1. Patterns in Mathematics

7 topics1 h

Chapter 1 of NCERT Mathematics for Class 6: Patterns in Mathematics. Three sections — What mathematics is for, Number sequences and Shape sequences. Seven videos, 1 h in all.

Worked answers to the 25 exercise questions in this chapter →

0 of 7 done — sign in to track this chapter

Part 1

What mathematics is for

9 minMathematics is the search for patterns and for why they holdA pattern doubles five times in a row and then breaks. Spotting the pattern is only half the job — the half that pays is knowing why.9 min · 12 partsहिंदी

Part 2

Number sequences

12 minEvery number sequence is a rule, not a listTwo rows of the same printed table both start 1, 2, 3 — and then one goes to 4 and the other to 5. No run of numbers can tell you which sequence you are looking at.12 min · 12 partsहिंदी13 minDrawing a sequence makes its rule visible“Triangular number” isn't a label — it's a claim that that many dots really do go into a triangle. Ten do. Eleven don't. Here's the whole of Table 2, drawn.13 min · 12 partsहिंदी10 minWhy adding the odd numbers gives the squaresSix lines of addition say the odd numbers add to a square six times. One cut of a square of dots says it happens every time — and a Class 6 student can make that cut.10 min · 12 partsहिंदी12 minSequences that turn out to be the same sequence in disguiseSix questions that look like six separate tricks are really one move done to different rows — and doing all six turns Table 1 from a list into a map.12 min · 12 partsहिंदी

Part 3

Shape sequences

11 minShapes come in sequences too, with rules of their ownFour of Table 3's five shape sequences let you draw the next shape. One doesn't — and the reason is not that the sequence stopped. It's that your pencil did.11 min · 12 partsहिंदी11 minCounting the parts of a shape sequence produces a number sequenceStacked squares and stacked triangles both give 1, 4, 9, 16, 25 — for reasons that have nothing to do with each other. Which is why the count is never the explanation.11 min · 12 partsहिंदी

What you will be able to do

  • State the two-part account of mathematics that §1.1 gives, in the student's own words
  • Distinguish a sequence from a finite list of its early values
  • Match each of the first seven rows of Table 1 to its picture in Table 2
  • Compute the running sums of the odd numbers and recognise the squares in them
  • Form the running totals of a given sequence and identify the sequence they produce
  • State what a shape sequence is and how it differs from a number sequence
  • Choose a countable feature of a shape sequence and produce the resulting number sequence

What this chapter assumes you already know

  • Reading and continuing a simple run of numbers from primary school
  • Counting a small collection of dots or objects reliably
  • The idea that a claim can be tested rather than believed
  • No content from any other chapter of Ganita Prakash is needed; this is the first topic of the book
  • Whole numbers and their order, from primary school
  • Adding and multiplying small whole numbers without a calculator
  • Knowing what "double it" and "add three" mean as instructions
  • Counting dots in a rectangular array without recounting

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "Mathematics is a pile of rules somebody already finished."
  • "If it works for the first few, it works."
  • "The 'why' is extra credit; the answer is the real work."
  • "Patterns are things printed in maths books."
  • "An explanation is only useful for the thing it explains."
  • "Art and science are opposites, so mathematics has to be one of them."
  • "If I can continue it, I know it."
  • "Every sequence goes up by a fixed amount."