A girl looks at a colorful, friendly mystery machine

Crack the Pattern Code!

Zara found a mystery machine. Every day it follows a secret rule and prints new numbers. Can you crack the code?

4th Grade Math

Step 1: Follow the Rule

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The machine starts with 1. Its rule is Add 3. What number does the machine print next?

1 + 3 = 4. The rule Add 3 means each new term is 3 more than the term before it.

Step 2: Keep the Pattern Going

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1

2

3

4

5

6

7

8

9

10

11

12

So far the pattern is 1, 4, 7. Start at 7 and hop 3 more spaces. What is the next term?

7 + 3 = 10. Each hop lands 3 spaces further along the line: 1, 4, 7, 10.

How to Generate a Pattern

To generate a pattern, you apply the rule again and again.

Pattern Power

          Step 1: Write the starting number.

          Step 2: Apply the rule to get the next term.

          Step 3: Repeat with each new term!

Step 3: Analyze the Pattern

1

4

7

10

13

Zara's full pattern is 1, 4, 7, 10, 13. Now analyze the terms. What do you notice?

1 is odd, 4 is even, 7 is odd, 10 is even, 13 is odd. Adding an odd number like 3 always flips odd to even and back again!

Watch Out!

A Sneaky Mistake

          The rule Add 3 does NOT mean every term is a
          multiple of 3.

          Zara's terms are 1, 4, 7, 10, 13.

          None of them are multiples of 3!

          The starting number changes everything.

Always check the start and the rule before you decide what a pattern will do.

Your Turn!

Rule: Add 6 | Start: 2

Which list shows the first four terms of this pattern?

Start at 2. Then 2 + 6 = 8, 8 + 6 = 14, and 14 + 6 = 20. The pattern is 2, 8, 14, 20.

Word Problem

Leo does 5 push-ups on day 1. Each day, he does 4 more than the day before. How many push-ups does Leo do on day 4?

Day 1: 5. Day 2: 5 + 4 = 9. Day 3: 9 + 4 = 13. Day 4: 13 + 4 = 17.

What Goes in the Blank?

40, 35, 30, ?, 20

The rule is Subtract 5. Find the missing term.

30 - 5 = 25. Check the next hop: 25 - 5 = 20, so the pattern still works.

Find the Rule

4, 8, 16, 32, 64

Determine the rule. It must work for every term, not just the first two!

Add 4 works for 4 to 8, but 8 + 4 = 12, not 16. Multiply by 2 works for every term: 4, 8, 16, 32, 64.

Analyze It!

7, 17, 27, 37, 47

Rule: Add 10. Start: 7. What hidden feature does this pattern show?

Adding 10 only changes the tens digit. The ones digit stays 7 forever: 7, 17, 27, 37, 47.

Challenge!

Rule: Add 3 | Start: 2

Zara wonders: will the number 30 ever appear in this pattern? Think before you list every term!

The terms are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32. The pattern hops from 29 straight to 32 and skips 30!

Where do you follow rules that make patterns in real life? Think about saving money each week or a plant growing taller.

Great Work!

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generate pattern rule multiple analyze determine