# Patterns Including Numbers

Home | 5th Grade Math Worksheets | **Patterns including numbers**

**Patterns**

Patterns are present everywhere! They are predictable arrangements following a certain rule.

In our daily life, we see patterns in animals, arrangement of leaves; numbers etc….These patterns make learning interesting for us and help us unwind our mind.

**Simple Patterns**

Are you familiar with these patterns?

3, 6, 9, 12, 15, ____

*Correct Answer**:* 18

### Triangular Numbers

Emma was watching a sports channel. She saw the following picture and asked her father what game they are playing?

The father replied that this is a game of bowling pins. The players roll a ball and knock down as many bowling pins as possible. She was surprised at the arrangement of the bowling pins. There were a total of 10 bowling pins. She drew the arrangement using dots in an increasing pattern.

She counted the number of dots in each pattern. They are 1, 3, 6 and 10.

The number of dots that can form a triangle-shaped pattern are called triangular numbers.

Let us observe the pattern and understand the rule to find the next numbers.

### Square Numbers

The next game on the channel was chess. Emma liked the pattern of squares on the chessboard and wanted to count them.

She started drawing the squares using dots in an increasing pattern.

She noted the number of dots in each square as 1, 4, 9 and 16.

Let us observe the pattern and understand the rule to find the next numbers.

### Turn the shape

Mia is printing on a drawing sheet with a block. Look at the beautiful pattern she has made:

Has she used different blocks to make the pattern?

We can create a pattern by simply turning a block in a particular way. We can also turn a block in different ways to create different designs.

Here, Mia has used the same block for printing. She turns the block one- fourth in a clockwise direction each time. Since the block is rotated by a one-fourth turn ever time, it is called a quarter turn.

Another way of creating a pattern is by rotating a block by half a turn each time. Since the block is rotated by turn, it is called half turn.

### Look at the first two pictures of the pattern shown below:

### Interesting number and alphabet patterns

The number 101 is used to make a pattern by taking a 1/4th turn every time.

After which turn does the number look the same?

*Correct Answer**:* 1/2 turn

The word ZOOZ is used to make a pattern by taking a 1/4th turn every time. After 1/4th turn, the word is read as NOON, but vertically.

After which turn does the number look the same?

*Correct Answer**:* 1/2 turn

### Check Point

- What is the missing number in this pattern?

1, 4, 27, 256, ______, 46656

- Which number should be placed in the empty triangle?

3. Which of these shapes will look the same after 1/2 a turn?

4. Study the pattern carefully and complete it:

1 × 1 × 1 = 1 = 1

2 × 2 × 2 = 8 = 3 + 5

3 × 3 × 3 = 27 = 7 + 9 + 11

4 × 4 × 4 = 64 = 13 + ____ + ____ + ____

5 × 5 × 5 = ___ = ____ + ____ + ____ + ____ + ____

5.Complete the pattern:

### Answer Key

- 3125 as 1
^{1 }= 1, 2^{2}= 4, 3^{3}= 9, 4^{4}= 256, 5^{5}= 3125, 6^{6}= 46656 - (7 – 3) × 3 = 4 × 3 = 12

(8 – 6) × 4 = 2 × 4 = 8

(8 – 5) × 3 = 3 × 3 = 9

(7 – 6) × 4 = 1 × 4 = 4

3.

4. 4 × 4 × 4 = 64 = 13 + 15 + 17 + 19

5 × 5 × 5 = 125 = 21 + 23 + 25 + 27 + 29

5.

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