Mathematics -- Class 3

Topic: Number Patterns and Sequences
Name: ____________________________Class: 3Date: ________________
Learning Objectives
Let Us Begin!

During Diwali, Meena lines up diyas in rows. The first row has 2 diyas, the second row has 4, the third row has 6, and the fourth row has 8. Do you see something special? Each row has 2 more diyas than the row before it!

This is called a number pattern. When numbers follow a rule and come one after another, we call them a sequence. Learning to spot the rule helps us figure out what number comes next.

Step-by-Step Explanation

What is a Number Pattern?

A number pattern is a list of numbers that follow a fixed rule. The rule tells us how to get from one number to the next.

Step 1: Look at the Numbers Carefully

Write down the numbers in the sequence. For example: 5, 10, 15, 20, ...

Step 2: Find the Difference

Subtract each number from the one that comes after it. 10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5. The difference is always 5.

Think about it: If the difference is the same every time, the rule is "add that number" or "subtract that number."

Step 3: State the Rule

For 5, 10, 15, 20, ... the rule is "add 5". So the next number is 20 + 5 = 25.

Growing Patterns (Adding)

When we add the same number each time, the sequence grows bigger. Examples:

Add 2: 4, 6, 8, 10, 12, ...   Add 3: 1, 4, 7, 10, 13, ...   Add 5: 10, 15, 20, 25, 30, ...

Shrinking Patterns (Subtracting)

When we subtract the same number each time, the sequence gets smaller. Examples:

Subtract 2: 20, 18, 16, 14, 12, ...   Subtract 5: 50, 45, 40, 35, 30, ...

Think about it: Aman has Rs 50 in his piggy bank. Every week he spends Rs 5. What will his money look like week by week? 50, 45, 40, 35, ... What is the rule?

How to Check Your Answer

After you find the rule, apply it to every pair of numbers in the sequence. If it works for all of them, your rule is correct.

Key Words and Meanings
WordMeaning
PatternA set of numbers or shapes that follow a fixed rule
SequenceNumbers written in order following a rule
RuleThe operation (add or subtract) used to go from one number to the next
Growing patternA pattern where numbers get bigger (we add)
Shrinking patternA pattern where numbers get smaller (we subtract)
DifferenceThe result when we subtract one number from another

Mathematics -- Class 3 (continued)

Topic: Number Patterns and Sequences -- Examples and Practice
Examples
Example 1: Find the Rule and the Next Number

Sequence: 2, 5, 8, 11, ?

Differences: 5 - 2 = 3, 8 - 5 = 3, 11 - 8 = 3. Rule: Add 3. Next number: 11 + 3 = 14.

Example 2: Shrinking Pattern

Sequence: 50, 45, 40, 35, ?

Differences: 50 - 45 = 5, 45 - 40 = 5, 40 - 35 = 5. Rule: Subtract 5. Next number: 35 - 5 = 30.

Example 3: Growing Pattern with Add 4

Sequence: 3, 7, 11, 15, ?

Differences: 7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4. Rule: Add 4. Next number: 15 + 4 = 19.

Key Points to Remember
Practice Questions

A. Find the Rule and Complete the Sequence

  1. 4, 6, 8, 10, ,   Rule:
  2. 7, 10, 13, 16, ,   Rule:
  3. 5, 10, 15, 20, ,   Rule:
  4. 40, 38, 36, 34, ,   Rule:
  5. 60, 55, 50, 45, ,   Rule:
  6. 11, 14, 17, 20, ,   Rule:
  7. 100, 90, 80, 70, ,   Rule:
  8. 6, 12, 18, 24, ,   Rule:

B. Multiple Choice Questions

  1. What is the rule for the sequence 3, 6, 9, 12, 15?
    (a) Add 2(b) Add 3(c) Add 4(d) Add 5
  2. What comes next in 30, 25, 20, 15, ?
    (a) 5(b) 10(c) 12(d) 20
  3. Which sequence follows the rule "Add 4"?
    (a) 2, 4, 6, 8(b) 1, 5, 9, 13(c) 3, 6, 9, 12(d) 5, 15, 25, 35

C. Fill in the Blanks

  1. In the sequence 10, 20, 30, 40, the rule is .
  2. A pattern where numbers get bigger is called a pattern.
  3. A pattern where numbers get smaller is called a pattern.
  4. The next number in 8, 11, 14, 17 is .

D. Short Answer

  1. Priya saves Rs 3 every day. She starts with Rs 3 on Monday. How much will she have saved in total by Friday? Write the pattern.
  2. Write a shrinking pattern that starts at 45 and uses the rule "subtract 5". Write at least 6 numbers.
Think and Do -- Fun Activity

Create Your Own Pattern: Choose a starting number and a rule (add or subtract any number from 2 to 10). Write your sequence below. Then ask your friend to find the rule!

My starting number: __________   My rule: __________________________

My sequence: __________, __________, __________, __________, __________, __________

Rangoli Pattern: Imagine you are making a rangoli with dots. Row 1 has 2 dots, Row 2 has 5 dots, Row 3 has 8 dots. How many dots will Row 4 and Row 5 have? Write the rule and the answer below.

Rule: __________________________   Row 4: __________   Row 5: __________