CBSE Class 4 Maths Chapter 10: Play with Patterns

What Are Patterns?

A pattern is simply a repeated design, sequence, or arrangement that follows a specific rule. Think of it like a secret code where you have to figure out what comes next! Patterns can be found everywhere: in nature (like the stripes on a zebra or the petals of a flower), in art (like the tiles on a floor or a design on a blanket), and especially in mathematics. Recognizing patterns helps us make predictions, solve problems, and even understand more complex mathematical ideas later on. It teaches our brains to look for order and structure. For example, if you see a sequence like Circle, Square, Circle, Square, Circle... you immediately know the next shape will be a Square, because you've identified the repeating unit (Circle, Square) and its rule: alternate between the two shapes.

Exploring Number Patterns

Just like shapes, numbers can also follow fascinating patterns. These are often created by adding, subtracting, or sometimes even multiplying a fixed number to get the next term. Let's look at some examples:

1. Adding Pattern: Consider the sequence: 2, 4, 6, 8, 10, ...

Here, each number is 2 more than the previous one. The rule is 'Add 2'. So, the next number would be 12 (10 + 2).

1. Subtracting Pattern: Look at this sequence: 20, 18, 16, 14, ...

In this pattern, each number is 2 less than the previous one. The rule is 'Subtract 2'. The next number would be 12 (14 - 2).

1. Mixed Pattern: Sometimes patterns can combine rules or change turns.

Consider: 1, 2, 4, 5, 7, 8, ...
Here, the pattern is 'Add 1, then Add 2'. (1+1=2, 2+2=4, 4+1=5, 5+2=7, 7+1=8). So the next number would be 8+2=10.

Identifying these rules is the key to mastering number patterns. Always observe the difference or relationship between consecutive numbers.

How to Find the Rule in a Pattern

1. Step 1: Observe Carefully — Look at all the elements in the pattern. Are they shapes, numbers, letters, or a combination? Notice how they are arranged and if any element repeats.
2. Step 2: Compare Consecutive Elements — If it's a number pattern, find the difference between the second and first number, then the third and second, and so on. See if there's a constant addition, subtraction, multiplication, or division. If it's a shape pattern, see how the shape changes or if a group of shapes repeats.
3. Step 3: Formulate the Rule — Based on your observations, state the rule in simple words. For example, 'add 3 to the previous number' or 'alternate between a star and a moon'.
4. Step 4: Test the Rule — Apply your rule to the next few known elements in the pattern to ensure it holds true. If it doesn't work for all parts, go back to Step 2 and look for a different rule.
5. Step 5: Extend the Pattern — Once you are confident about your rule, use it to find the missing or next elements in the pattern.

Worked Examples: Completing Patterns

• Example 1: Shape Pattern
  Complete the pattern:

  ▲, ▼, ▲, ▼, ___, ___, ___

  Solution:

  1. Observe: The pattern consists of an upward-pointing triangle (▲) and a downward-pointing triangle (▼).
  2. Compare: The shapes alternate. The sequence is ▲ then ▼, then ▲ then ▼.
  3. Rule: The rule is to alternate between an upward-pointing triangle and a downward-pointing triangle.
  4. Extend: Following this rule, after the last ▼, the next shape will be ▲. Then ▼, then ▲.

  Completed Pattern: ▲, ▼, ▲, ▼, ▲, ▼, ▲

• Example 2: Number Pattern
  Complete the pattern:

  5, 10, 15, 20, ___, ___

  Solution:

  1. Observe: The pattern consists of numbers.
  2. Compare: Let's find the difference between consecutive numbers:

  10 - 5 = 5
  15 - 10 = 5
  20 - 15 = 5
  The difference is consistently 5.

  1. Rule: The rule is to 'add 5' to the previous number to get the next number.
  2. Extend: Following this rule:

  The number after 20 will be 20 + 5 = 25.
  The number after 25 will be 25 + 5 = 30.

  Completed Pattern: 5, 10, 15, 20, 25, 30

YoLearn AI Tutor Exam Tip

When solving pattern questions, always check your identified rule with at least two or three pairs of elements in the given sequence, not just one. Sometimes, a pattern might seem simple at first glance but could have a slightly more complex rule (like alternating additions). Also, draw or write clearly. For shape patterns, using different colours or sizes can sometimes help you spot the repetition more easily. Don't rush; careful observation is your best tool!

Practice Questions with Solutions

• Q: Complete the pattern: A, B, A, B, ___, ___, ___
  A: Step 1: Observe the pattern. It has two letters, A and B, which repeat.
  Step 2: Identify the repeating unit. The unit is "A, B".
  Step 3: Apply the rule. After B, A comes next, then B, then A.
  Final answer: A, B, A, B, A, B, A

• Q: Find the next two numbers in the sequence: 3, 6, 9, 12, ___, ___
  A: Step 1: Look at the difference between consecutive numbers.
  6 - 3 = 3
  9 - 6 = 3
  12 - 9 = 3
  Step 2: Identify the rule. Each number is 3 more than the previous one (Add 3).
  Step 3: Apply the rule to find the next two numbers.
  12 + 3 = 15
  15 + 3 = 18
  Final answer: 3, 6, 9, 12, 15, 18

• Q: Complete the pattern: ⬜, ⚫, ⬜, ⚫, ___, ___
  A: Step 1: Observe the shapes. There is a white square (⬜) and a black circle (⚫).
  Step 2: Identify the repeating unit. The unit is "⬜, ⚫".
  Step 3: Apply the rule. After the black circle, the white square comes next, then the black circle.
  Final answer: ⬜, ⚫, ⬜, ⚫, ⬜, ⚫

• Q: What comes next in the sequence: 10, 8, 6, 4, ___, ___
  A: Step 1: Look at the difference between consecutive numbers.
  8 - 10 = -2 (or 10 - 8 = 2, meaning it decreases by 2)
  6 - 8 = -2
  4 - 6 = -2
  Step 2: Identify the rule. Each number is 2 less than the previous one (Subtract 2).
  Step 3: Apply the rule to find the next two numbers.
  4 - 2 = 2
  2 - 2 = 0
  Final answer: 10, 8, 6, 4, 2, 0

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