Number Patterns (Grade 4)
A number pattern is a sequence of numbers that follows a rule. The rule tells you how to get from one number to the next. Patterns can involve addition, subtraction, multiplication, division, or a combination of operations.
In Class 4, you will work with more complex patterns — including two-step rules, decreasing sequences, and patterns involving multiplication.
What is Number Patterns - Class 4 Maths (Patterns)?
A number pattern (or number sequence) is an ordered list of numbers where each number is obtained from the previous one by applying a consistent rule.
Types of number patterns:
- Increasing pattern: Numbers get larger (e.g., 5, 10, 15, 20 — rule: add 5)
- Decreasing pattern: Numbers get smaller (e.g., 100, 90, 80, 70 — rule: subtract 10)
- Multiplying pattern: Numbers are multiplied (e.g., 2, 4, 8, 16 — rule: multiply by 2)
- Two-step pattern: Two operations alternate (e.g., 2, 6, 4, 8, 6 — rule: add 4, subtract 2)
Solved Examples
Example 1: Example 1: Simple addition pattern
Problem: Find the next 3 numbers: 7, 14, 21, 28, ?, ?, ?
Solution:
Step 1: Differences: 14−7=7, 21−14=7, 28−21=7. Rule: add 7.
Step 2: 28+7=35, 35+7=42, 42+7=49
Answer: 35, 42, 49
Example 2: Example 2: Subtraction pattern
Problem: Complete: 95, 87, 79, 71, ?, ?
Solution:
Step 1: Differences: 95−87=8, 87−79=8, 79−71=8. Rule: subtract 8.
Step 2: 71−8=63, 63−8=55
Answer: 63, 55
Example 3: Example 3: Multiplication (doubling) pattern
Problem: Find the next 3 numbers: 3, 6, 12, 24, ?, ?, ?
Solution:
Step 1: 6÷3=2, 12÷6=2, 24÷12=2. Rule: multiply by 2.
Step 2: 24×2=48, 48×2=96, 96×2=192
Answer: 48, 96, 192
Example 4: Example 4: Increasing difference pattern
Problem: Find the next 2 numbers: 1, 2, 4, 7, 11, ?, ?
Solution:
Step 1: Differences: 1, 2, 3, 4. The differences increase by 1 each time.
Step 2: Next difference = 5: 11+5=16
Step 3: Next difference = 6: 16+6=22
Answer: 16, 22
Example 5: Example 5: Two-step pattern
Problem: Find the rule: 5, 15, 10, 20, 15, 25, ?
Solution:
Step 1: 5→15 (+10), 15→10 (−5), 10→20 (+10), 20→15 (−5), 15→25 (+10)
Step 2: Rule: alternately add 10 and subtract 5.
Step 3: Next: 25−5=20
Answer: The next number is 20. Rule: +10, −5, +10, −5, ...
Example 6: Example 6: Square number pattern
Problem: 1, 4, 9, 16, 25, ?, ?
Solution:
Step 1: These are perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25
Step 2: 6²=36, 7²=49
Answer: 36, 49. The pattern is n² (square numbers).
Example 7: Example 7: Finding a missing number in the middle
Problem: 12, 19, ?, 33, 40
Solution:
Step 1: Check differences: 19−12=7, 33−?=?, 40−33=7. Constant difference = 7.
Step 2: Missing number = 19+7 = 26
Step 3: Check: 26+7=33 ✓
Answer: The missing number is 26.
Example 8: Example 8: Division pattern
Problem: 8000, 4000, 2000, 1000, ?, ?
Solution:
Step 1: 4000÷8000=½, 2000÷4000=½. Rule: divide by 2.
Step 2: 1000÷2=500, 500÷2=250
Answer: 500, 250
Example 9: Example 9: Word problem
Problem: Ria saves ₹10 in week 1, ₹20 in week 2, ₹30 in week 3. If the pattern continues, how much does she save in week 8?
Solution:
Step 1: Rule: add ₹10 each week. Savings in week n = 10 × n.
Step 2: Week 8 = 10 × 8 = ₹80
Answer: Ria saves ₹80 in week 8.
Example 10: Example 10: Finding the rule
Problem: What is the rule for: 2, 5, 11, 23, 47?
Solution:
Step 1: Differences: 3, 6, 12, 24 — these double each time.
Step 2: Alternatively, each number = previous × 2 + 1: 2×2+1=5, 5×2+1=11, 11×2+1=23, 23×2+1=47 ✓
Answer: Rule: multiply by 2 and add 1.
Key Points to Remember
- A number pattern follows a consistent rule from one number to the next.
- Find the rule by looking at differences between consecutive numbers.
- Common rules: add a fixed number, subtract, multiply, divide, or combine two operations.
- If differences themselves form a pattern, it is a growing difference pattern.
- Square numbers (1, 4, 9, 16, 25, ...) form a special pattern where differences increase by 2 each time (3, 5, 7, 9, ...).
- Always verify your rule by checking it against all given numbers.
- Patterns can be used to predict any term without listing all numbers before it.
Practice Problems
- Find the next 3 numbers: 4, 11, 18, 25, ?, ?, ?
- Complete: 200, 180, 160, 140, ?, ?
- Find the rule and next number: 1, 3, 9, 27, ?
- What is the missing number? 8, 15, ?, 29, 36
- Aman earns ₹5 on day 1, ₹10 on day 2, ₹20 on day 3. How much on day 6?
- Find the next 2 numbers: 2, 3, 5, 8, 12, ?, ?
- What is the rule for: 100, 50, 25, 12.5?
Frequently Asked Questions
Q1. What is a number pattern?
A number pattern is a sequence of numbers where each number follows a specific rule from the one before it. Examples include 2, 4, 6, 8 (add 2) and 3, 9, 27, 81 (multiply by 3).
Q2. How do you find the rule of a number pattern?
Calculate the differences between consecutive numbers. If the differences are constant, the rule is adding or subtracting that amount. If differences change, look for multiplication, division, or a growing difference pattern.
Q3. What is an increasing pattern?
An increasing pattern is one where the numbers get larger from left to right. The rule usually involves addition or multiplication.
Q4. What is a decreasing pattern?
A decreasing pattern is one where the numbers get smaller. The rule involves subtraction or division.
Q5. What are square numbers?
Square numbers are the result of multiplying a number by itself: 1×1=1, 2×2=4, 3×3=9, 4×4=16, 5×5=25. They form the pattern 1, 4, 9, 16, 25, 36, ...
Q6. Can a pattern have two different rules?
Yes. Some patterns alternate between two rules, like +5 then −2, or multiply by 2 then add 1. These are called two-step patterns.
Q7. How do you find a missing number in the middle of a pattern?
First find the rule using the numbers you do have. Then apply the rule forward or backward to fill in the missing number. Verify that the rule works for all numbers.
Q8. What is the difference between a number pattern and a geometric pattern?
A number pattern uses numbers in a sequence. A geometric pattern uses shapes arranged according to a rule. Many geometric patterns can be described with number patterns (e.g., triangle count: 1, 3, 6, 10).
