Level 4: Letters for numbers

Algebra · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 a letter stood for one hidden number. In this level letters become a language. You write expressions like \(3n + 2\) from stories, put numbers into them (negative ones too), tidy them by collecting like terms, and solve equations by keeping the balance. Then you turn word problems into equations, solve inequalities on the number line (and find out why a negative flips the sign), and finally prove why the mind-reading trick always works.

Lesson	You will be able to
Variables and expressions	Read \(3n + 2\) in words, write expressions from stories, and explain why \(3n\) means \(3 \times n\)
Substitution	Evaluate expressions and formulas, including with negative numbers, squares and brackets
Like terms	Simplify \(3x + 5 + 2x - 1\) and explain with tiles why \(x\) and \(x^2\) cannot be collected
Solving one- and two-step equations	Solve equations like \(3x - 5 = 16\) by doing the same to both sides, and check the solution
Equations from stories	Define a variable, turn a word problem into an equation, solve it and answer in a sentence
Inequalities on the number line	Solve \(x + 4 > 9\), draw it with open and closed dots, and explain why multiplying by a negative flips the sign
The mind-reading trick explained	Prove tricks like \(\dfrac{2n + 10}{2} - n = 5\) with algebra and invent your own

Previous: Level 3: symbols for unknowns · Next: Level 5: equations and linear relations · Algebra topic page