What does a problem look like?

A short situation with one unknown, such as a cyclist riding x laps of a 5-kilometer route, followed by the quantity to write: the distance in kilometers. The answer key gives 5 × x. Six problems per print, one difficulty level, and a fresh set of situations each time.

Why does the answer key sometimes write 6b and sometimes 5 × x?

Both mean the same thing. A number next to a letter is a multiplication with the sign left out. Your child can write either form, and it is worth saying that out loud once so 6b is not misread as a two-digit number.

How is this different from the evaluating expressions sheet?

That sheet gives the expression and a value and asks for a number. This one starts with words and stops at the expression. There is nothing to compute, which is why defining the variable matters so much: it is the only place the situation and the symbols meet.

6th grade writing algebraic expressions

6th grade writing algebraic expressions worksheets

Writing algebraic expressions worksheets for 6th grade describe an everyday situation with one unknown, such as x visitors shared equally among 4 guides, and ask your child to write the expression for the quantity named: x ÷ 4. Six problems per print. Nothing is solved or evaluated. The work is naming what the variable stands for and choosing the operation the situation calls for.

Free printable PDF worksheet, aligned to Common Core 6.EE.B.6.

Each print is a different sheet with its own answer key. You don't need to sign up.

The kind of problems you'll get

Complete each problem. Show your reasoning where asked.

One tour has x visitors shared equally among 4 guides. Write the number of visitors per guide.
Answer: x ÷ 4
A team has x returning members, including 7 captains. Write the number of returning members who are not captains.
Answer: x − 7
A cyclist rides x laps of a 5-kilometer route. Write the distance in kilometers; x can vary by ride.
Answer: 5 × x

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on each sheet

Writing algebraic expressions. Complete each problem. Show your reasoning where asked. 6 problems per page.

Every version prints on US Letter or A4, with its answer key after the problems.

This sheet is one of the versions on the 6th grade evaluating expressions page, with its own difficulty choices and its own answer key.

How to teach this

Have your child write "Let x be" before every expression and finish that sentence with the unit: the number of visitors, the number of laps. That one line is most of standard 6.EE.B.6, and it stops the variable from floating free. Then ask which operation the situation describes. Shared equally means divide. Some of a group set aside means subtract. Repeated trips of the same length mean multiply. The trap is writing an equation, with an equals sign and a number on the other side, when the sheet asks for an expression. The Remember box draws the line: an expression describes a quantity, an equation says two quantities are equal. One check: substitute a small number for x and see if the result makes sense. If x is 12 visitors and there are 4 guides, x ÷ 4 gives 3 each, which sounds right.

Watch for: Kids write x − 7 as 7 − x because the 7 was mentioned first. The team has x members and 7 of them are captains, so the captains come off the total, not the other way around. Kids add an equals sign and pick a number for x to finish the problem. The sheet asks for an expression that works for any value of x, and the answer key shows 5 × x, not 5 × 3 = 15.

Common questions about 6th grade writing algebraic expressions

What does a problem look like?: A short situation with one unknown, such as a cyclist riding x laps of a 5-kilometer route, followed by the quantity to write: the distance in kilometers. The answer key gives 5 × x. Six problems per print, one difficulty level, and a fresh set of situations each time.
Why does the answer key sometimes write 6b and sometimes 5 × x?: Both mean the same thing. A number next to a letter is a multiplication with the sign left out. Your child can write either form, and it is worth saying that out loud once so 6b is not misread as a two-digit number.
How is this different from the evaluating expressions sheet?: That sheet gives the expression and a value and asks for a number. This one starts with words and stops at the expression. There is nothing to compute, which is why defining the variable matters so much: it is the only place the situation and the symbols meet.

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Aligned to Common Core 6.EE.B.6. Reviewed by the One more sheet team. Content version 241, updated September 2026.

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