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Number Sense

Build a strong foundation in numbers, counting, place value, and number relationships.

Topic Areas

Total Lessons

Grade Levels

Number Sense, grade by grade

Taught from Kindergarten through Grade 8. Each grade band below lists the skills its lessons teach, with one real problem from that band solved step by step.

Kindergarten–Grade 2

Taught through Counting (Grades K–1), Number Bonds (Grades K–2), Place Value (Grades 1–2) and Comparing Numbers (Grade 1) — 44 lessons.

Kindergarten · Counting
- Counting 1-5
- Counting 1-10
- Counting 1-20
- Counting to 50
- Counting to 100
- Skip Counting by 2s
- Skip Counting by 5s
- Skip Counting by 10s
8 lessons with worksheets
Kindergarten · Number Bonds
- Number Bonds Within 5
- Number Bonds Within 10
- Making 10
- Bonds of 3
- Bonds of 5
6 lessons with worksheets
Grade 1 · Number Bonds
- Number Bonds 11-15
- Number Bonds Within 20
- Bonds of 20
- Fact Families
6 lessons with worksheets
Grade 1 · Place Value
- Tens and Ones
- Building 2-Digit Numbers
- Identify Digits
- Expanded Form
5 lessons with worksheets
Grade 1 · Counting
- Counting 1-10
- Counting 1-20
- Counting to 100
- Skip Counting by 2s
- Skip Counting by 5s
- Skip Counting by 10s
6 lessons with worksheets
Grade 1 · Comparing Numbers
- Greater Than, Less Than (1-10)
- Greater Than, Less Than (1-20)
- Equal To, Not Equal
- Ordering Numbers
4 lessons with worksheets
Grade 2 · Number Bonds
- Number Bonds to 20
- Number Bonds to 50
- Number Bonds to 100
4 lessons with worksheets
Grade 2 · Place Value
- The Hundreds Place
- Building 3-Digit Numbers
- Expanded Form
- Comparing 3-Digit Numbers
5 lessons with worksheets

Worked example · Grade 1 Place Value

Which digit is in the ones place of 31?

Each digit’s value depends on its place. Look at the ones place in 31.
Counting from the right, the ones place is the first digit.
The digit in the ones place is 1.

Answer: 1

More Grade 1 place value

Grades 3–5

Taught through Place Value (Grade 4) — 6 lessons.

Grade 4 · Place Value
- Thousands Place
- Millions Place
- Rounding Numbers
- Comparing Large Numbers
- Expanded Form
6 lessons with worksheets

Worked example · Grade 4 Place Value

Round 35,474 to the nearest 10

To round 35,474 to the nearest ten, look at the digit in the ones place.
That digit is 4, which is less than 5, so round DOWN.
So 35,474 rounded to the nearest ten is 35,470.

Answer: 35,470

More Grade 4 place value

Grades 6–8

Taught through Integers (Grade 6), Rational Numbers (Grade 7) and Irrational Numbers (Grade 8) — 16 lessons.

Grade 6 · Integers
- Integers on Number Line
- Absolute Value
- Adding Integers
- Subtracting Integers
- Multiplying Integers
- Dividing Integers
7 lessons with worksheets
Grade 7 · Rational Numbers
- Add/Subtract Rationals
- Multiply/Divide Rationals
- All Operations
- Word Problems
4 lessons with worksheets
Grade 8 · Irrational Numbers
- Rational vs Irrational
- Approximating Irrationals
- Comparing Numbers
- Number Line
5 lessons with worksheets

Worked example · Grade 7 Rational Numbers

(−2) × 3 = ?

Multiply the numbers without their signs: 2 × 3 = 6.
The signs are different, so the answer is negative.
(−2) × 3 = −6

Answer: −6

More Grade 7 rational numbers

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Frequently Asked Questions

What is number sense and why is it important?

Number sense is the intuitive understanding of numbers, their relationships, and how they work together. It includes understanding quantity, place value, and mental math strategies. Strong number sense is the foundation for all math learning—students with good number sense learn new concepts faster and make fewer errors.

How do I build number sense in my child?

Build number sense through daily activities: count objects, compare quantities, play dice and card games, practice estimation, use manipulatives, and discuss numbers in everyday life. Singapore Math number bonds and mental math strategies are particularly effective for developing strong number sense.

At what age should number sense develop?

Number sense begins developing in infancy and continues through elementary school. By kindergarten, children should recognize quantities to 10. By second grade, they should understand place value and relationships between numbers to 100. Formal number sense instruction continues through all grades with increasing complexity.

Need help finding the right level?

Take our placement quiz to find exactly where your child should start.