Maths Chapter 7: Can You See the Pattern — CBSE Class 5 NCERT Guide

Understanding Pattern Rules: The Magic of Turns

Patterns are created by repeating shapes under a specific rule. In this chapter, we focus heavily on rotational patterns. To understand these, imagine the face of a clock with the hand pointing at 12 o'clock.

• 1/4 Turn (Quarter Turn): If a shape starts pointing up (at 12) and turns clockwise to point right (at 3), it has taken a $\frac{1}{4}$ turn. This is a 90-degree rotation.
• 1/2 Turn (Half Turn): If the shape turns to point directly downwards (at 6), it has turned upside down. This is a $\frac{1}{2}$ turn (180-degree rotation).
• 3/4 Turn (Three-Quarter Turn): If the shape turns further to point left (at 9), it has made a $\frac{3}{4}$ turn (270-degree rotation).
• 1 Full Turn: The shape rotates all the way back to its original position (at 12).

By observing how much a shape rotates from one step to the next, we can easily find the 'pattern rule' and predict the upcoming shapes in the series.

How to Find and Extend a Shape Pattern

1. Step 1: Check the starting position — Look closely at the first shape in the pattern. Identify which way its top, arrows, or unique features are pointing (e.g., pointing UP).
2. Step 2: Observe the next shape — See where the same feature points in the second shape (e.g., pointing RIGHT). This tells you which direction it is rotating.
3. Step 3: Determine the turn fraction — Calculate how big the turn is. Moving from UP to RIGHT is a clockwise 1/4 turn. Moving from UP to DOWN is a 1/2 turn.
4. Step 4: Apply the rule to draw the next patterns — Continue applying the exact same turn rule to find the subsequent shapes in the pattern chain.

Magical Number Patterns: Squares, Hexagons, and Palindromes

• Magic Squares (Sum 150): A 3x3 grid filled with numbers from 46 to 54, where every row, column, and diagonal adds up to exactly 150. Example configuration: Top row (53, 46, 51), Middle row (48, 50, 52), Bottom row (49, 54, 47). Calculate: 53 + 46 + 51 = 150; 53 + 48 + 49 = 150; 53 + 50 + 47 = 150.
• Magic Hexagons: A layout of circles and squares. Rule: The number in any square box is the result of multiplying the numbers in the two circles next to it. For example, if circle A has 7 and circle B has 10, the square box between them must be 70.
• Palindromes (Special Numbers): Numbers that read the same forwards and backwards, like 121, 343, or 5005. You can turn any number into a special number! Take 28 -> Reverse it to get 82 -> Add them: 28 + 82 = 110 -> Not special yet? Reverse 110 to get 011 -> Add them: 110 + 11 = 121 (A special palindromic number!).

Exam Tip: Avoiding Common Turn Mistakes

Many students get confused between clockwise (turning to the right like a clock hand) and anti-clockwise (turning to the left) movements. Always trace the rotation with your finger on the paper. Also, look out for shapes that look identical after a $\frac{1}{2}$ turn (like a rectangle or the letter 'H') vs. shapes that look different (like a triangle). Drawing a tiny dot at the top of your test-paper shape can help you track where the 'top' moves after each turn!

Practice Questions with Solutions

• Q: An arrow points upwards. It turns by a 1/4 turn clockwise in each step. What direction will the arrow point on its 5th step (excluding the starting position)?
  A: Step 1: Analyze the turns starting from UP.
  Step 2: 1st turn (1/4 clockwise) = Points RIGHT.
  Step 3: 2nd turn (1/4 clockwise) = Points DOWN.
  Step 4: 3rd turn (1/4 clockwise) = Points LEFT.
  Step 5: 4th turn (1/4 clockwise) = Points UP.
  Step 6: 5th turn (1/4 clockwise) = Points RIGHT.
  Final answer: The arrow will point to the RIGHT on the 5th step.

• Q: Fill in the missing numbers for this Magic Hexagon link: One circle has the number 12, and the connected square box has the number 84. What is the number in the other connected circle?
  A: Step 1: Recall the rule for Magic Hexagons: Circle 1 × Circle 2 = Square Box.
  Step 2: We are given Circle 1 = 12, and Square Box = 84. Let Circle 2 be 'x'.
  Step 3: Set up the equation: 12 × x = 84.
  Step 4: Solve for x: x = 84 ÷ 12 = 7.
  Final answer: The number in the other circle is 7.

• Q: Turn the number 48 into a special palindrome number using the reverse-and-add method.
  A: Step 1: Start with the number 48.
  Step 2: Reverse the digits to get 84.
  Step 3: Add the two numbers: 48 + 84 = 132 (Not a palindrome yet).
  Step 4: Take 132 and reverse its digits to get 231.
  Step 5: Add these two numbers: 132 + 231 = 363.
  Step 6: Check if 363 reads the same backward and forward. Yes, it does!
  Final answer: The special palindrome number is 363.

• Q: Find the secret number using these clues: It is larger than half of 100. It is more than 7 tens and less than 8 tens. The tens digit is three more than the ones digit. Together, the digits add up to 11.
  A: Step 1: 'Larger than half of 100' means the number is greater than 50.
  Step 2: 'More than 7 tens and less than 8 tens' means the number is in the 70s (between 70 and 80). So, the tens digit is 7.
  Step 3: 'The tens digit is three more than the ones digit'. Let the tens digit be T = 7. Let the ones digit be O. So, 7 = O + 3, which means O = 7 - 3 = 4.
  Step 4: Check the last clue: 'Together the digits add up to 11'. 7 + 4 = 11. This matches perfectly!
  Final answer: The secret number is 74.

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