6. Algebra Play

Part II, printed Chapter 66 topics59 min

Chapter 6 of NCERT Mathematics for Class 8 (Part II, printed Chapter 6): Algebra Play. Three sections — Algebra as explanation, Patterns you can prove and Optimising and justifying. Six videos, 59 min in all.

Worked answers to the 19 exercise questions in this chapter →

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Part 1

Algebra as explanation

10 minWhy a "think of a number" trick always works, and how to invent oneThink of a number, double it, add four, halve it, take away the number. It always works, and testing it is not what makes it true.10 min · 12 parts

Part 2

Patterns you can prove

10 minNumber pyramids: what the top cell is made ofThe top of a number pyramid is not something you have to climb to. Put 1, 9, 4 along the bottom and the top is already decided.10 min · 12 parts9 minCalendar magic: the position in the grid is the whole secretA friend circles four dates on a calendar and tells you only their total. You name all four — because position is the whole secret.9 min · 12 parts9 minAlgebra grids: every row is an equation, and the shapes are the unknownsA grid of drawn shapes with a number at the end of each row is a system of equations wearing a picture.9 min · 12 parts

Part 3

Optimising and justifying

11 minArranging given digits to make the largest productPut 2, 3 and 5 into a two-digit number and a single multiplier. Six arrangements, and the largest product is not where most people look.11 min · 12 parts10 minDecoding a divisibility trick with algebraReverse a two-digit number, subtract the smaller from the larger, divide by nine. It comes out exactly — every time, and you can see why.10 min · 12 parts

What you will be able to do

  • Follow a stated chain of arithmetic instructions with a letter in place of the starting number, writing the expression after each instruction
  • State the pyramid rule and use it to fill a pyramid upward from a complete bottom row
  • State the two constant steps of a calendar grid and justify them from how the month is laid out
  • Read a row of an algebra grid as an equation and write it out in letters
  • Count and list every way three given digits can fill a two-digit-by-one-digit frame, without missing or repeating one
  • Write a two-digit number and its reversal as expressions in the same two digits

What this chapter assumes you already know

  • Writing an unknown quantity as a letter and building an expression from it step by step — the Class 7 work the chapter's opening section says it is continuing
  • Multiplying an expression by a whole number, and adding a number to it
  • Dividing an expression by a whole number when every part of it divides cleanly
  • Collecting like parts, so that a letter added and then taken away leaves nothing
  • Solving a one-step equation of the form "something times the unknown equals a number"
  • That the digits of a whole number carry different weights, so 126 holds a 1 in the hundreds and a 26 in the last two places (Part I, printed Chapter 5 uses this throughout)
  • Adding and subtracting whole numbers, and reading subtraction as the reverse of addition
  • Writing an unknown as a letter and building an expression from it

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.

  • "It works because I tried it and it worked."
  • "Halving undoes the doubling, so the +4 goes away too."
  • "The prediction is 2 because the trick says so."
  • "The final subtraction is what makes the answer constant."
  • "The date trick works the same way as the first one."
  • "Any change to the steps keeps 165."
  • "The trick would work whatever the day was."
  • "The performer must be doing mental arithmetic very fast."