Building Strong Number Sense in Primary Students

Number sense is the intuitive understanding of numbers, their relationships, and how they work. It’s the difference between a child who can recite “2 + 2 = 4” and a child who truly understands what that means. Students with strong number sense can estimate, reason numerically, and recognize when answers don’t make sense. It’s the foundation upon which all other maths skills are built.

What is Number Sense?

Number sense includes:

• Understanding what numbers represent
• Recognizing number relationships (5 is one more than 4, 10 is double 5)
• Knowing relative size (47 is closer to 50 than to 40)
• Estimating quantities without counting
• Mental computation strategies
• Flexibility with numbers (knowing 8 + 7 is the same as 7 + 8, or thinking of it as 10 + 5)

Children don’t develop number sense automatically through memorization – it develops through rich experiences with numbers in meaningful contexts.

Why Number Sense Matters

Students with strong number sense:

• Solve problems more efficiently
• Recognize errors in their calculations
• Develop flexible thinking strategies
• Feel more confident with maths
• Perform better on standardized tests
• Find real-world maths applications easier

Conversely, students who lack number sense struggle even when they’ve memorized procedures. They might know the algorithm for long division but can’t estimate whether 156 ÷ 4 should be around 20, 40, or 200.

Developmental Stages of Number Sense

Foundation Years (Ages 5-6):

• Counting with understanding
• Recognizing small quantities without counting (subitizing)
• One-to-one correspondence
• Understanding more/less

Years 1-2 (Ages 6-8):

• Part-whole relationships (6 can be 5+1, 4+2, 3+3)
• Place value basics (23 is 2 tens and 3 ones)
• Number patterns
• Basic addition/subtraction strategies

Years 3-4 (Ages 8-10):

• Place value to thousands
• Relationships between operations
• Estimation and rounding
• Mental computation strategies

Years 5-6 (Ages 10-12):

• Fraction and decimal sense
• Proportional reasoning
• Complex mental strategies
• Understanding negative numbers

Practical Activities to Build Number Sense

1. Daily Number Talks (5-10 minutes)

Present a simple problem and ask students to solve it mentally, then share strategies:

Example: “How did you figure out 25 + 26?”

• “I did 25 + 25 = 50, then added 1 more = 51”
• “I rounded 26 to 30, so 25 + 30 = 55, then minus 4 = 51”
• “I know 20 + 20 = 40, and 5 + 6 = 11, so 40 + 11 = 51”

This shows there are multiple valid strategies and builds flexible thinking.

2. Estimation Jars

Fill jars with objects (blocks, counters, pasta) and have students estimate:

• Too young to count? Compare to a known quantity
• Older students: Develop estimation strategies (count a section, multiply)
• Discuss: What made it hard? What helped you estimate?

3. Benchmark Numbers

Help students use 5, 10, 100 as reference points:

• “Is 7 closer to 5 or 10?”
• “Is 47 closer to 40 or 50?”
• “About how many blocks fit in this box?” (compare to 100-block benchmark)

4. Number Lines

Physical number lines help students visualize number relationships:

• Place numbers on blank number lines
• Jump along lines to show addition/subtraction
• Identify missing numbers
• Compare fractions visually

5. Subitizing Activities

Recognize quantities instantly without counting:

• Flash dot cards (1-2 seconds)
• Ten-frames showing different arrangements of 6
• Dice patterns
• Dominoes

This builds automatic number recognition and part-whole understanding.

6. Decomposing Numbers

Practice breaking numbers apart in different ways:

• “Show me different ways to make 8”
• Use counters, fingers, drawings
• 10-frames: “8 is 5 and 3 more” or “8 is 10 minus 2”

7. Comparison Activities

Develop understanding of relative size:

• Which is greater: 47 or 52?
• Order these from smallest to largest: 235, 253, 205
• True or False: 0.7 > 0.65
• Always explain HOW they know

8. Real-World Contexts

Make numbers meaningful:

• Shopping with a budget
• Cooking with measurements
• Sports scores and statistics
• Time and schedules
• Money calculations

Teaching Strategies That Work

Use Manipulatives: Hands-on materials make abstract concepts concrete. Base-ten blocks, counters, fraction strips, and measuring tools give students physical experiences with mathematical ideas.

Encourage Multiple Strategies: Never teach “the one right way.” When students share different approaches, they develop flexibility and deeper understanding.

Ask “How Do You Know?” This question pushes thinking beyond memorization. Students must explain their reasoning, which deepens understanding.

Make Mistakes Valuable: When students make errors, use them as learning opportunities. “Let’s figure out what happened here” is more valuable than “That’s wrong.”

Connect to What They Know: Always link new concepts to existing knowledge. “Remember when we…” builds connections.

Activities by Year Level

Foundation-Year 1:

• Count collections daily
• Subitizing games
• Number songs and chants
• Simple comparison (more/less)
• Making 5 and 10 in different ways

Years 2-3:

• Mental addition/subtraction strategies
• Place value with base-10 blocks
• Number lines to 100, then 1000
• Estimation games
• Part-whole relationships

Years 4-5:

• Multi-digit operations mentally
• Fraction sense (visual models)
• Decimal place value
• Rounding and estimation in context
• Large number relationships

Years 5-6:

• Fraction, decimal, percentage connections
• Ratio and proportion
• Negative number sense
• Order of operations understanding
• Problem-solving with multiple steps

Common Mistakes to Avoid

Over-Reliance on Counting: Students who count everything (including on fingers for 8+5 in Year 4) haven’t developed number sense. Encourage strategies like “use a double” (8+8=16, so 8+5 is 3 less = 13).

Teaching Algorithms Too Early: Standard algorithms can interfere with number sense development. Let students develop their own strategies first, then introduce formal methods.

Rushing Through Concepts: Number sense takes time. Better to deeply understand numbers to 20 than superficially “cover” numbers to 100.

Not Allowing Think Time: Silence isn’t wasted time – it’s thinking time. Wait at least 5-10 seconds after asking questions.

Assessment of Number Sense

Look for:

• Can they explain their thinking?
• Do they use efficient strategies?
• Can they estimate reasonably?
• Do they recognize when answers don’t make sense?
• Can they solve problems in multiple ways?

Don’t just focus on:

• Speed
• Getting the right answer
• Following algorithms correctly

Resources and Tools

Physical Materials:

• Base-ten blocks
• Counters and linking cubes
• Number lines (floor-sized and desk-sized)
• Ten-frames
• Place value charts

Games:

• Number card games (Make 10, Go Fish with numbers)
• Dice games
• Board games with dice
• Number puzzles

Digital Tools:

• Interactive number lines
• Virtual manipulatives
• Number sense apps (choose carefully – many focus on speed rather than understanding)

The Bottom Line

Building number sense isn’t about drilling facts or rushing through curriculum. It’s about providing rich, meaningful experiences with numbers over time. Students need opportunities to:

• Play with numbers
• Explore relationships
• Develop their own strategies
• Make and learn from mistakes
• Apply numbers to real contexts

When we invest time in developing strong number sense in the early years, we create confident, capable mathematicians who can tackle increasingly complex concepts. The foundation you build now determines their mathematical success for years to come.

Remember: Number sense develops gradually through many experiences. Be patient, provide variety, make it meaningful, and celebrate thinking over speed. Your students’ mathematical futures depend on this crucial foundation.