Here is fun with triangular numbers. First complete the list and then write them in the table as shown. 1 , 3 , 6 , 10 , _____ , _____ , _____ , 36 , 45 . 1 3 6 10 36 1 3 6 10 36 Now add them together and write the sum in the bottom row. What can you say about the numbers formed in this row? Write your conclusion in the form of a statement.

We know that, A number is termed as a triangular number if we can represent it in the form of a triangular grid of dots such that the dots form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. The triangular numbers are 1 1 + 2 = 3 ( 1 + 2 ) + 3 = 6 ( 1 + 2 + 3 ) + 4 = 10 ( 1 + 2 + 3 + 4 ) + 5 = 15 ( 1 + 2 + 3 + 4 + 5 ) + 6 = 21 ( 1 + 2 + 3 + 4 + 5 + 6 ) + 7 = 28 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) + 8 = 36 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 ) + 9 = 45 Triangular numbers = 1 , 3 , 6 , 10 , 15 , 21 , 28 , 36 , 45 Let us add the triangular numbers, 3 + 1 = 4 , 6 + 3 = 9 , 10 + 6 = 16 , 15 + 10 = 25 , 21 + 15 = 36 , 28 + 21 = 49 , 36 + 28 = 64 , 45 + 36 = 81 1 3 6 10 15 21 28 36 45 1 3 6 10 15 21 28 36 4 9 16 25 36 49 64 81 Conclusion = all the numbers are square numbers. Hence, the required answer is shown above.

Observe the given table. Multiplication table of 3 Triangular numbers Square numbers 3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18 3 × 7 = 21 3 × 8 = 24 3 × 9 = 27 3 × 10 = 30 3 , 6 , 15 , 21 9 Write multiplications tables of 4 . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

We need to find the triangular number and square number in multiplication table of 4 . We know that, A number is termed as a triangular number if we can represent it in the form of a triangular grid of dots such that the dots form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. The triangular numbers are ( 1 + 2 + 3 + 4 + 5 + 6 ) + 7 = 28 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) + 8 = 36 We know that, A square has all sides of the same length. The area of a square is the product of its width times its height, and for a square, these numbers are the same. So, any whole number which is a product of a number with itself is called a square number as they form the shape of the square. For instance, 3 × 3 = 9 so 9 is a square number. 2 × 2 = 4 , 4 × 4 = 16 , 6 × 6 = 36 Completed table. Multiplication table of 4 Triangular numbers Square numbers 4 × 1 = 4 4 × 2 = 8 4 × 3 = 12 4 × 4 = 16 4 × 5 = 20 4 × 6 = 24 4 × 7 = 28 4 × 8 = 32 4 × 9 = 36 4 × 10 = 40 28 , 36 4 , 16 , 36 Hence, the required answer is shown above table.

Observe the given table. Multiplication table of 3 Triangular numbers Square numbers 3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18 3 × 7 = 21 3 × 8 = 24 3 × 9 = 27 3 × 10 = 30 3 , 6 , 15 , 21 9 Write multiplications tables of 5 . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

We need to find the triangular number and square number in multiplication table of 5 . We know that, A number is termed as a triangular number if we can represent it in the form of a triangular grid of dots such that the dots form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. The triangular numbers are ( 1 + 2 + 3 ) + 4 = 10 ( 1 + 2 + 3 + 4 ) + 5 = 15 We know that, A square has all sides of the same length. The area of a square is the product of its width times its height, and for a square, these numbers are the same. So, any whole number which is a product of a number with itself is called a square number as they form the shape of the square. For instance, 3 × 3 = 9 so 9 is a square number. 5 × 5 = 25 Completed table. Multiplication table of 5 Triangular numbers Square numbers 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25 5 × 6 = 30 5 × 7 = 35 5 × 8 = 40 5 × 9 = 45 5 × 10 = 50 10 , 15 25 Hence, the required answer is shown above table.

Observe the given table. Multiplication table of 3 Triangular numbers Square numbers 3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18 3 × 7 = 21 3 × 8 = 24 3 × 9 = 27 3 × 10 = 30 3 , 6 , 15 , 21 9 Write multiplications tables of 6 . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

We need to find the triangular number and square number in multiplication table of We know that, A number is termed as a triangular number if we can represent it in the form of a triangular grid of dots such that the dots form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. The triangular numbers are ( 1 + 2 ) + 3 = 6 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) + 8 = 36 We know that, A square has all sides of the same length. The area of a square is the product of its width times its height, and for a square, these numbers are the same. So, any whole number which is a product of a number with itself is called a square number as they form the shape of the square. For instance, 3 × 3 = 9 so 9 is a square number. 6 × 6 = 36 Completed table. Multiplication table of 6 Triangular numbers Square numbers 6 × 1 = 6 6 × 2 = 12 6 × 3 = 18 6 × 4 = 24 6 × 5 = 30 6 × 6 = 36 6 × 7 = 42 6 × 8 = 48 6 × 9 = 54 6 × 10 = 60 6 , 36 36 Hence, the required answer is shown above table.

List the first four square numbers and triangular numbers Represent them through dot diagrams

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Solve the following numbers.
Write the numbers from $1$ to $50 .$
Colour the square numbers in red and triangular numbers in blue.

$1$	$2$



		$50$

List the square numbers.

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Solve the following numbers.Write the numbers from $1$ to $50 .$
Colour the square numbers in red and triangular numbers in blue.

$1$	$2$



		$50$

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Here is fun with triangular numbers. First complete the list and then write them in the table as shown.

$1, 3, 6, 10$ , _____ , _____ , _____ , $36, 45$ .

$1$	$3$	$6$	$10$		$36$
	$1$	$3$	$6$	$10$		$36$

Now add them together and write the sum in the bottom row.

What can you say about the numbers formed in this row?

Write your conclusion in the form of a statement.

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Observe the given table.

Multiplication table of $3$	Triangular numbers	Square numbers
$3 \times 1 = 3 3 \times 2 = 6 3 \times 3 = 9 3 \times 4 = 12 3 \times 5 = 15 3 \times 6 = 18 3 \times 7 = 21 3 \times 8 = 24 3 \times 9 = 27 3 \times 10 = 30$	$3, 6, 15, 21$	$9$

Write multiplications tables of $4$ . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Observe the given table.

Multiplication table of $3$	Triangular numbers	Square numbers
$3 \times 1 = 3 3 \times 2 = 6 3 \times 3 = 9 3 \times 4 = 12 3 \times 5 = 15 3 \times 6 = 18 3 \times 7 = 21 3 \times 8 = 24 3 \times 9 = 27 3 \times 10 = 30$	$3, 6, 15, 21$	$9$

Write multiplications tables of $5$ . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

HARD

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.1>Q I

Observe the given table.

Multiplication table of $3$	Triangular numbers	Square numbers
$3 \times 1 = 3 3 \times 2 = 6 3 \times 3 = 9 3 \times 4 = 12 3 \times 5 = 15 3 \times 6 = 18 3 \times 7 = 21 3 \times 8 = 24 3 \times 9 = 27 3 \times 10 = 30$	$3, 6, 15, 21$	$9$

Write multiplications tables of $6$ . In each table, circle the triangular numbers as shown in the example. Draw a box for square numbers. List them in columns as shown.

MEDIUM

5th Karnataka Board

IMPORTANT

Mathematics Standard 5 Part 2>Chapter 10 - Patterns>Exercise 10.2>Q I

Complete the border design.

Question Image