What is a Pattern with Mixed Operations?

S1-SA5-0217

Grade Level:

Class 4

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

Definition

What is it?

A pattern with mixed operations is a sequence of numbers or shapes that follows a rule involving more than one type of mathematical operation (like addition, subtraction, multiplication, or division). You need to figure out the exact rule by looking at how the numbers change from one step to the next.

Simple Example

Quick Example

Imagine your older sibling is saving money. They start with ₹100. Each week, they add ₹50 but also spend ₹20 on a snack. So, the money changes like this: ₹100, then (100 + 50 - 20) = ₹130, then (130 + 50 - 20) = ₹160. This is a pattern using both addition and subtraction.

Worked Example

Step-by-Step

Let's find the next two numbers in this pattern: 5, 12, 10, 17, 15, ___, ___.

Step 1: Look at the first two numbers: 5 and 12. To get from 5 to 12, we add 7 (5 + 7 = 12).
---Step 2: Look at the next two numbers: 12 and 10. To get from 12 to 10, we subtract 2 (12 - 2 = 10).
---Step 3: Look at the next two numbers: 10 and 17. To get from 10 to 17, we add 7 (10 + 7 = 17).
---Step 4: Look at the next two numbers: 17 and 15. To get from 17 to 15, we subtract 2 (17 - 2 = 15).
---Step 5: The pattern rule is clear: Add 7, then Subtract 2, then Add 7, then Subtract 2. So, the next operation should be Add 7.
---Step 6: Apply the rule to 15: 15 + 7 = 22.
---Step 7: The next operation should be Subtract 2. Apply the rule to 22: 22 - 2 = 20.
---Answer: The next two numbers in the pattern are 22 and 20.

Why It Matters

Understanding patterns with mixed operations helps you predict future outcomes, which is useful in many fields. For example, financial analysts use these to predict stock market trends, and data scientists use them to find insights in large datasets. Even game developers use patterns to create challenges and levels in video games!

Common Mistakes

MISTAKE: Only looking for one type of operation (e.g., just addition or just subtraction) when the pattern actually uses multiple operations. | CORRECTION: Always check if the operation changes from one step to the next. Look for alternating operations like add, then subtract, then add, etc.

MISTAKE: Applying the found rule incorrectly to the next number. For example, if the rule is +5, -2, and the last number was 10, incorrectly calculating 10 + 5 = 15 instead of continuing with -2. | CORRECTION: Carefully follow the sequence of operations. If the pattern is +A, -B, +A, -B, make sure to apply the correct operation (+A or -B) for the next step in the sequence.

MISTAKE: Confusing the order of operations if the rule involves multiple operations within a single step (e.g., multiply by 2 then add 3). | CORRECTION: For Class 4, patterns usually involve one operation per step (e.g., first add, then multiply). If there are two operations in one step, always do multiplication/division before addition/subtraction, or follow brackets if they are given.

Practice Questions

Try It Yourself

QUESTION: What are the next two numbers in the pattern: 2, 6, 4, 8, 6, ___, ___? | ANSWER: 10, 8

QUESTION: Find the missing number: 100, 90, 95, 85, 90, ___, 85. | ANSWER: 80

QUESTION: A small shop sells samosas. On Monday, they sold 20. Each day they sell 5 more than the previous day, but also throw away 2 unsold samosas from the previous day's stock. How many samosas did they sell on Thursday? (Assume they start fresh with 20 on Monday, and the pattern applies from Monday to Tuesday, etc.) | ANSWER: 26

MCQ

Quick Quiz

Which rule describes the pattern: 3, 9, 6, 18, 15, ...?

Add 6, then subtract 3

Multiply by 3, then subtract 3

Add 6, then divide by 3

Multiply by 3, then add 6

The Correct Answer Is:

To go from 3 to 9, you multiply by 3. To go from 9 to 6, you subtract 3. This rule (multiply by 3, then subtract 3) continues for the next steps (6 * 3 = 18, 18 - 3 = 15).

Real World Connection

In the Real World

Think about how your mobile data plan works. You might get 1GB of data every day (+1GB), but then you use some of it for watching videos (-0.5GB). This creates a daily pattern of data remaining. Understanding such patterns helps you manage your data usage and avoid extra charges, just like managing a budget for your pocket money involves mixed operations.

Key Vocabulary

Key Terms

PATTERN: A sequence of numbers or shapes following a rule | OPERATION: A mathematical action like addition, subtraction, multiplication, or division | SEQUENCE: An ordered list of numbers or items | RULE: The instruction that tells you how to get from one number to the next in a pattern

What's Next

What to Learn Next

Great job learning about patterns with mixed operations! Next, you can explore patterns that involve fractions or decimals, or even look at patterns that grow very quickly, like exponential patterns. This will build on your skill of finding rules and predicting outcomes.