What is a Shrinking Pattern?

S1-SA5-0126

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

A shrinking pattern is a sequence of numbers, shapes, or objects where each new item is smaller than the one before it, or the quantity decreases by a fixed amount or a rule. It shows a decrease or reduction as you move forward in the pattern.

Simple Example

Quick Example

Imagine you have 10 ladoos on a plate. If you eat 2 ladoos every hour, the number of ladoos on the plate will shrink. It would go from 10, then 8, then 6, and so on. This is a shrinking pattern!

Worked Example

Step-by-Step

Let's find the next two numbers in the shrinking pattern: 25, 20, 15, __, __

1. Look at the first two numbers: 25 and 20.
2. Find the difference: 25 - 20 = 5.
3. Check the next pair: 20 and 15. The difference is 20 - 15 = 5.
4. This means the pattern is shrinking by 5 each time.
5. To find the next number, subtract 5 from 15: 15 - 5 = 10.
6. To find the number after that, subtract 5 from 10: 10 - 5 = 5.

Answer: The next two numbers are 10 and 5.

Why It Matters

Understanding shrinking patterns helps you predict outcomes and manage resources. In finance, it helps track money decreasing from a bank account due to expenses. Scientists use it to study how things decay or reduce over time, like the amount of medicine in a body.

Common Mistakes

MISTAKE: Confusing shrinking patterns with growing patterns. | CORRECTION: Remember, in a shrinking pattern, numbers get smaller. In a growing pattern, they get larger.

MISTAKE: Not finding the correct rule (the amount by which the pattern shrinks). | CORRECTION: Always check the difference between at least two pairs of consecutive numbers to confirm the rule.

MISTAKE: Adding instead of subtracting when finding the next terms. | CORRECTION: For shrinking patterns, you always subtract the rule from the previous number to find the next number.

Practice Questions

Try It Yourself

QUESTION: What is the next number in this pattern: 30, 27, 24, __? | ANSWER: 21

QUESTION: Find the missing number: 50, 45, __, 35, 30. | ANSWER: 40

QUESTION: A mobile phone battery starts at 100%. If it loses 10% charge every hour, what will be its charge after 3 hours? | ANSWER: 70%

MCQ

Quick Quiz

Which of these is a shrinking pattern?

5, 10, 15, 20

100, 90, 80, 70

2, 4, 8, 16

3, 3, 3, 3

The Correct Answer Is:

Option B (100, 90, 80, 70) shows numbers decreasing by 10 each time, making it a shrinking pattern. The other options show growing patterns or constant patterns.

Real World Connection

In the Real World

When you buy a mobile data pack, say 1 GB, and use a fixed amount of data (like 100 MB) every day, the remaining data balance forms a shrinking pattern. You can check your balance on apps like Jio or Airtel to see this decrease.

Key Vocabulary

Key Terms

SEQUENCE: An ordered list of numbers or objects | DECREASE: To become less or smaller | RULE: The instruction that tells you how to get from one term to the next in a pattern | TERM: Each number or item in a pattern

What's Next

What to Learn Next

Great job understanding shrinking patterns! Next, you can explore 'Growing Patterns' to see how sequences can increase. Then, you can learn about 'Mixed Patterns' which combine both growing and shrinking rules!