L2 · Evaluating expressions

Learning goal

“I can evaluate an expression - substitute the given value(s) for the variable(s) and calculate carefully, following the order of operations.”

Evaluate — find the numerical value of an expression for particular values of its variables.

Substitute — replace each variable with its given number (review: L2 of G7U05 used it to test equivalence).

Value of the expression — the single number the expression works out to after substituting.

Order of operations — brackets first, then powers, then x and /, then + and - (review from Grade 6).

Worked example

Evaluate 3x + 4 when x = 5. Step 1: Substitute - rewrite the expression with the number in place of the letter: 3(5) + 4. Writing the rewrite down is not optional; mental substitution is where errors breed. Step 2: Follow the order of operations: multiply before adding: 3(5) = 15. Step 3: Finish: 15 + 4 = 19. The value of the expression at x = 5 is 19. Say it plainly: the same expression gives different values for different inputs - 3x + 4 is 13 at x = 3 and 19 at x = 5. Evaluating is always: substitute, then calculate.

Check yourself — explain it

When evaluating 3x + 4 at x = 5, why do we multiply before we add?

Paired problem — example still visible

Evaluate 2n + 6 when n = 7. -> 20 (2(7) + 6 = 14 + 6)

Faded completion — last step is yours

"5m - 2 at m = 4: 5(4) - 2 = ___" -> 18

Ready to practise?

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

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