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Section 2.1 · Algebra

Constructing expressions

Use letters to represent numbers, use the correct order of operations in algebraic expressions, and write and understand expressions.

6 teaching slides 56 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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Full-screen dark deck for the projector — bullets reveal one at a time, the videos for this section are built in, plus an interactive tool, quick check questions and speaker notes. One self-contained file: download it and it works with nothing else installed.

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2 · Key words

expressionA collection of numbers and letters with no equals sign, such as 5n + 4.
equationNumbers and letters together with an equals sign, such as 5n + 4 = 19.
termOne part of an expression. 5n + 4 has two terms: 5n and 4.
variableA letter that can take different values.
unknownA letter standing for a number you do not yet know.
coefficientThe number multiplying a variable. In 5n the coefficient is 5.
constantA number on its own, whose value never changes.
equivalent expressionAn expression with the same value as another one, however it is written.

3 · Summary of the sectionrevise from this

  • In algebra a letter stands for an unknown number.
  • An expression has no equals sign; an equation does.
  • Write the number before the letter: x × 3 is written 3x, never x3.
  • Never write the 1: 1 × a is written a.
  • Write division as a fraction: n ÷ 4 is written n/4.
  • a × a is written a² and a × a × a is written a³.
  • “More than” means add; “less than” means subtract, but watch the order — “x less than y” is y − x, not x − y.
  • “Doubled” means × 2, “tripled” means × 3, “half of” means ÷ 2.
PDFPrintable worksheet All 56 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons4 videos

Algebra Basics: What Is Algebra?

American mathantics

Why we use letters at all, and what an expression means — the right video to open the whole unit with.

Writing Algebraic Expressions (One Operation)

American Math with Mr. J

Turning a phrase such as “5 more than n” into an expression, one operation at a time.

Writing Algebraic Expressions (Two Operations)

American Math with Mr. J

The harder wording — “4 more than twice a number” — where the order of the operations decides the answer.

Writing Expressions with Variables

American stretchMath with Mr. J

More practice at translating words into algebra, with worked examples.

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4 · Practice56 questions, easiest first

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2.2 Using expressions and formulae