Worked example 1
Write an expression: “8 more than three times a number x.”
“Three times a number x” is 3x. “8 more than” means add 8. So 3x + 8.
Answer: 3x + 8
Grade 6 Math · Topic 42
Writing Algebraic Expressions
An algebraic expression uses numbers, variables (like x or n), and operations to represent a quantity. To write one, translate the words: sum, more than, plus → +; difference, less than, minus → -; product, times, of → ×; quotient, per, divided by → ÷.
Lesson alignment: 6.EE.A.2 · 6.EE.B.6 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Build an algebraic expression with tiles
Each x-tile stands for the same unknown amount. Add unit tiles to represent the constant.
Think first: How many x-tiles and unit tiles do you expect the expression to contain?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Grade 6 core skill · 6.EE.B.6
A variable can be an unknown or a changing number
In an equation such as n + 8 = 15, n is an unknown number to find. In a rule such as C = 3g + 2, g can take different values from a set, and C changes with it. The situation tells you how the variable is being used.
Example: A game costs $3 per play plus a $2 entry fee.
If g is the number of games and C is the total cost, then C = 3g + 2. For g = 0, 1, or 2, the matching costs are $2, $5, and $8.
g is an input; C depends on g.
Read the question before deciding what a letter means. It may name a specific missing value, or it may stand for any value allowed in the situation.
Quick check: In p = 12s, what can s represent?
If the problem says s is the number of equal groups, s can vary across allowed whole-number values. Then p changes with s; p is dependent on s.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Write an expression: “half of the sum of y and 6.”
“Sum of y and 6” is (y + 6). “Half of” means divide by 2. So (y + 6)/2.
Answer: (y + 6)/2
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- 7 more than x
Check
x+7
- 4 less than y
Check
y-4
- twice n
Check
2n
- the product of 5 and a
Check
5a
- the quotient of 12 and b
Check
12/(b)
- 3 more than twice x
Check
2x+3
- 10 minus the product of 4 and k
Check
10-4k
- half the sum of x and 8
Check
(x+8)/2
Try this situation 1
Tom is 4 years older than Anna. If Anna is a years old, write an expression for Tom's age.
Show a worked solution
Answer: a + 4.
“4 older than” means add 4 to Anna's age.
Try this situation 2
A taxi charges $3 plus $2 per mile. Write an expression for the total cost of m miles.
Show a worked solution
Answer: 3 + 2m.
$3 fixed plus $2 for each of m miles.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.