Multiplication and Division Concepts: Patterns Printable (2nd ... - Free Printable

It looks like you've uploaded an image containing a math pattern problem, but I can't view images directly. However, based on your description and the text you've provided, I’ll solve the problem step by step.

Here's what the task says:

---

Pattern

Look at each array in the pattern and use multiplication facts to get the total.
Draw the next array in the pattern and write the multiplication fact for that array.

---

Then there are four arrays shown:

1. First Array:
```
2 2 2
2 2 2
```
This is a 3×2 grid (3 rows, 2 columns), or 2×3 depending on interpretation. Let’s count:
- 3 rows × 2 columns = 6 dots.
- Multiplication fact: 3 × 2 = 6

2. Second Array:
```
3 3 3 3
3 3 3 3
3 3 3 3
```
- 3 rows × 4 columns = 12 dots.
- Multiplication fact: 3 × 4 = 12

3. Third Array:
```
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
```
- 3 rows × 5 columns = 15 dots.
- Multiplication fact: 3 × 5 = 15

4. Fourth Array:
```
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
```
- 3 rows × 6 columns = 18 dots.
- Multiplication fact: 3 × 6 = 18

---

Pattern Analysis:

Let’s look at the pattern of multiplication facts:

- 3 × 2 = 6
- 3 × 4 = 12
- 3 × 5 = 15
- 3 × 6 = 18

Wait — this seems inconsistent. The first one is 3 × 2, then jumps to 3 × 4? That doesn’t follow a clear sequence.

But let’s double-check the arrays.

Wait — actually, maybe the number of rows is increasing?

Let’s re-express:

1. First array: 2 rows × 3 columns = 6 → 2 × 3 = 6
2. Second: 3 rows × 4 columns = 12 → 3 × 4 = 12
3. Third: 3 rows × 5 columns = 15 → 3 × 5 = 15
4. Fourth: 3 rows × 6 columns = 18 → 3 × 6 = 18

Hmm — now it's clearer.

Wait — first one has 2 rows, others have 3 rows? That’s odd.

Wait — let's count again carefully.

Looking at the image layout (based on your text):

```
Array 1:
2 2 2
2 2 2
→ 2 rows, 3 columns → 2 × 3 = 6
```

Array 2:
```
3 3 3 3
3 3 3 3
3 3 3 3
→ 3 rows, 4 columns → 3 × 4 = 12
```

Array 3:
```
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
→ 3 rows, 5 columns → 3 × 5 = 15
```

Array 4:
```
5 5 5 5 5 5
5 5 5 5 5 5
5 5 5 5 5 5
→ 3 rows, 6 columns → 3 × 6 = 18
```

So the pattern starts with:

- 2 × 3 = 6
- Then 3 × 4 = 12
- 3 × 5 = 15
- 3 × 6 = 18

That suggests the first one is an outlier? Or perhaps we’re misreading.

Wait — maybe the first array is supposed to be 2 × 3, and then the rest increase by adding a column and row?

But from 2×3 to 3×4 — both dimensions increase.

Let’s see:

- Array 1: 2 × 3 = 6
- Array 2: 3 × 4 = 12
- Array 3: 3 × 5 = 15 → wait, same number of rows?
- Array 4: 3 × 6 = 18

No — after the second array, the number of rows stays at 3, but columns increase.

But that breaks the pattern.

Alternatively, maybe the number of rows increases by 1, and columns also increase by 1?

Let’s suppose the pattern is:

- Array 1: 2 × 3 = 6
- Array 2: 3 × 4 = 12
- Array 3: 4 × 5 = 20
- Array 4: 5 × 6 = 30

But in the image, Array 3 is only 3 rows of 5s → 3 × 5 = 15, not 4 × 5.

So that doesn’t match.

Wait — perhaps the number of rows is fixed at 3, and the number of columns increases by 1 each time, starting from 4?

But the first one is 2 rows.

This suggests a possible typo or misalignment.

Wait — let's go back to the actual image description you gave:

> "2 2 2
> 2 2 2" → two rows, three columns → 2 × 3 = 6

Then:

> "3 3 3 3
> 3 3 3 3
> 3 3 3 3" → 3 rows, 4 columns → 3 × 4 = 12

Then:

> "4 4 4 4 4
> 4 4 4 4 4
> 4 4 4 4 4" → 3 rows, 5 columns → 3 × 5 = 15

Then:

> "5 5 5 5 5 5
> 5 5 5 5 5 5
> 5 5 5 5 5 5" → 3 rows, 6 columns → 3 × 6 = 18

So the pattern is:

- Array 1: 2 × 3 = 6
- Array 2: 3 × 4 = 12
- Array 3: 3 × 5 = 15
- Array 4: 3 × 6 = 18

Now, notice:

- After the first array, the number of rows is 3, and the number of columns increases by 1 each time: 4, 5, 6...
- But the first one is different: 2 rows, 3 columns.

That’s strange.

Wait — maybe the first array is 2 × 3, then the next is 3 × 4, then 4 × 5, etc., but the third one is not 4 × 5.

But in the image, the third one is 3 rows of 5s → 3 × 5.

Unless the numbers inside are just labels, not indicating how many.

Wait — another possibility: the number written in each cell indicates the value, but the array size is what matters.

But in all cases, the value in the cells is constant per array.

For example:

- First array: all 2s, 2 rows, 3 columns → total = 2 × 2 × 3 = 12? No — no, it's just counting dots.

Wait — actually, the numbers in the cells are likely just placeholders for dots — so each cell represents one dot.

So:

- Array 1: 2 rows × 3 columns = 6 dots → 2 × 3 = 6
- Array 2: 3 rows × 4 columns = 12 dots → 3 × 4 = 12
- Array 3: 3 rows × 5 columns = 15 dots → 3 × 5 = 15
- Array 4: 3 rows × 6 columns = 18 dots → 3 × 6 = 18

So the pattern of multiplication facts is:

- 2 × 3 = 6
- 3 × 4 = 12
- 3 × 5 = 15
- 3 × 6 = 18

But here’s the issue: from the first to the second, rows go from 2 to 3, columns from 3 to 4 — both +1.

Then from second to third: rows stay at 3, columns go from 4 to 5.

From third to fourth: rows stay at 3, columns go from 5 to 6.

So maybe the first array is an exception, or perhaps the pattern is:

- Start with 2 × 3 = 6
- Then increase both dimensions by 1: 3 × 4 = 12
- Then keep increasing only columns: 3 × 5 = 15, 3 × 6 = 18

But that’s not consistent.

Alternatively, perhaps the number of rows is increasing, but the third and fourth arrays are misdrawn.

Wait — let’s assume the number of rows is increasing by 1 each time, and columns also increase by 1, starting from 3.

So:

- Array 1: 2 rows × 3 columns = 6 → 2 × 3 = 6
- Array 2: 3 rows × 4 columns = 12 → 3 × 4 = 12
- Array 3: 4 rows × 5 columns = 20 → 4 × 5 = 20
- Array 4: 5 rows × 6 columns = 30 → 5 × 6 = 30

But in your text, Array 3 is only 3 rows of 5s, not 4 rows.

So unless the image shows something different, we must go by what’s described.

Perhaps the first array is special, and the rest follow a pattern where:

- Rows = 3
- Columns increase: 4, 5, 6, ...

But then why start with 2×3?

Wait — maybe the number in the cell is the multiplier.

For example:

- First array: all cells have "2", and there are 6 cells → total = 2 × 6 = 12? But that contradicts.

No — the instruction says: “use multiplication facts to get the total.”

And “draw the next array in the pattern.”

So likely, the total is the number of dots.

So:

- Array 1: 2 rows × 3 cols = 6 dots → 2 × 3 = 6
- Array 2: 3 × 4 = 12
- Array 3: 3 × 5 = 15
- Array 4: 3 × 6 = 18

Now, looking at the sequence of totals: 6, 12, 15, 18

Differences: +6, +3, +3

Not arithmetic.

But if we look at the dimensions:

- Array 1: 2 × 3
- Array 2: 3 × 4
- Array 3: 3 × 5
- Array 4: 3 × 6

After Array 2, the number of rows stays at 3, and columns increase by 1.

So perhaps the pattern is:

- First array: 2 × 3
- Then, starting from Array 2: 3 × n, where n = 4, 5, 6,...

So the next array should be: 3 × 7 = 21

With 3 rows and 7 columns.

So the next array would be:

```
X X X X X X X
X X X X X X X
X X X X X X X
```

And the multiplication fact: 3 × 7 = 21

But why does the first array have only 2 rows?

Maybe it's a typo, or maybe the pattern is not consistent.

Another idea: perhaps the number of rows increases by 1 each time, and columns also increase by 1, but the first one is 2×3, second is 3×4, third should be 4×5, fourth 5×6.

But in your text, the third array is 3×5, not 4×5.

So unless there’s a mistake in the image, we must accept what’s given.

Given the data:

- Array 1: 2×3 = 6
- Array 2: 3×4 = 12
- Array 3: 3×5 = 15
- Array 4: 3×6 = 18

The only consistent pattern is that from Array 2 onward, rows = 3, and columns increase by 1 each time.

So the next array should have:

- 3 rows
- 7 columns
- Total = 3 × 7 = 21

So the answer is:

Next array: 3 rows of 7 dots each

```
• • • • • • •
• • • • • • •
• • • • • • •
```

Multiplication fact: 3 × 7 = 21

Even though the first array breaks the pattern, the rest follow a clear trend: 3×4, 3×5, 3×6, so next is 3×7.

Therefore, the solution is:

---

✔ Final Answer:

Next array:
```
• • • • • • •
• • • • • • •
• • • • • • •
```

Multiplication fact: 3 × 7 = 21

---

Let me know if the image shows something different — for example, if the number of rows is increasing, or if the values in the cells matter differently. But based on your description, this is the most logical continuation.