Visualising Number Sequences

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.3

Learn

Many sequences can be drawn as pictures, and a picture helps us see the pattern. Triangular numbers make triangles of dots. Each new picture adds a row (coral) that is one dot longer.

1 + 2 + 3 + 4 + 5 = 15

Square numbers make squares of dots. Going from a 4 × 4 square to a 5 × 5 square adds an L-shaped border (coral). That is why they are called squares.

5 × 5 = 25

Cube numbers build cubes from small blocks. A cube 3 blocks wide, 3 deep and 3 tall has 27 blocks.

3 × 3 × 3 = 27

Some numbers can be drawn in two ways. 36 dots make a triangle of 8 rows, and they also make a 6 by 6 square. So 36 is a triangular number and a square number.

Hexagonal numbers: 1, 7, 19, 37 … Each new ring goes all the way around (coral). The rings have 6, 12, 18 … dots. The next hexagonal number is 37 + 24 = 61.

1 + 6 + 12 + 18 = 37

Powers of 2 as pictures: each picture is two copies of the picture before it: 1, 2, 4, 8, 16.

Explore: build the dot pictures yourself. Add or remove a row and count the dots.

1. Build the triangle that has 10 dots.
2. Build the square that has 25 dots.
3. Build the hexagonal number 19.

Remember

• Pictures help us see why a sequence grows the way it does.
• Triangular numbers make triangles, square numbers make squares, cube numbers make cubes.

Quick check

How many dots are in a triangle picture with 6 rows?

1. 18
2. 21
3. 28
4. 36

Think about it

Is 21 a triangular number? Is it a square number? Build it with dots to check.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.