Writing Algebraic Expressions from Words (Grade 6)
Algebra lets us write a phrase as math using a letter for an unknown.
Understanding writing algebraic expressions
"Five more than a number" becomes n + 5; "twice a number" becomes 2n; "three less than a number" becomes n − 3. The trick is to translate each word: more/sum → add, less/difference → subtract, times/product/twice → multiply, split/quotient → divide — and watch the order ("3 less than n" is n − 3, not 3 − n).
Seeing it in action
Worked example
Write "7 more than twice a number n."
"twice a number" = 2n; "7 more than" that = 2n + 7. → 2n + 7.
“7 more than twice a number” is 2n + 7. The n blocks can be any size, so the 7 is drawn as its own, different block.
A common mistake, and the fix
Writing “less than” in the order the words come.
“3 less than a number n” means start with n and take 3 away: n − 3. Writing 3 − n subtracts the other way and gives a different value (for n = 10, n − 3 is 7 but 3 − n is −7). Ask “less than what?” and start from that.
Try a few
"4 less than a number x"
"the product of 5 and a number y"
"a number n divided by 3, plus 1"
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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