L1 · Algebraic expressions with one or two terms; evaluating by substitution

Learning goal

“I can read and write algebraic expressions with one or two terms - using coefficient form like 3n and fraction form like n/4 - and evaluate an expression by substituting a number for the variable.”

Variable — a letter that stands for a specific unknown value, like n or k. The letter can be replaced by a number.

Algebraic expression — a mathematical phrase that includes a variable, like 4n or 3n + 2. It has no equals sign.

Term — one part of an expression: a product with a variable (4n), a quotient with a variable (n/4), or a plain number (2) each count as one term.

Coefficient — the number multiplied by the variable in a term: in 4n, the coefficient is 4.

Worked example

Start with repeated addition: n + n + n + n. Step 1: The same variable added 4 times is 4 groups of n - a product. Step 2: Write it in coefficient form, with NO multiplication sign: 4n. Read it as "4 times n" or "4 groups of n." Step 3: Evaluate by substitution. When n = 5: 4n = 4 x 5 = 20. A quotient term works the same way, written as a fraction: n/4 means n divided by 4. When n = 20: n/4 = 20 / 4 = 5. Arrow view, in words: n -> (x4) -> 4n. Substituting runs the arrow forward with a real number.

Check yourself — explain it

In 4n, why is there no multiplication sign, and what does the 4 tell you?

Paired problem — example still visible

Write k + k + k in coefficient form, then evaluate it when k = 6 -> 3k; 3 x 6 = 18

Faded completion — last step is yours

"When m = 12, m/3 = 12 / 3 = ___" -> 4

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz