Worksheet for learning multiplication using arrays.

Let’s solve this step by step.

We are given a table with 4 columns:
Array, Factors, Repeated Addition, and Product

The first row is already filled in as an example:
- Array: 2 rows of 5 dots → total 10 dots
- Factors: 5 × 2 (or 2 × 5 — order doesn’t matter for multiplication)
- Repeated Addition: 2 + 2 + 2 + 2 + 2 = 10 (adding the number in each column, 5 times) OR you could do 5 + 5 = 10 (adding rows). But since they wrote “2+2+2+2+2”, they’re adding the *columns* — so we’ll follow that pattern.
- Product: 10

Now let’s go row by row.

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Row 2: Array shows 3 rows of 6 dots

→ So, factors: 6 × 3 (or 3 × 6 — but to match the repeated addition style, if we add columns, it would be 3 added 6 times? Wait — let’s check the example again.)

In the example:
Array was 2 rows, 5 columns → they wrote factors as “5x2” and repeated addition as “2+2+2+2+2” → that means they took the *number per column* (which is 2) and added it as many times as there are columns (5 times).

So general rule from example:
- Factors: [number of columns] × [number of rows]
- Repeated Addition: [number of rows] added [number of columns] times
- Product: total dots

Wait — actually, in the example:
They have 2 rows, 5 columns → total 10 dots.
They wrote factors as “5x2” → which is columns × rows.
Repeated addition: “2+2+2+2+2” → that’s adding the row count (2), five times (once per column).
Product: 10.

So yes — pattern is:
- Factors: columns × rows
- Repeated Addition: rows added columns times
- Product: columns × rows

But note: sometimes people write rows × columns. The key is consistency with the repeated addition shown.

Since the example used “5x2” and “2+2+2+2+2”, we will follow:

For any array:
- Count how many dots in one column → that’s the number of rows.
- Count how many columns → that’s the number of groups in repeated addition.
- Factors: (columns) × (rows)
- Repeated Addition: (rows) + (rows) + ... (columns times)
- Product: same as multiplication result.

Alternatively, you can think:
If you have R rows and C columns, then:
- You can say C × R or R × C — both give same product.
- But for repeated addition matching the example: if they added the row-value multiple times equal to column-count, then we do that.

Actually, looking at the example again:
Array has 2 rows → so each column has 2 dots.
There are 5 columns → so they added 2, five times → 2+2+2+2+2.

So for Row 2:
Array has 3 rows → each column has 3 dots.
How many columns? Let’s count: 6 columns.
So:
- Factors: 6 × 3
- Repeated Addition: 3 + 3 + 3 + 3 + 3 + 3 (six 3s)
- Product: 6 × 3 = 18

Check: 3×6=18, and 3+3+3+3+3+3=18 → correct.

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Row 3: Array shows 4 rows of 3 dots

→ Rows = 4, Columns = 3
→ Factors: 3 × 4
→ Repeated Addition: 4 + 4 + 4 (three 4s)
→ Product: 3 × 4 = 12

Check: 4+4+4=12 → correct.

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Row 4: Array shows 2 rows of 4 dots

→ Rows = 2, Columns = 4
→ Factors: 4 × 2
→ Repeated Addition: 2 + 2 + 2 + 2 (four 2s)
→ Product: 4 × 2 = 8

Check: 2+2+2+2=8 → correct.

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Row 5: Array shows 3 rows of 3 dots

→ Rows = 3, Columns = 3
→ Factors: 3 × 3
→ Repeated Addition: 3 + 3 + 3 (three 3s)
→ Product: 9

Check: 3+3+3=9 → correct.

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Row 6: Array shows 2 rows of 7 dots

→ Rows = 2, Columns = 7
→ Factors: 7 × 2
→ Repeated Addition: 2 + 2 + 2 + 2 + 2 + 2 + 2 (seven 2s)
→ Product: 14

Check: 2×7=14, and seven 2s sum to 14 → correct.

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Row 7: Array shows 5 rows of 4 dots

→ Rows = 5, Columns = 4
→ Factors: 4 × 5
→ Repeated Addition: 5 + 5 + 5 + 5 (four 5s)
→ Product: 20

Check: 5×4=20, and 5+5+5+5=20 → correct.

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Now let’s fill the table:

| Array | Factors | Repeated Addition | Product |
|--------------|---------|--------------------------|---------|
| (given) | 5x2 | 2+2+2+2+2 | 10 |
| 3 rows x 6 cols | 6x3 | 3+3+3+3+3+3 | 18 |
| 4 rows x 3 cols | 3x4 | 4+4+4 | 12 |
| 2 rows x 4 cols | 4x2 | 2+2+2+2 | 8 |
| 3 rows x 3 cols | 3x3 | 3+3+3 | 9 |
| 2 rows x 7 cols | 7x2 | 2+2+2+2+2+2+2 | 14 |
| 5 rows x 4 cols | 4x5 | 5+5+5+5 | 20 |

All calculations verified.

Final Answer:

Row 2: Factors = 6x3, Repeated Addition = 3+3+3+3+3+3, Product = 18
Row 3: Factors = 3x4, Repeated Addition = 4+4+4, Product = 12
Row 4: Factors = 4x2, Repeated Addition = 2+2+2+2, Product = 8
Row 5: Factors = 3x3, Repeated Addition = 3+3+3, Product = 9
Row 6: Factors = 7x2, Repeated Addition = 2+2+2+2+2+2+2, Product = 14
Row 7: Factors = 4x5, Repeated Addition = 5+5+5+5, Product = 20