Free original lessons
Learn to read short scenarios and choose or write the matching algebraic expression. Includes worked example, practice tasks, rubric, and a planned worksheet with answer key.
Many algebra problems ask you to translate a situation into symbols before you solve anything. This lesson focuses only on that translation step: reading a context word problem and selecting or writing an equivalent expression. You will not solve equations or evaluate expressions numerically here. Instead, you will practice identifying the quantities, the operations, and the structure that make two expressions equivalent in meaning. The convention for handwritten work is simple: write expressions on a baseline, use a clear variable letter, and show grouping with parentheses when needed. Letter styles vary, so any legible handwriting that preserves the mathematical structure is acceptable.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
Start by naming what the problem counts or measures. A variable represents an unknown or changing quantity. Constants represent fixed amounts. Then look for operation words: total, more than, less than, times, per, split, remaining. These words signal addition, subtraction, multiplication, or division.
Be careful with order. 'Five less than a number' means x - 5, not 5 - x. 'Three more than twice a number' means 2x + 3. Reading the phrase in the order of the operations often prevents reversal errors.
Two expressions can use different letters or different order and still be equivalent. For example, 3(x + 2) and 3x + 6 are equivalent because distributing gives the same result. When matching, compare the structure: how many groups, how many items per group, and what is combined or removed.
A common trap is matching a keyword to the wrong operation. 'Shared equally among four friends' suggests division by 4, while 'four more than a number' suggests addition of 4. Read the whole sentence before choosing.
In a multiple-choice match, eliminate options that reverse subtraction or misplace parentheses. In a write-in box, you must produce the expression yourself. Use parentheses to protect a sum or difference that is multiplied or divided. For instance, 'twice the sum of a number and 7' is 2(x + 7), not 2x + 7.
Keep units consistent. If a scenario uses dollars and cents, write the expression in dollars or in cents, but do not mix them. Label any numerical example you invent as hypothetical, and measure real equipment if a task involves physical materials.
A school buys 4 boxes of pencils. Each box contains p pencils. The school already has 12 pencils. Write an expression for the total number of pencils.
4p + 12
Why: Four boxes with p pencils each gives 4p pencils from the boxes. The 12 pencils already owned are added to that total. The expression 4p + 12 keeps the two contributions separate and adds them.
Check: Test p = 5. Four boxes give 20 pencils, plus 12 already owned gives 32. The expression 4(5) + 12 = 20 + 12 = 32. The match holds.
A jar starts with 18 marbles. Then m marbles are removed. Write an expression for the number of marbles remaining.
18 - m
Why: The starting amount is 18. Removing m marbles means subtracting m from 18. The remaining count is 18 - m.
Check: Test m = 5. Starting with 18 and removing 5 leaves 13. The expression 18 - 5 = 13. The match holds.
A taxi charges a fixed fee of 3 dollars plus 2 dollars per mile. Write an expression for the total cost in dollars for a trip of d miles.
3 + 2d
Why: The fixed fee is 3 dollars. The mileage charge is 2 dollars for each of d miles, giving 2d dollars. The total cost is the sum 3 + 2d.
Check: Test d = 4. The mileage charge is 2 times 4 = 8 dollars, plus the 3-dollar fee gives 11 dollars. The expression 3 + 2(4) = 3 + 8 = 11. The match holds.
A rectangle has length L and width 5. Write an expression for its perimeter.
2L + 10 or 2(L + 5)
Why: Perimeter is twice the length plus twice the width. Twice the length is 2L and twice the width is 10, so 2L + 10. Factoring gives 2(L + 5), which is equivalent.
Check: Test L = 6. The perimeter is 2(6) + 2(5) = 12 + 10 = 22. The expression 2(6 + 5) = 2(11) = 22. Both forms match.
A bag contains n nickels and 7 dimes. Write an expression for the total value in cents.
5n + 70
Why: Each nickel is worth 5 cents, so n nickels are worth 5n cents. Each dime is worth 10 cents, so 7 dimes are worth 70 cents. The total value in cents is 5n + 70.
Check: Test n = 3. Three nickels are 15 cents and seven dimes are 70 cents, giving 85 cents. The expression 5(3) + 70 = 15 + 70 = 85. The match holds.
No. This lesson stops at translation. You only need to select or write an expression that preserves the meaning of the scenario.
Yes. For example, 3(x + 2) and 3x + 6 are equivalent because distributing gives the same result for every value of x.
Any clear variable letter is acceptable as long as it represents the same unknown quantity consistently.
Substitute a simple test value into the scenario and into your expression. If both give the same result, the match is likely correct.