Grade 3 Number Pattern interactive worksheet - Free Printable

Problem Analysis

The task involves identifying patterns in number sequences and using those patterns to find missing numbers. Let's solve each part step by step.

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Example 1

#### Sequence:
32, 42, 52, 62, ?, ?, 92, ?

#### Rule Identification:
- The sequence increases by 10 each time.
- This can be written as: \( n_{i+1} = n_i + 10 \).

#### Finding Missing Numbers:
1. The next number after 62 is:
\( 62 + 10 = 72 \).
2. The next number after 72 is:
\( 72 + 10 = 82 \).
3. The next number after 92 is:
\( 92 + 10 = 102 \).

#### Final Sequence:
32, 42, 52, 62, 72, 82, 92, 102

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Example 2

#### Sequence:
127, 125, 123, 121, ?, 117, ?, ?

#### Rule Identification:
- The sequence decreases by 2 each time.
- This can be written as: \( n_{i+1} = n_i - 2 \).

#### Finding Missing Numbers:
1. The next number after 121 is:
\( 121 - 2 = 119 \).
2. The next number after 117 is:
\( 117 - 2 = 115 \).
3. The next number after 115 is:
\( 115 - 2 = 113 \).

#### Final Sequence:
127, 125, 123, 121, 119, 117, 115, 113

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Problem 1

#### Sequence:
68, 64, 60, 56, ?, 48, ?

#### Rule Identification:
- The sequence decreases by 4 each time.
- This can be written as: \( n_{i+1} = n_i - 4 \).

#### Finding Missing Numbers:
1. The next number after 56 is:
\( 56 - 4 = 52 \).
2. The next number after 48 is:
\( 48 - 4 = 44 \).

#### Final Sequence:
68, 64, 60, 56, 52, 48, 44

#### Rule:
Subtract 4.

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Problem 2

#### Sequence:
246, 241, 236, 231, ?, ?, 216, ?

#### Rule Identification:
- The sequence decreases by 5 each time.
- This can be written as: \( n_{i+1} = n_i - 5 \).

#### Finding Missing Numbers:
1. The next number after 231 is:
\( 231 - 5 = 226 \).
2. The next number after 226 is:
\( 226 - 5 = 221 \).
3. The next number after 216 is:
\( 216 - 5 = 211 \).

#### Final Sequence:
246, 241, 236, 231, 226, 221, 216, 211

#### Rule:
Subtract 5.

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Problem 3

#### Sequence:
376, 387, 398, 409, ?, 431, ?

#### Rule Identification:
- The sequence increases by 11 each time.
- This can be written as: \( n_{i+1} = n_i + 11 \).

#### Finding Missing Numbers:
1. The next number after 409 is:
\( 409 + 11 = 420 \).
2. The next number after 431 is:
\( 431 + 11 = 442 \).

#### Final Sequence:
376, 387, 398, 409, 420, 431, 442

#### Rule:
Add 11.

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Final Answers

1. Sequence: 68, 64, 60, 56, 52, 48, 44
Rule: Subtract 4.

2. Sequence: 246, 241, 236, 231, 226, 221, 216, 211
Rule: Subtract 5.

3. Sequence: 376, 387, 398, 409, 420, 431, 442
Rule: Add 11.

Boxed Final Answer

\[
\boxed{
\begin{aligned}
1. & \text{ Sequence: } 68, 64, 60, 56, 52, 48, 44; \text{ Rule: Subtract 4.} \\
2. & \text{ Sequence: } 246, 241, 236, 231, 226, 221, 216, 211; \text{ Rule: Subtract 5.} \\
3. & \text{ Sequence: } 376, 387, 398, 409, 420, 431, 442; \text{ Rule: Add 11.}
\end{aligned}
}
\]