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NCERT Class 6 Maths Chapter 1, Patterns in Mathematics, explained simply

CMDLearn · 12 October 2026

The new NCERT Maths textbook for Class 6 is called Ganita Prakash, and it opens with a chapter that surprises many parents: Patterns in Mathematics. There are no long sums to practise. Instead, the chapter asks children to look at numbers and shapes, find the rule, and explain why the rule works.

This guide walks through the chapter section by section, in plain words, with the answers worked out and a short practice set at the end. Keep the textbook open next to it. Our explanations are our own; the textbook is the authority.

The one big idea

The chapter begins with a definition worth remembering: mathematics is, in large part, "the search for patterns, and for the explanations as to why those patterns exist."

Two halves matter: finding the pattern, and explaining it. Throughout this chapter, a child who only says "the next number is 36" has done half the work. The other half is "because...".

1. Number sequences (section 1.2)

A sequence is a list of numbers that follows a rule. The textbook's Table 1 lists ten famous ones. Here they are with the rule in simple words and the next three numbers, which is exactly what the first "Figure it Out" asks for.

Virahānka numbers are worth a moment: they carry the name of the Indian scholar Virahānka, and each number is the sum of the two before it: 13 + 21 = 34.

2. Seeing sequences as pictures (section 1.3)

Many sequences become obvious when you draw them as dots:

• Triangular numbers are dots arranged in a triangle: 1 dot, then a row of 2 under it (3), then a row of 3 (6), and so on. Each new row is one dot longer, which is why you add 2, then 3, then 4.
• Square numbers are dots in a square: 2 rows of 2, 3 rows of 3. That is why 3 × 3 is called "3 squared".
• Cubes are blocks stacked into a cube: 2 × 2 × 2 = 8 small cubes.

The textbook points out that 36 is both triangular and square: 36 dots make an 8-row triangle (1 + 2 + ... + 8 = 36) and a 6 × 6 square. One number, two shapes.

It also introduces hexagonal numbers, 1, 7, 19, 37, ..., dots arranged in a hexagon. The next one is 61. (Each step adds a ring of dots: 6, then 12, then 18, then 24, and 37 + 24 = 61.)

3. The star result: odd numbers add up to squares (section 1.4)

Add the odd numbers one at a time:

• 1 = 1
• 1 + 3 = 4
• 1 + 3 + 5 = 9
• 1 + 3 + 5 + 7 = 16

Every answer is a square number. The textbook asks the real question: why, and does it go on forever?

The picture that explains it: draw a square of dots. Now split it into L-shapes, starting from one corner. The corner is 1 dot. The next L wrapped around it has 3 dots. The next L has 5, then 7. Each L is 2 dots bigger than the last, because it adds one dot on each side plus the corner. So a 4 × 4 square is exactly 1 + 3 + 5 + 7. Because you can do this for a square of any size, the pattern goes on forever.

That is why:

• the sum of the first 10 odd numbers is 10 × 10 = 100, and
• the sum of the first 100 odd numbers is 100 × 100 = 10,000.

Adding up and down

The chapter shows a second road to squares: 1 + 2 + 1 = 4, 1 + 2 + 3 + 2 + 1 = 9, and so on. Picture the square tilted on its corner, like a diamond: count the dots row by row and you get 1, 2, 3, ... up to the middle and back down. So 1 + 2 + ... + 99 + 100 + 99 + ... + 2 + 1 = 100 × 100 = 10,000.

Answers to the "Figure it Out" in section 1.4

4. Patterns in shapes (sections 1.5 and 1.6)

The second half of the chapter does the same thing with shapes. Table 3 shows shape sequences: regular polygons, complete graphs, stacked squares, stacked triangles and the Koch snowflake.

• Regular polygons: triangle, quadrilateral, pentagon, hexagon, ... The number of sides goes 3, 4, 5, 6, ..., and so does the number of corners, because every side ends at a corner shared with the next side.
• Complete graphs (K2, K3, K4, ...): dots where every dot is joined to every other dot. The number of lines goes 1, 3, 6, 10, 15: the triangular numbers again. A new dot must be joined to every dot already there, so you add 2, then 3, then 4.
• Stacked squares: 1, 4, 9, 16 small squares, the square numbers.
• Stacked triangles: 1, 4, 9, 16 small triangles, also the square numbers. Row by row, a stacked triangle has 1, 3, 5, 7 small triangles, and adding odd numbers gives squares, as we saw.
• Koch snowflake: each straight line is replaced by a line with a bump in it, made of 4 smaller lines. So the number of lines goes 3, 12, 48, 192, ...: multiply by 4 each time.

This is the chapter's quiet lesson: the same number patterns turn up in dots, sums and shapes. Seeing the link is what mathematicians do.

Practice: 8 questions with answers

Try these on paper first. Answers are below.

1. What is 1 + 3 + 5 + ... + 19 (the first 10 odd numbers)?
2. What is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1?
3. What is the 8th triangular number?
4. Add the 5th and 6th triangular numbers (15 + 21). What kind of number do you get?
5. What is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128?
6. How many lines does the complete graph on 7 dots (K7) have?
7. Write the next three Virahānka numbers after 34, 55, 89.
8. What comes next: 2, 5, 10, 17, 26, ...? Explain the rule.

Answers: 1) 100, since the first 10 odd numbers make a 10 × 10 square. 2) 64, an 8 × 8 square. 3) 36. 4) 36, a square number (6 × 6). 5) 255, one less than 256, the next power of 2. 6) 21, the 6th triangular number (1 + 2 + 3 + 4 + 5 + 6). 7) 144, 233, 377. 8) 37: each number is a square plus 1 (1 + 1, 4 + 1, 9 + 1, 16 + 1, 25 + 1, then 36 + 1).

Tips for parents and teachers

• Ask "why?" more than "what?". The chapter is built around explanations. "How do you know?" is the best question you can ask at home.
• Use real objects. Coins, buttons, rajma or pebbles make triangles and squares quickly, and children remember what they build.
• Let them draw. Dot pictures are not decoration in this chapter; they are the proof.
• Do not rush to the formula. The point is for the child to discover that odd numbers make squares, not to memorise it.

For more practice, our free printable worksheets cover Class 1 to 10 in English, Hindi and Marathi with answer keys. If your child uses an AI chatbot for maths, our guide on using ChatGPT for homework without cheating shows how to ask for hints instead of answers.

Where CMDLearn fits

CMDLearn is building an AI tutor for Classes 1 to 10 in Hindi, Marathi and English that works the way this chapter does: it asks the child "what do you notice?" and "why?" instead of handing over answers. It is not available yet; join the waitlist to hear when early access to the AI tutor opens.

Source

• NCERT, Ganita Prakash, Mathematics textbook for Grade 6, Chapter 1 "Patterns in Mathematics" (Reprint 2026-27): ncert.nic.in/textbook/pdf/fegp101.pdf

Section numbers and the opening quote are from the NCERT chapter. All explanations, answers and practice questions on this page are our own; every number was checked by calculation.

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