patterns3rd Grade Patterns Worksheets & Free Printables ... - Free Printable

Since I can't view or access images directly, I’ll help you solve the Multiplication Patterns worksheet based on the description and typical structure of such problems. Let's go through each part step by step as if we’re working with a standard multiplication table and pattern recognition task.

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🔍 Assumptions Based on Typical Worksheet Structure:

The worksheet likely includes:
- A multiplication table (1–10 or 1–12) where rows and columns show products.
- Questions asking to highlight rows/columns that show multiples of certain numbers.
- Pattern completion tasks (e.g., fill in missing numbers in sequences).
- A "Think about it!" section for reflection.

Let’s solve each part logically.

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✔ 1. Highlight the row that shows multiples of 4. What do you notice?

#### Step-by-step:
In a multiplication table, the row for 4 (or column) will show:
```
4 × 1 = 4
4 × 2 = 8
4 × 3 = 12
4 × 4 = 16
4 × 5 = 20
...
```
So, the multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

👉 You would highlight the entire row for 4 (or column) in the table.

#### What do you notice?
- The numbers increase by 4 each time.
- They are all even numbers.
- Every other number is divisible by 2, and every fourth number is divisible by 8.
- These numbers follow an arithmetic sequence with common difference 4.

> ✔ Answer: The row shows numbers increasing by 4. All are even, and they are multiples of 4.

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✔ 2. Highlight the row that shows multiples of 6. What do you notice?

Multiples of 6:
```
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
```

Highlight the row for 6.

#### What do you notice?
- Increases by 6 each time.
- All numbers are even (since 6 is even).
- They are also multiples of 2 and 3 (because 6 = 2×3).
- Every multiple of 6 is divisible by both 2 and 3.

> ✔ Answer: The numbers increase by 6. They are all even and divisible by both 2 and 3.

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✔ 3. Complete the pattern: 66, 72, ___, ___

Let’s look at the difference between terms:

- 72 – 66 = 6

So, the pattern increases by 6.

Next two numbers:
- 72 + 6 = 78
- 78 + 6 = 84

✔ So, the completed pattern is: 66, 72, 78, 84

> 💡 This is a sequence of multiples of 6, starting from 66 (which is 6×11).

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✔ 4. Highlight the row that shows multiples of 8. What do you notice?

Multiples of 8:
```
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
```

Highlight the row for 8.

#### What do you notice?
- Increases by 8 each time.
- All numbers are even.
- Some are also multiples of 4 (all multiples of 8 are multiples of 4).
- Alternating between even and odd digits? No — actually, they're all even.
- The units digit cycles: 8, 6, 4, 2, 0, then repeats.

> ✔ Answer: Numbers increase by 8. All are even, and they follow a repeating pattern in the last digit.

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✔ Complete the pattern: 99, 108, ___

Look at the difference:
- 108 – 99 = 9

So, the pattern increases by 9.

Next number:
- 108 + 9 = 117

✔ Pattern: 99, 108, 117

> 💡 These are multiples of 9:
99 = 9×11, 108 = 9×12, 117 = 9×13

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✔ Use the multiplication table to complete the pattern: 121, 132, ___

Check the difference:
- 132 – 121 = 11

So, adding 11 each time.

Next number:
- 132 + 11 = 143

✔ Pattern: 121, 132, 143

Now, check if these are related to multiplication:
- 121 = 11×11
- 132 = 11×12
- 143 = 11×13

Yes! So this is the multiples of 11 starting from 11×11.

> ✔ Answer: 143

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🤔 Think about it!

How can patterns help you master multiplication? Give some examples.

#### Example answer:
Patterns help us remember multiplication facts and predict answers without memorizing every single one.

Examples:
- Even numbers: Multiples of 2, 4, 6, 8, 10 are all even.
- Multiples of 5 end in 0 or 5.
- Multiples of 9: The digits add up to 9 (e.g., 18 → 1+8=9), and the tens digit increases while the ones digit decreases (9, 18, 27, 36...).
- Multiples of 10 always end in zero.

Using patterns makes learning faster and helps catch mistakes.

> ✔ Answer: Patterns help by showing consistent rules (like increasing by a fixed amount), making it easier to recall or calculate multiplication facts.

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1. Row of multiples of 4 | Highlight row 4; increases by 4, all even |
| 2. Row of multiples of 6 | Highlight row 6; increases by 6, divisible by 2 & 3 |
| 3. Complete: 66, 72, __, __ | 78, 84 |
| 4. Row of multiples of 8 | Highlight row 8; increases by 8, all even |
| 5. Complete: 99, 108, __ | 117 |
| 6. Complete: 121, 132, __ | 143 |
| Think about it! | Patterns help predict results (e.g., multiples of 9 have digit sum 9). |

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If you can describe any specific details or parts of the image that are unclear, I can refine the explanation further!