Year 4 Number Sequences sheets - Free Printable

Problem Analysis:

The task involves completing a grid of numbers based on some underlying pattern. Let's analyze the given grid step by step to identify the patterns and fill in the missing values.

#### Grid Structure:
The grid is composed of 5 rows and 7 columns. Some cells are filled with numbers, while others are empty. Our goal is to determine the missing values based on the observed patterns.

#### Given Grid:
```
3 13 23 33 43
6 14 22 30 38
87 80 66 59 45
93 85 69 53 45 37
54 55
```

Step-by-Step Solution:

#### Row 1:
The first row is:
```
3 13 23 33 43
```
This sequence increases by 10 each time:
- \( 3 + 10 = 13 \)
- \( 13 + 10 = 23 \)
- \( 23 + 10 = 33 \)
- \( 33 + 10 = 43 \)

#### Row 2:
The second row is:
```
6 14 22 30 38
```
This sequence also increases by 8 each time:
- \( 6 + 8 = 14 \)
- \( 14 + 8 = 22 \)
- \( 22 + 8 = 30 \)
- \( 30 + 8 = 38 \)

To find the missing value at the beginning of Row 2, we need to determine the starting point. Since the pattern is consistent, we can infer that the missing value is:
- \( 6 - 8 = -2 \)

So, Row 2 becomes:
```
-2 6 14 22 30 38
```

#### Row 3:
The third row is:
```
87 80 66 59 45
```
Here, the pattern is not immediately obvious. Let's examine the differences between consecutive terms:
- \( 87 - 80 = 7 \)
- \( 80 - 66 = 14 \)
- \( 66 - 59 = 7 \)
- \( 59 - 45 = 14 \)

The differences alternate between 7 and 14. Following this pattern, the next difference should be 7:
- \( 45 - 7 = 38 \)

So, Row 3 becomes:
```
87 80 66 59 45 38
```

#### Row 4:
The fourth row is:
```
93 85 69 53 45 37
```
Let's examine the differences between consecutive terms:
- \( 93 - 85 = 8 \)
- \( 85 - 69 = 16 \)
- \( 69 - 53 = 16 \)
- \( 53 - 45 = 8 \)
- \( 45 - 37 = 8 \)

The pattern here alternates between differences of 8 and 16. Following this pattern, the next difference should be 16:
- \( 37 - 16 = 21 \)

So, Row 4 becomes:
```
93 85 69 53 45 37 21
```

#### Row 5:
The fifth row is:
```
54 55
```
This row has only two values, and no clear pattern is provided from the other rows. However, since the grid appears to follow arithmetic or alternating patterns, we can infer that the missing values might continue a similar trend. Without additional context, we can assume a simple increment or decrement pattern. For now, let's leave it as is unless more information is provided.

Final Completed Grid:

Based on the identified patterns, the completed grid is:
```
3 13 23 33 43
-2 6 14 22 30 38
87 80 66 59 45 38
93 85 69 53 45 37 21
54 55
```

Final Answer:

\[
\boxed{
\begin{array}{ccccccc}
3 & 13 & 23 & 33 & 43 & & \\
-2 & 6 & 14 & 22 & 30 & 38 & \\
87 & 80 & 66 & 59 & 45 & 38 & \\
93 & 85 & 69 & 53 & 45 & 37 & 21 \\
& & 54 & 55 & & &
\end{array}
}
\]