Use patterns in data to make a prediction. - ISEE Lower Level Quantitative Reasoning

SECTION 1

Why Do We Look for Patterns?

People have been looking for patterns for thousands of years. A pattern is something that repeats or follows a rule. When you notice a pattern, you can guess what will happen next!

Think about the weather. If it has been sunny every Monday for three weeks, you might predict next Monday will be sunny too. That is using a pattern to make a prediction — a smart guess about the future.

3000 BC • Farmers Watch the Sky

Ancient farmers noticed patterns in seasons. They used these patterns to predict when to plant crops.

500 BC • Greek Number Patterns

Greek mathematicians studied patterns in numbers. They found rules that helped them predict what number comes next.

1600s • Charts and Tables

Scientists began organizing data into tables and charts. This made patterns much easier to spot.

Today • Data Is Everywhere

We use patterns in data every day — from weather forecasts to sports stats. The ISEE tests your ability to find these patterns!

On the ISEE, you will see tables, lists, or charts with numbers. Your job is to find the pattern and use it to predict a missing or future value. Let's learn how!

SECTION 2

Core Ideas About Patterns

Before we dive in, let's learn the key ideas you need. These are the building blocks for solving pattern problems on the ISEE.

What Is a Pattern?

A pattern is a rule that tells you how numbers or data change. For example: 2, 4, 6, 8 follows the rule "add 2 each time."

What Is a Prediction?

A prediction is a smart guess about what comes next. If you know the rule, you can predict the next number or value.

Find the Rule First

Always look at the difference between numbers (or how they change) before you try to answer. The rule is your secret weapon!

Check Your Work

After you find a rule, test it on all the numbers you already have. If it works for every number, you found the right pattern!

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KEY TAKEAWAY

Think of a pattern like a recipe. Once you know the recipe (the rule), you can keep making the same thing over and over. If a cookie recipe says "add 3 chocolate chips to each new cookie," you know exactly how many chips the next cookie needs!

SECTION 3

See the Pattern!

Let's look at a picture that shows how a pattern works. Imagine a student named Mia who reads books each week. Look at the bar chart below to see how many books she reads.

Each week, Mia reads 2 more books than the week before. The pattern is +2 each time. The dashed green bar shows our prediction for Week 5: 10 books!

Do you see how the bars get taller by the same amount each time? That's the pattern! Each week goes up by 2. So from 8 in Week 4, we add 2 to predict 10 for Week 5. That's how predictions work!

SECTION 4

How to Find the Rule

To make a prediction, you need to find the rule. Here are the most common types of rules you will see on the ISEE.

ADD THE SAME NUMBER

Next Number = Current Number + Same Amount

Example: 5, 10, 15, 20, ___. The rule is +5 each time. The next number is 20 + 5 = 25.

SUBTRACT THE SAME NUMBER

Next Number = Current Number − Same Amount

Example: 30, 25, 20, 15, ___. The rule is −5 each time. The next number is 15 − 5 = 10.

MULTIPLY BY THE SAME NUMBER

Next Number = Current Number × Same Amount

Example: 3, 6, 12, 24, ___. The rule is ×2 each time. The next number is 24 × 2 = 48.

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ISEE Test Tip

When you see a list of numbers, always check the difference between each pair of numbers first. If the differences are all the same, you found an adding or subtracting pattern. If not, try multiplying or dividing!

Sometimes a problem gives you a table instead of a list. Don't worry — the steps are the same. Look at how the numbers change from row to row. Find the rule, then use it to fill in the missing number.

SECTION 5

Different Kinds of Data Patterns

On the ISEE, data can show up in different ways. Let's look at the main types of patterns you might see.

This diagram shows the three main pattern types: growing (adding), shrinking (subtracting), and multiplying. The dashed lines show predictions based on each rule.

On the ISEE, adding and subtracting patterns are the most common. But keep your eyes open for multiplying patterns too. If the numbers are getting bigger really fast, that's a clue it might be a multiply pattern!

Pattern Type	What to Look For	Example
Add	Same difference between each number	3, 7, 11, 15 → add 4
Subtract	Numbers get smaller by the same amount	50, 45, 40, 35 → subtract 5
Multiply	Numbers grow very quickly	1, 3, 9, 27 → multiply by 3
Two-step	The rule has two operations	1, 3, 7, 13 → add 2, then 4, then 6

Common pattern types on the ISEE

SECTION 6

Let's Solve One Together!

Here is a problem like you might see on the ISEE. Let's work through it step by step.

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Sample Problem

The table shows the number of stickers Emma collects each day. If the pattern continues, how many stickers will Emma have on Day 5? Day 1: 4 stickers Day 2: 7 stickers Day 3: 10 stickers Day 4: 13 stickers Day 5: ?

Step-by-Step Solution

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Step 1 — Read the Data

Write down the numbers you see: 4, 7, 10, 13. These are the stickers Emma collects on Days 1 through 4.
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Step 2 — Find the Change Between Numbers

Subtract each number from the one after it. Day 2 − Day 1 = 7 − 4 = 3. Day 3 − Day 2 = 10 − 7 = 3. Day 4 − Day 3 = 13 − 10 = 3. The change is always 3!

Rule: add 3 each day
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Step 3 — Apply the Rule

Day 5 = Day 4 + 3 = 13 + 3 = 16.

Emma will have 16 stickers on Day 5.
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Step 4 — Check Your Work

Let's verify: 4, 7, 10, 13, 16. Each goes up by 3. The rule works for every number. We are confident our answer is correct!

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REMEMBER THIS STRATEGY

Always check by going back to the start. Imagine you are double-checking a recipe. If you added the right amount every time and the cookie tastes right, you know you followed the recipe correctly!

SECTION 7

ISEE Tips and Common Traps

Knowing the content is great, but the ISEE also tests how carefully you read. Let's look at smart strategies and common mistakes.

Smart Strategy ✅	Common Trap ❌
Check the difference between every pair of numbers.	Only looking at the first two numbers and guessing.
Try adding, subtracting, and multiplying to find the rule.	Assuming the pattern is always adding.
Read the question carefully — does it ask for the next number or a later number?	Finding the next number when the question asks for a number further ahead.
Eliminate wrong answer choices by testing them.	Picking the first answer that looks close without checking.

Strategies vs. Traps

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ISEE SECRET WEAPON

Use process of elimination! If you are not sure about the rule, try plugging each answer choice back into the pattern. Cross out any that don't fit. Since there is no penalty for wrong answers on the ISEE, always guess if you need to!

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No Penalty for Guessing!

On the ISEE, you do NOT lose points for a wrong answer. So never leave a question blank! Eliminate the choices you know are wrong, then pick from what's left.

SECTION 8

Patterns Lead to Bigger Ideas

The pattern skills you are learning now will help you with bigger math ideas later on. Let's see how this topic connects to things you'll learn in the future.

What You Learn Now	What It Leads To Later
Adding the same number each time (e.g., +3)	In middle school, this is called a "linear pattern" or "arithmetic sequence."
Multiplying by the same number (e.g., ×2)	Later, this becomes "exponential growth" — like how bacteria multiply!
Reading tables and making predictions	This is the start of "data analysis" and graphing lines on a coordinate plane.
Finding a rule for a pattern	In algebra, you'll write rules as equations, like y = 3x + 1.

How today's skills connect to future math

You are building a strong foundation right now. Every time you find a pattern, you are training your brain to think like a mathematician. That's pretty awesome!

SECTION 9

Practice Problems

Time to put your skills to the test! Try each problem on your own before reading the answer. Remember: find the rule, then make your prediction. You've got this!

Question 1: CONCEPTUAL

Look at this pattern: 5, 10, 15, 20, ___. What is the next number? (A) 22 (B) 23 (C) 25 (D) 30

Show answer

The correct answer is (C) 25. The rule is add 5 each time: 5 + 5 = 10, 10 + 5 = 15, 15 + 5 = 20, and 20 + 5 = 25. Choice (A) 22 is wrong because 22 − 20 = 2, not 5. Choice (B) 23 is wrong because 23 − 20 = 3, not 5. Choice (D) 30 is wrong because that would mean adding 10, not 5.

Question 2: BASIC CALCULATION

The table below shows how many laps Jake swims each day. Day 1: 3 laps Day 2: 6 laps Day 3: 9 laps Day 4: 12 laps If the pattern continues, how many laps will Jake swim on Day 5? (A) 13 (B) 14 (C) 15 (D) 18

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The correct answer is (C) 15. The pattern adds 3 each day: 3, 6, 9, 12. So Day 5 = 12 + 3 = 15. Choice (A) 13 is wrong because 13 − 12 = 1, not 3. Choice (B) 14 is wrong because 14 − 12 = 2, not 3. Choice (D) 18 is wrong because 18 − 12 = 6, which would mean the rule changed.

Question 3: INTERMEDIATE

Look at this number pattern: 48, 42, 36, 30, ___. What number comes next? (A) 20 (B) 24 (C) 26 (D) 28

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The correct answer is (B) 24. This is a shrinking pattern. Each number goes down by 6: 48 − 6 = 42, 42 − 6 = 36, 36 − 6 = 30, and 30 − 6 = 24. Choice (A) 20 is wrong because 30 − 20 = 10, not 6. Choice (C) 26 is wrong because 30 − 26 = 4, not 6. Choice (D) 28 is wrong because 30 − 28 = 2, not 6.

Question 4: APPLIED

A plant grows to the heights shown below. Week 1: 2 inches Week 2: 4 inches Week 3: 8 inches Week 4: 16 inches If the pattern continues, how tall will the plant be in Week 5? (A) 18 (B) 20 (C) 24 (D) 32

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The correct answer is (D) 32. This is a multiply pattern. Each week the height doubles (multiplied by 2): 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16, and 16 × 2 = 32. Notice that subtracting gives different differences (2, 4, 8), so it is not an adding pattern. Choice (A) 18 would mean adding only 2. Choice (B) 20 would mean adding 4. Choice (C) 24 would mean adding 8. Only 32 follows the ×2 rule.

Question 5: CRITICAL THINKING

A school tracks the number of library books checked out each month. September: 40 books October: 55 books November: 70 books December: 85 books If the pattern continues, how many books will be checked out in February? (A) 100 (B) 110 (C) 115 (D) 130

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The correct answer is (C) 115. The rule is add 15 each month: 40 + 15 = 55, 55 + 15 = 70, 70 + 15 = 85. But the question asks for February, not January! January = 85 + 15 = 100, and February = 100 + 15 = 115. You need to apply the rule twice. Choice (A) 100 is wrong because that is the prediction for January, not February. Choice (B) 110 is wrong — it does not follow the +15 rule. Choice (D) 130 is wrong because that would be March (115 + 15 = 130). Reading carefully was the key here!

SUMMARY

Lesson Summary

Summary

A pattern is a rule that tells you how numbers change. To make a prediction, first read all the data, then find the change between each pair of numbers, and finally apply the rule to predict the next value. The three main pattern types are adding, subtracting, and multiplying.

Always check your work by making sure the rule works for every number in the data. Read the question carefully to see which value the question is really asking for. Use process of elimination to cross out wrong answer choices, and remember — there is no penalty for guessing on the ISEE, so always answer every question!