Lesson 4: Number Patterns

For Grade 5 Students (Ages 10-11) - Let's discover the rules behind number sequences!

What we will learn today:

In this lesson, you will learn to:

  • Identify number patterns.
  • Determine the rule of a number pattern (addition, subtraction, multiplication, division).
  • Extend number patterns by applying the rule.
  • Solve simple problems involving number patterns.

Introduction to Number Patterns

Hello, young mathematicians! Welcome to Lesson 4 of Math Lanka. Today, we're going to explore the exciting world of number patterns.

What are number patterns? Imagine a line of numbers that follow a special rule. If you can figure out the rule, you can predict what numbers come next! It's like solving a secret code.

Number patterns are all around us, not just in math, but also in nature, music, and art. Understanding them helps us think logically and solve problems.

What is a Number Pattern?

A number pattern is a sequence of numbers that are arranged according to a specific rule. This rule can involve addition, subtraction, multiplication, division, or even a combination of these operations.

Let's look at some examples to understand this better.

Examples of Number Patterns

Example 1: Simple Addition Pattern

Consider the sequence: $2, 4, 6, 8, \dots$

  • What do you notice about these numbers?
  • How do you get from $2$ to $4$? (Add $2$)
  • How do you get from $4$ to $6$? (Add $2$)
  • How do you get from $6$ to $8$? (Add $2$)

The rule for this pattern is "Add 2 to the previous number".

So, the next number would be $8 + 2 = 10$.

The pattern continues: $2, 4, 6, 8, 10, 12, 14, \dots$

Example 2: Simple Subtraction Pattern

Consider the sequence: $20, 18, 16, 14, \dots$

  • Are the numbers getting bigger or smaller? (Smaller)
  • How do you get from $20$ to $18$? (Subtract $2$)
  • How do you get from $18$ to $16$? (Subtract $2$)
  • How do you get from $16$ to $14$? (Subtract $2$)

The rule for this pattern is "Subtract 2 from the previous number".

So, the next number would be $14 - 2 = 12$.

The pattern continues: $20, 18, 16, 14, 12, 10, 8, \dots$

Example 3: Simple Multiplication Pattern

Consider the sequence: $3, 6, 12, 24, \dots$

  • How do you get from $3$ to $6$? (Multiply by $2$)
  • How do you get from $6$ to $12$? (Multiply by $2$)
  • How do you get from $12$ to $24$? (Multiply by $2$)

The rule for this pattern is "Multiply the previous number by 2".

So, the next number would be $24 \times 2 = 48$.

The pattern continues: $3, 6, 12, 24, 48, 96, \dots$

Example 4: Mixed Operation Pattern

Sometimes, patterns can be a bit trickier and involve more than one operation.

Consider the sequence: $1, 2, 4, 7, 11, \dots$

Let's find the difference between consecutive numbers:

  • $2 - 1 = 1$
  • $4 - 2 = 2$
  • $7 - 4 = 3$
  • $11 - 7 = 4$

The differences themselves form a pattern: $1, 2, 3, 4, \dots$ (adding $1$ each time).

So, the next difference will be $5$.

Therefore, the next number in the original sequence is $11 + 5 = 16$.

The pattern continues: $1, 2, 4, 7, 11, 16, 22, \dots$

How to Find the Rule of a Pattern

Here are some steps to help you find the rule of a number pattern:

  1. Look at the difference between consecutive numbers:
    • If the numbers are increasing, try addition or multiplication.
    • If the numbers are decreasing, try subtraction or division.
  2. Check if the difference is constant: If you add or subtract the same number each time, that's your rule!
  3. Check for multiplication or division: If the numbers are growing or shrinking very quickly, try multiplying or dividing.
  4. Look for a pattern in the differences: If the first differences aren't constant, find the differences between those differences. Sometimes, the pattern is in the "pattern of patterns"!

Practice Time!

Now it's your turn to find the rule and the next three numbers for each pattern. Write your answers in the boxes below.

$1. \quad 5, 10, 15, 20, \dots$

$2. \quad 30, 27, 24, 21, \dots$

$3. \quad 2, 6, 18, 54, \dots$

$4. \quad 1, 4, 9, 16, \dots$ (Hint: Think about what happens when you multiply a number by itself)

$5. \quad 100, 90, 80, 70, \dots$

Answers to Practice Time

Let's check your answers!

  1. Pattern: $5, 10, 15, 20, \dots$

    Rule: Add 5

    Next three numbers: $25, 30, 35$

  2. Pattern: $30, 27, 24, 21, \dots$

    Rule: Subtract 3

    Next three numbers: $18, 15, 12$

  3. Pattern: $2, 6, 18, 54, \dots$

    Rule: Multiply by 3

    Next three numbers: $162, 486, 1458$

  4. Pattern: $1, 4, 9, 16, \dots$

    Rule: The numbers are $1 \times 1, 2 \times 2, 3 \times 3, 4 \times 4$. So, the rule is "Square the position number" or "Add consecutive odd numbers" ($1+3=4, 4+5=9, 9+7=16$).

    Next three numbers: $25 (5 \times 5), 36 (6 \times 6), 49 (7 \times 7)$

  5. Pattern: $100, 90, 80, 70, \dots$

    Rule: Subtract 10

    Next three numbers: $60, 50, 40$

You've completed Lesson 4!

Great job, Math Lanka students! You've learned how to identify and extend number patterns. This skill is very important in mathematics and will help you in many ways as you continue your learning journey. Keep practicing and looking for patterns everywhere!

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