NCERT Class 4 Maths Chapter 10 Play with Patterns | Grade1to6.com - Free Printable

Problem Analysis and Solution

The worksheet provided involves two main sections: Number Towers and a Pattern Completion task. Let's solve each section step by step.

---

#### Section 1: Number Towers

The task is to complete the number towers based on the given hint: "Two numbers from the bottom line make the number on the top, and so on."

##### Example Tower
The first tower is already completed:
```
70
/ \
30 40
/ \ / \
10 20 30
```
Here, the rule is clear:
- The top number is the sum of the two numbers directly below it.
- For example, \(30 + 40 = 70\).

##### Tower 2
```
90
/ \
? ?
/ \ / \
? 20 ?
```
Using the same rule:
1. The top number (90) is the sum of the two numbers below it.
2. Let the two numbers below 90 be \(x\) and \(y\). So, \(x + y = 90\).
3. The number 20 is part of the bottom row. Let the other two numbers in the bottom row be \(a\) and \(b\). So, \(a + b = 20\).

To solve:
- Assume the bottom row is \(a, 20, b\).
- The second row will be \(a + 20\) and \(20 + b\).
- The top number is \((a + 20) + (20 + b) = 90\).

Let's assign values:
- Bottom row: \(10, 20, 30\) (since \(10 + 30 = 40\) and \(40 + 50 = 90\)).
- Second row: \(10 + 20 = 30\) and \(20 + 30 = 50\).

So, the completed tower is:
```
90
/ \
30 60
/ \ / \
10 20 30
```

##### Tower 3
```
80
/ \
? ?
/ \ / \
? ? ?
```
Using the same rule:
1. The top number (80) is the sum of the two numbers below it.
2. Let the two numbers below 80 be \(x\) and \(y\). So, \(x + y = 80\).
3. The number 50 is part of the bottom row. Let the other two numbers in the bottom row be \(a\) and \(b\). So, \(a + b = 50\).

To solve:
- Assume the bottom row is \(30, 20, 30\) (since \(30 + 20 = 50\) and \(50 + 30 = 80\)).
- Second row: \(30 + 20 = 50\) and \(20 + 30 = 50\).

So, the completed tower is:
```
80
/ \
50 30
/ \ / \
30 20 30
```

##### Circle Pattern
The pattern involves circles with numbers:
```
60
/ \
? 20
/ \ / \
? ? ? ?
```
Using the same rule:
1. The top number (60) is the sum of the two numbers below it.
2. Let the two numbers below 60 be \(x\) and 20. So, \(x + 20 = 60\). Thus, \(x = 40\).
3. The number 20 is part of the bottom row. Let the other three numbers in the bottom row be \(a, b,\) and \(c\). So, \(a + b = 40\) and \(b + c = 20\).

To solve:
- Assume the bottom row is \(10, 30, 10, 10\) (since \(10 + 30 = 40\) and \(30 + 10 = 40\)).

So, the completed pattern is:
```
60
/ \
40 20
/ \ / \
10 30 10 10
```

Similarly, for the other two circle patterns:
1. Second Circle Pattern:
```
100
/ \
? ?
/ \ / \
? ? ? ?
```
Solution:
```
100
/ \
70 30
/ \ / \
40 30 30 0
```

2. Third Circle Pattern:
```
140
/ \
? ?
/ \ / \
? ? ? ?
```
Solution:
```
140
/ \
80 60
/ \ / \
30 50 30 30
```

---

#### Section 2: Pattern Completion

The task is to complete the next pattern in the sequence of shapes.

##### Pattern 1
The given sequence is:
```
Diamond, Triangle, Pentagon, Square, Diamond
```
The pattern alternates between increasing and decreasing the number of sides:
- Diamond (4 sides)
- Triangle (3 sides)
- Pentagon (5 sides)
- Square (4 sides)
- Diamond (4 sides)

The next shape should have 3 sides (Triangle).

##### Pattern 2
The given sequence is:
```
Rectangle, Hexagon, Diamond, Circle, ?
```
The pattern alternates between increasing and decreasing the number of sides:
- Rectangle (4 sides)
- Hexagon (6 sides)
- Diamond (4 sides)
- Circle (infinite sides)

The next shape should have 4 sides (Square).

---

Final Answers

1. Number Towers
- Tower 2:
```
90
/ \
30 60
/ \ / \
10 20 30
```
- Tower 3:
```
80
/ \
50 30
/ \ / \
30 20 30
```
- Circle Patterns:
```
60
/ \
40 20
/ \ / \
10 30 10 10

100
/ \
70 30
/ \ / \
40 30 30 0

140
/ \
80 60
/ \ / \
30 50 30 30
```

2. Pattern Completion
- Pattern 1: Triangle
- Pattern 2: Square

Boxed Final Answer

\[
\boxed{
\text{Tower 2: }
\begin{array}{c}
90 \\
/ \, \backslash \\
30 \quad 60 \\
/ \, \backslash \quad / \, \backslash \\
10 \quad 20 \quad 30
\end{array},
\text{Tower 3: }
\begin{array}{c}
80 \\
/ \, \backslash \\
50 \quad 30 \\
/ \, \backslash \quad / \, \backslash \\
30 \quad 20 \quad 30
\end{array},
\text{Patterns: } \text{Triangle, Square}
}
\]