Write Algebraic Expressions from Word Phrases

Students translate verbal descriptions into algebraic expressions using variables. They recognize key words that signal each operation and write expressions that accurately represent the mathematical relationship described in words.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 6 · Expressions and Properties · question 1 of 3

0 of 20

20 rungs. A star at the top.

Which expression means 2 more than a number n?

n + 2

2 − n

n − 2

How it is taught

0:00 of 3:54

Words hide operations.

A letter stands for the unknown number.

Half of a number means that number divided by 2.

Read it: Words into an expression

"8 less than a number x" starts with x and takes 8 away. On a tape, 8 comes off the end of the x bar, and the part that is left is x − 8.

Find the number you do not know and give it a letter and a bar.
Find what the words do to it: more and sum add, less and decreased take away, times and product multiply, quotient and half divide.
Write the whole first and then what happens to it: x − 8 is x with 8 taken away.

The tape shows which number is the whole and which is the part taken off.

Adding and multiplying can go either way around: x + 8 is the same as 8 + x.

Taking away and dividing cannot: x − 8 and 8 − x are different numbers.

Write the number being changed first, then what is done to it: "less than" and "more than" turn the words around.

Writing 8 − x for "8 less than a number x".

Less than takes 8 away from x, so x comes first: x − 8.

Write "a number k divided by 3" as an expression. — k ÷ 3. k ÷ 3, not 3 ÷ k: k is the bar that is cut.

Five more than twice a number → 2n + 5

Sometimes math hides inside words. Let's translate this phrase into an algebraic expression.

First, look for the unknown. The phrase says 'a number' — we don't know what it is yet, so we'll call it n.

Next, 'twice' means two times. So 'twice a number' is two times n, which we write as 2n.

Now, 'five more than' tells us to add five.

Put it together: five more than 2n is 2n plus 5.

Let's read it back: two times a number, then add five. That matches the phrase exactly!

Grade 6 · Translating words into algebra

Our algebraic expression is 2n plus 5. Nice work turning words into math!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free