Pattern class 5 worksheet - Free Printable

Problem Breakdown and Solution

The worksheet contains two main sections:
1. Pattern Completion
2. Number Grid Filling

Let's solve each section step by step.

---

#### Section 1: Pattern Completion

##### Problem 1
The pattern given is:
```
😊 😐 😕 [] []
```
The task is to complete the pattern by dragging from the box below.

Observation:
- The sequence shows a progression of facial expressions:
- 😊 (happy)
- 😐 (neutral)
- 😕 (sad)

Pattern Rule:
The expressions are changing in a specific order, likely cycling through different emotions.

Solution:
The next two expressions should continue the cycle. Based on the provided options:
```
😊 😐 😕 ❤️ 💔
```
The next two expressions are:
```
❤️ 💔
```

So, the completed pattern is:
```
😊 😐 😕 ❤️ 💔
```

##### Problem 2
The pattern given is:
```
❤️ ❤️ ❤️ [] []
```
The task is to complete the pattern by dragging from the box below.

Observation:
- The sequence shows a progression of heart shapes:
- ❤️ (solid heart)
- ❤️ (solid heart)
- ❤️ (solid heart)

Pattern Rule:
The hearts are consistent in shape but may change in orientation or style.

Solution:
The next two shapes should follow the same pattern. Based on the provided options:
```
😊 😐 😕 ❤️ 💔
```
The next two shapes are:
```
😊 😐
```

So, the completed pattern is:
```
❤️ ❤️ ❤️ 😊 😐
```

---

#### Section 2: Number Grid Filling

The task is to fill a 3x3 grid using all the numbers from 46 to 54 such that the total of each line (row, column, and diagonal) is 150.

##### Given Information:
- Numbers to use: 46, 47, 48, 49, 50, 51, 52, 53, 54.
- Total for each row, column, and diagonal: 150.
- Partially filled grid:
```
| | | 49 |
| 46| | |
| | 52| 47 |
```

##### Step-by-Step Solution:

1. Sum of All Numbers:
The sum of numbers from 46 to 54 is:
\[
46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 = 450
\]
Since the grid is 3x3, the sum of each row, column, and diagonal must be:
\[
\frac{450}{3} = 150
\]

2. Fill the First Row:
The first row already has `49` in the last column. Let the first row be:
\[
[a, b, 49]
\]
The sum of the first row is:
\[
a + b + 49 = 150 \implies a + b = 101
\]

3. Fill the Second Row:
The second row already has `46` in the first column. Let the second row be:
\[
[46, c, d]
\]
The sum of the second row is:
\[
46 + c + d = 150 \implies c + d = 104
\]

4. Fill the Third Row:
The third row already has `52` in the second column and `47` in the third column. Let the third row be:
\[
[e, 52, 47]
\]
The sum of the third row is:
\[
e + 52 + 47 = 150 \implies e + 99 = 150 \implies e = 51
\]

5. Complete the Grid:
Now we have:
\[
\begin{array}{|c|c|c|}
\hline
a & b & 49 \\
\hline
46 & c & d \\
\hline
51 & 52 & 47 \\
\hline
\end{array}
\]
Using the constraints:
- \(a + b = 101\)
- \(c + d = 104\)
- The sum of each column and diagonal must also be 150.

6. Solve for Remaining Variables:
- From the first column: \(a + 46 + 51 = 150 \implies a + 97 = 150 \implies a = 53\).
- From the second column: \(b + c + 52 = 150 \implies b + c = 98\).
- From the third column: \(49 + d + 47 = 150 \implies d + 96 = 150 \implies d = 54\).
- From \(c + d = 104\) and \(d = 54\): \(c + 54 = 104 \implies c = 50\).
- From \(b + c = 98\) and \(c = 50\): \(b + 50 = 98 \implies b = 48\).

7. Final Grid:
Substituting all values, the completed grid is:
\[
\begin{array}{|c|c|c|}
\hline
53 & 48 & 49 \\
\hline
46 & 50 & 54 \\
\hline
51 & 52 & 47 \\
\hline
\end{array}
\]

---

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
53 & 48 & 49 \\
\hline
46 & 50 & 54 \\
\hline
51 & 52 & 47 \\
\hline
\end{array}
}
\]