concepts · 13
- 01
Balancing Mobiles And Scales: Find The Hidden Weights
Find unknown weights on mobiles and scales: both sides weigh the same, and taking equal weights off both sides keeps the balance.
- 02
From Patterns And Pictures To Equations
Write an equation for an unknown from a pattern or a balance picture, and learn the words equation, LHS, RHS and solving.
- 03
Guessing Vs Balancing: Two Ways To Solve
Solve by trial and error, see why it can be slow, and learn that doing the same thing to both sides keeps an equation true.
- 04
Solving Equations Step By Step
Get the unknown alone by removing terms and factors from both sides, collect unknowns on one side, and always check your answer.
- 05
Shortcut Moves: Moving Terms Across The Equals Sign
Use the shortcut where a term changes sign as it crosses '=', and know why it works.
- 06
Word Problems Into Equations: Tiles, Parties And Savings
Choose an unknown, write an equation from a real situation, solve it, and answer in words; solve bracketed equations in more than one way.
- 07
Number Tricks And Problems With Two Unknowns
Explain 'think of a number' tricks with algebra, and solve two-unknown problems by writing one unknown using the other.
- 08
Working Backwards: Make Equations With A Given Solution
Build equations with a chosen solution by doing the same thing to both sides, and use one equation to find related values without solving.
- 09
Practice Lab: Solve, Check And Find Your Way Out
Solve many kinds of equations, check every answer, and use your solutions to find a path through the book's equation maze.
- 10
Puzzles And Real Life: Machines, Blobs, Bricks And Giraffes
Turn puzzles, number machines, pictures and stick patterns into equations and solve them.
- 11
Mind The Mistake, Mend The Mistake
Find the exact step where a solution goes wrong, say what the mistake is, and correct it.
- 12
A Pinch Of History: Bījagaṇita And Brahmagupta's Formula
See how algebra grew in India and travelled the world, read equations in old Indian notation, and use Brahmagupta's formula for Ax + B = Cx + D.
- 13
Review: Finding The Unknown
Check what you can now do with equations, revise the key moves, and solve fresh problems on your own.