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Play with Patterns - Number Patterns

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A number pattern is a sequence of numbers that follow a specific rule to find the next numbers. Imagine a row of blocks where each block has a number written on it, like 2,4,6,82, 4, 6, 8; these blocks follow a predictable path.

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The 'Rule' of a pattern is the mathematical operation (addition or subtraction) applied to one number to get the next. For example, if we have 10,20,3010, 20, 30, the rule is to 'Add 1010' to the previous number.

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Growing patterns are sequences where the numbers increase. Visually, this looks like a staircase going up, where each step is higher than the last, such as 5,10,15,205, 10, 15, 20.

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Shrinking or decreasing patterns are sequences where the numbers get smaller. Imagine a countdown for a rocket launch or walking down a ladder, such as 50,40,30,2050, 40, 30, 20.

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Skip counting is a common way to form patterns. When you skip count by 22, you jump over one number to land on the next, creating a sequence like 2,4,6,8,102, 4, 6, 8, 10 on a number line.

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Even and Odd number patterns follow specific sequences. Even numbers always end in 0,2,4,6,80, 2, 4, 6, 8, while odd numbers always end in 1,3,5,7,91, 3, 5, 7, 9. On a 10×1010 \times 10 number grid, these often form vertical stripes of color.

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Number patterns can also be found in Grids or Tables. In a 10×1010 \times 10 square, moving down a column usually increases the number by 1010 (e.g., 4,14,24,344, 14, 24, 34), while moving across a row increases it by 11.

📐Formulae

Rule for Increasing Pattern:Next Number=Current Number+Gap\text{Rule for Increasing Pattern}: \text{Next Number} = \text{Current Number} + \text{Gap}

Rule for Decreasing Pattern:Next Number=Current Number−Gap\text{Rule for Decreasing Pattern}: \text{Next Number} = \text{Current Number} - \text{Gap}

Even Numbers={2,4,6,8,10,...}\text{Even Numbers} = \{2, 4, 6, 8, 10, ...\}

Odd Numbers={1,3,5,7,9,11,...}\text{Odd Numbers} = \{1, 3, 5, 7, 9, 11, ...\}

💡Examples

Problem 1:

Identify the rule and find the next two numbers in the pattern: 21,25,29,33,…21, 25, 29, 33, \dots

Solution:

Step 1: Find the difference between the first two numbers: 25−21=425 - 21 = 4. \ Step 2: Check if the same difference applies to the next pair: 29−25=429 - 25 = 4. \ Step 3: The rule is 'Add 44'. \ Step 4: Add 44 to the last number: 33+4=3733 + 4 = 37. \ Step 5: Add 44 to that result: 37+4=4137 + 4 = 41. \ The next two numbers are 3737 and 4141.

Explanation:

To solve an increasing pattern, find the 'gap' by subtracting a number from the one following it, then use that gap to continue the sequence.

Problem 2:

Complete the decreasing pattern: 90,80,70,…,…,4090, 80, 70, \dots, \dots, 40

Solution:

Step 1: Observe the change: 9090 becomes 8080, which is a decrease of 1010 (90−10=8090 - 10 = 80). \ Step 2: The rule is 'Subtract 1010'. \ Step 3: Apply the rule to 7070: 70−10=6070 - 10 = 60. \ Step 4: Apply the rule to 6060: 60−10=5060 - 10 = 50. \ Step 5: Verify the last step: 50−10=4050 - 10 = 40. \ The missing numbers are 6060 and 5050.

Explanation:

In a shrinking pattern, the numbers go down by a fixed amount. We subtract the rule value from the previous number to find the next one.