanding and working with numbers. These interconnected abilities are crucial for building a strong mathematical foundation. By understanding these key components, parents and teachers can better support children in developing their math skills. Let’s break down the essential elements that contribute to number sense.

Counting and Recognizing Small Groups

The first step in developing number sense is learning to count accurately and recognizing small groups of objects instantly, a skill known as subitizing.

Even toddlers, as young as two, can often identify one, two, or three objects without actually counting them [1]. This early ability is fundamental for more complex numerical understanding. However, subitizing has its limits - even for adults, the maximum number that can be instantly recognized is typically five [2].

"Students come to understand that numbers are meaningful and outcomes are sensible and expected", says Marilyn Burns [3].

For example, recognizing four dots at a glance helps children grasp numbers as whole units, rather than just collections of individual items. This mental flexibility is essential for later math skills.

Teachers can nurture this ability by introducing quick and interactive activities. Flashing dot cards or rolling dice are fun ways to encourage instant recognition. These methods challenge children to move beyond counting and develop strategies for quickly identifying quantities [3].

How Numbers Connect to Each Other

Numbers don’t exist in isolation - they are deeply connected. Understanding these relationships is a key part of number sense. This includes:

• Comparing numbers (e.g., knowing that 7 is greater than 5)

• Part-whole relationships (e.g., recognizing that 8 can be split into 3 + 5 or 2 + 6)

• Identifying patterns in number sequences

Part-whole relationships are particularly important. For instance, when a child sees the number 6 and can think, "That could be 4 and 2, or 3 and 3, or 5 and 1", they’re demonstrating flexible thinking about numbers [2]. This kind of understanding helps children move beyond memorizing facts to truly grasping how numbers interact.

As children develop this relational understanding, they begin to see the connections between operations like addition and subtraction. For example, they might use subtraction to check their addition work, reinforcing the idea that math isn’t just about rote memory but about logical relationships.

"Number sense is defined as a good intuition about numbers and their relations. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms", explains Howden [3].

Working with Numbers in Different Ways

A key feature of strong number sense is the ability to switch effortlessly between different representations of numbers - numerals, objects, pictures, and words. For example, a child might understand the number 15 as:

• The numeral "15"

• Fifteen individual objects

• Ten and five more

• Three groups of five

This flexibility extends to understanding place value - knowing that the "1" in 15 represents ten, not just one. When children can move between these forms easily, they develop what Christina Tondevold refers to as "chunking" ability.

Strong number sense also means being able to solve problems in multiple ways. For instance, a child might solve 8 + 7 by thinking, "8 + 2 = 10, then 10 + 5 = 15", instead of counting on their fingers. This kind of flexible thinking makes math quicker, more efficient, and less prone to mistakes. It also lays the groundwork for using technology-based learning tools effectively.

The ultimate goal is to help children build "a well-organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" [2].

Activities to Build Number Sense

To help kids grasp counting, relationships, and flexible thinking, hands-on activities are a fantastic way to make abstract math concepts more relatable. The most effective activities engage multiple senses and tie math to everyday experiences. Below are some practical ideas that work well at home or in the classroom.

Using Physical Objects and Tools

Using physical items can transform abstract numbers into something kids can touch and see, making math feel less intimidating and more approachable.

• Build Bead Strings: String beads together, adding one for each number counted. This creates a visual representation of numbers. You can mix it up by using beads of different colors or shapes to create patterns, like necklaces or bracelets[4].

Advanced beads patterning in the Funexpected Math app

• Egg Carton Math: Take an egg carton, label each section with a number, and have kids place small objects - like marbles or beans - into each section to match the numbers. This activity helps connect numerals with quantities and reinforces one-to-one correspondence[4].

• Cup and Straw Bundles: For place value practice, label cups with "ones", "tens", and "hundreds." Bundle straws into groups of ten and place them in the appropriate cups. Combine bundles to visually demonstrate concepts like tens turning into hundreds[4].

• Lego Towers: Give kids a set number of Lego blocks and have them build towers. You can also introduce patterns by assigning specific colors to certain numbers[4].

• Addition and Subtraction Objects: Use everyday items - buttons, cereal, toy cars, or cotton balls - to create simple addition and subtraction problems. Add items to a group for addition or remove them for subtraction[4].

• Footprint Measurement: Have kids measure distances using their shoe prints. Compare their footprints to those of family members to explore measurement and comparison in a fun way[4].

These hands-on activities lay the groundwork for interactive games that further strengthen number sense.

Games and Daily Number Practice

Games are a great way to combine learning with fun. They also teach social skills like turn-taking and cooperation while reinforcing math concepts.

• Number Toy Hunt: Write numbers (1–10) on pieces of paper and draw circles on each to match the number. Kids then hunt for toys and place the correct number of items on each paper[5].

• Candy Land Game Modification: Add a deck of number cards to the classic Candy Land game. Players draw a number card, identify it, then proceed with the game as usual[6].

• Hopscotch Math: Draw a hopscotch grid with numbers. Kids can solve simple math problems by hopping to the correct answer or use a number line to physically move forward or backward while solving equations[4].

Daily routines also offer opportunities for practicing numbers:

• Liquid Measurement in the Kitchen: Let kids measure water, rice, or other ingredients using cups and spoons while cooking. This hands-on activity introduces concepts of volume and capacity[4].

• Store Shopping Game: Set up a pretend store with priced items and play money. Kids can "shop", calculate totals, and practice counting change[4].

• Musical Numbers: Incorporate numbers into songs. Kids can sing, clap, or play instruments while counting along, making learning rhythmic and engaging[7].

Working Together in Groups

Group activities not only build math skills but also encourage collaboration, communication, and confidence.

• Make-A-Ten Go Fish: In this card game, teams work together to find pairs of cards that add up to ten. It’s a simple yet effective way to practice addition while fostering teamwork[8].

• Operation Math Relay: Divide kids into teams and have them solve puzzles involving addition, subtraction, multiplication, and division. This activity combines quick thinking with collaboration[8].

• Think-Pair-Share: Students first think about a problem individually, then discuss their ideas with a partner, and finally share with the group. It’s a versatile method that works for any grade level[8].

"Collaboration in the classroom helps students talk and work together, leading to deeper thinking and stronger self-confidence. It also has positive relationships among the students. By making tasks clear and easy to understand, teachers allow students to focus more on solving problems together." [9] - Zina A

• Counting Collections: Provide groups with a collection of items to count, sort, and organize. This activity encourages discussion about strategies while reinforcing counting skills[10].

For group activities to run smoothly, assign clear roles (like recorder, presenter, or facilitator) and ensure everyone gets a chance to contribute. Encourage an open environment where all ideas are welcome, and give kids time to think individually before diving into group discussions[8].

Using Technology to Teach Number Sense

Physical manipulatives and interactive games have long been effective in developing number sense. But when you add thoughtfully designed digital tools into the mix, the learning experience becomes even more dynamic and tailored. Rather than replacing traditional methods, technology enhances them, offering new ways to engage young learners.

How Math Apps Help Children Learn

Math apps designed for kids bring unique advantages to building number sense. The best apps use interactive elements that allow children to manipulate virtual objects, hear explanations, and explore multiple representations of math concepts - all while receiving instant feedback. This kind of environment encourages kids to experiment, make mistakes, and learn from them. Research even shows that high-quality math apps can accelerate learning, achieving in six months what might traditionally take 18 months [11][12].

What makes these apps so effective? Many are built on principles of educational science, incorporating structured curriculums, repetition, rewards, and tools for self-regulation. They’re especially effective on touch-screen tablets, where kids can physically interact with the content [11]. One standout example is the Funexpected Math app, which combines hands-on learning with the power of interactive technology.

What Funexpected Math Offers

Funexpected Math takes these research-backed strategies and turns them into a vibrant, engaging experience for young learners. The app’s AI tutor adapts lessons to each child’s pace, offering hints, asking guiding questions, and introducing math vocabulary.

To keep things fun, the app includes talking buddies that celebrate milestones and sprinkle humor into the process.

The curriculum is packed with over 10,000 tasks spread across 675 lessons, covering 50+ topics. These are organized into six learning programs and six study formats, ensuring a comprehensive learning journey [12].

Here’s what users are saying about it:

"The challenges start off easy, and when you begin completing each creative game you'll find that your mind begins to be challenged even by the simplest test. Yet every game has a positive effect and gives me confidence." [12] - PSTASHIO

One parent shared their experience:

"My daughter's Montessori teacher says her engagement with math themes has increased wildly. I think this product makes a huge difference in children's lives." [12] - Melis

Another user highlighted the app’s diverse curriculum:

"I have a math background myself and I wanted to find an app with a wide curriculum. Smth about logic and geometry, not just counting. And this one was the perfect choice. I see how my daughter starts to understand even complex concepts." [12] - Jon Favertt969

For families, just two 15-minute sessions each week can lead to noticeable progress. The app’s quality has been recognized with awards like The Webby Award for Best Visual Design, Kidscreen Award for Best Original Educational App, and the Mom’s Choice Award (Gold winner). It’s also earned praise for its classroom tools, such as detailed progress reports, easy rostering, and support for English Language Learners - all while ensuring student privacy through compliance with COPPA and FERPA standards.

A number sense task in the Funexpected Math app

Tips for Parents and Teachers

Helping kids build number sense doesn’t require fancy tools or special training. Often, the best learning happens in everyday moments when adults notice and create opportunities for kids to engage with math. Here are some practical ways to make math a natural part of life at home and in the classroom.

Finding Math in Everyday Activities

Math is everywhere, and it’s easy to weave it into daily routines. These small moments can spark big learning opportunities for kids.

Incorporate math into routines like calendar time or simple questions, such as, "What’s one more than 15?"

These activities encourage flexible thinking about numbers. For example, you can add one straw for each day of school, bundling groups of ten to demonstrate place value. Using ten-frames to track days is another hands-on way to make abstract concepts easier to grasp [13].

Cooking and shopping are perfect for practical math practice. Measuring ingredients teaches fractions, while comparing prices introduces addition and estimation. These real-world examples show kids how math applies outside the classroom.

These small exercises not only build number sense but also expand vocabulary, improve problem-solving skills, and encourage logical thinking [14]. The ultimate goal is to get kids talking about math - thinking critically and discussing their ideas. These daily math moments also help build confidence through positive interactions.

Building Confidence Through Questions and Support

How adults respond to kids’ math thinking can either boost their confidence or create anxiety. Research highlights that kids remember more of what they say than what they hear, making conversations and thoughtful questions essential for deeper learning.

"Our students remember far more of what they say than what they hear. While listening to a teacher, not nearly as much goes on in the brain as when students put their thoughts together, verbalize their thinking, and interact with others who might have different information or a different point of view. So, if our goal is understanding and retention, our best course is to frequently stop talking and let our students talk."
– Dr. Spencer Kagan [14]

When a child makes a mistake, don’t rush to correct them. Instead, ask questions like, "How did you figure that out?" or "What else could we try?" This approach encourages problem-solving and resilience [15].

Praise effort rather than natural ability. For instance, instead of saying, "You’re so good at math", try, "I love how you kept trying different ways until you figured it out", or "Great job explaining your thinking!" [15]. Also, avoid negative comments about math, like "I’m not good at math" or "I hated math in school" [16]. Kids can pick up on these attitudes and develop their own doubts.

Tailor these conversations to match each child’s learning pace, ensuring they feel supported and encouraged.

Matching Activities to Each Child's Needs

Every child learns math at their own pace, so it’s essential to adjust activities to suit their individual needs. Watch how they count and solve problems, and adapt the difficulty to challenge advanced learners while reinforcing basics for those who need extra help. Using tools like objects, images, or number lines can cater to different learning styles [17].

Start by observing how a child approaches counting or problem-solving. Do they count items one by one, or can they recognize small groups without counting? These observations can guide your next steps.

For kids struggling with number recognition, focus on games that highlight patterns and symbols. If counting is a challenge, use hands-on tools and one-on-one practice to strengthen their skills [18].

Quick activities like "Number Bounce" (counting forward and backward), "Base Ten Toss" (using place value terms), or "Amazing Race" (breaking numbers into parts) are easy to adapt for various skill levels [19]. These short exercises, lasting 5 to 15 minutes, can be added to any elementary math lesson and adjusted on the fly based on how kids respond.

Building Strong Math Foundations

Understanding how numbers work - often referred to as number sense - is the cornerstone of all future math learning. A solid grasp of this concept lays the groundwork for academic success in mathematics.

"Number sense – making sense of numbers – is the foundation for higher conceptual understanding and mathematical knowledge and relies on the links between number relationships, operations, and processes." - Kathleen Palmieri [20]

Research highlights just how critical early development of number sense can be. For example, studies show that children with strong number sense in preschool are more likely to excel in math by third grade. Even more striking, a 2023 study found that 12-month-old infants who showed sensitivity to changes in quantity were more likely to develop strong symbolic math skills by age 4 [21]. While children may naturally have some sensitivity to numbers, nurturing this ability early on is essential.

The benefits of early math skills extend well beyond the preschool years. Research indicates that preschool math knowledge can predict math achievement up to age 15 [22]. Additionally, early math skills at kindergarten entry are closely tied to later academic success [23]. One meta-analysis even revealed that early number knowledge and understanding of order have twice the impact on later reading achievement compared to early reading skills themselves [22].

To build a strong math foundation, a mix of teaching approaches works best. Combining physical activities with digital tools, such as Funexpected Math, helps children engage with abstract concepts in a hands-on, interactive way. Everyday activities like cooking or shopping also show kids how math connects to real life, making the subject more relatable and practical.

When parents and teachers join forces to create meaningful math experiences - whether through counting games, technology-based learning, or casual conversations about numbers - they help children develop not just math skills, but also confidence and curiosity. These early experiences are the key to fostering a lifelong love of learning.

"Early numeracy is foundational to long-term academic success and equity. By prioritizing numeracy development in early learning, educators can set students on a path toward lifelong achievement." - Sheila Robitaille, 3P Learning [23]

FAQs

How can parents help their child develop number sense at home?

Parents can help their kids develop a strong sense of numbers by weaving math into everyday life. For instance, you can turn routine tasks into learning opportunities - counting apples as you unpack groceries, counting plates while setting the table, or grouping toys by type or color. These simple activities introduce concepts like one-to-one matching and number order in a natural way.

Another way to keep math exciting is through games and puzzles. Try board games that involve numbers, work on simple math puzzles, or use tools like number lines and hundreds charts. These activities make exploring numbers feel like play, encouraging curiosity and understanding. By blending these approaches into your daily routine, you can help your child build confidence and skills that will serve them well in math down the road.

Why is developing number sense early important for a child's success in math?

Building a strong number sense early on is crucial as it forms the backbone for understanding math concepts, tackling problems, and feeling confident in math. Kids who develop solid number sense can see how numbers connect, spot patterns, and use this understanding to handle more complex math as they grow.

Studies highlight that early number sense is a strong indicator of future success in mathematics. It equips children to understand ideas like quantity, comparisons, and basic operations - key skills for advancing in math. Without this early foundation, students may find themselves struggling with math throughout school and even later in life.

How do digital tools and apps help young children develop number sense?

Digital tools and apps have become invaluable in helping young children develop number sense by making math more interactive and engaging. These resources often incorporate visual aids and hands-on features, like virtual manipulatives and dynamic models, to show kids how numbers function and connect to one another.

Gamified learning apps add another layer by making math enjoyable. They transform abstract ideas into fun, approachable activities. With personalized, multisensory experiences, these tools adapt to various learning styles, ensuring kids stay engaged while building a solid foundation in math.

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