Level 3: Symbols for unknowns

Algebra · level 3 of 8 · rough age 9-10 (a guide for parents; anyone can start anywhere)

In level 2 a missing number hid behind a question mark. In this level it gets a proper name: a shape like □ or a letter like \(n\). You learn to undo two-step machines in the right order, to hunt for a mystery number with smart guesses, to describe a whole crowd of numbers at once with < and >, and to use formulas written in words. The level ends with a mind-reading trick, and with the reason it can never fail.

Lesson	You will be able to
Letters and shapes for unknowns	Solve number sentences like □ + 9 = 23 and \(n \times 4 = 36\), knowing that one symbol means one number in a sentence
Two-step machines	Run a "times 3, then add 2" machine forwards and backwards, and find a machine's rule from its inputs and outputs
Guess and check, and undoing	Find a mystery number with a table of better and better guesses, and choose between guessing and undoing
Inequalities in words and symbols	Read and write <, >, "at least" and "at most", and list every whole number that makes \(n + 3 < 8\) true
Formulas in words	Use rules like perimeter = 2 × length + 2 × width, fill in values, and work a formula backwards
A mind-reading trick	Perform the "your answer is 5" trick, explain it with cups and counters, and change it to give other answers

Previous: Level 2: boxes and machines · Next: Level 4: letters for numbers · Algebra topic page