Pre-algebra and algebraGrade 6
Evaluating algebraic expressions worksheets
This generator prints expressions such as 3a + b or 2(a + b) − c, each followed by the values of its letters. Students substitute, simplify and write one number. Choose 6 to 30 problems, with an answer key.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
What evaluating means here
To evaluate an expression is to replace each letter with a number you are told to use, then do the arithmetic. Nothing is being solved and no letter is left at the end. The answer is a single number. That makes it the gentlest first step into algebra: the student already knows how to add, multiply and use parentheses, and the only new idea is that a letter is a placeholder.
This sheet suits sixth graders meeting variables for the first time, and older students who need a warm-up before equations. Before it, students should be comfortable with the order of operations. After it, the natural move is one-step equations, where the letter becomes the unknown.
What the sheet looks like
Each line shows an expression, then the phrase "when" and the values it needs, for example ab + c when a, b, c. Only the letters that appear in the expression are given values, so students never hunt for a number they do not need. The letters are a, b and c. The values for a and b run from 1 to 10 and c from 1 to 6, which keeps every product small enough to do on paper.
The expressions include a coefficient next to a letter (3a), two letters side by side (ab, meaning multiplication), a squared letter (a²), a bracket (4(a + c)) and a few with two operations. Problems are laid out in two columns, each with a short blank for the answer.
Choosing the settings
- Skill. Leave this on "Evaluate expressions" for this page. The other two choices switch the sheet to the distributive property or order of operations.
- Number of problems. Sixteen fills a page nicely. Use 6 to 8 for a quick check at the end of a lesson, or go up toward 30 for a homework page with spiral review.
- Level and Distributive form. These menus belong to the other two skills and do not change an evaluate sheet.
Because the key lists every answer, a parent can check a whole page in under a minute and then look only at the lines that were missed.
Worked example: 2(a + b) − c when a = 4, b = 3, c = 5
- Write the expression with brackets where the letters were. 2(4 + 3) − 5. Keeping the brackets stops a student from reading 2(a + b) as "2 then a then b."
- Do the inside of the parentheses first. 4 + 3 = 7, so the line becomes 2(7) − 5.
- Multiply. A number touching a bracket means multiply: 2 × 7 = 14.
- Subtract. 14 − 5 = 9.
The answer is 9. If the same expression were given with a = 1, b = 1 and c = 5, the result would be 2(2) − 5 = −1, so a few lines can come out negative. Students who have not met integers yet can circle those for a class discussion.
Mistakes to look for on the key
- Joining digits. For ab with a = 6 and b = 4, a student writes 64 instead of 6 × 4 = 24. The wrong answer will be a two-digit number that is far too large.
- Squaring as doubling. For a² with a = 5, writing 10 instead of 25. Ask the student to write 5 × 5 on the line first.
- Subtracting in the wrong direction. In 6c − a, some students compute a − 6c. A negative or oddly small answer is the clue.
- Ignoring the bracket. In 4(a + c) with a = 2, c = 3, writing 4 × 2 + 3 = 11 instead of 4 × 5 = 20.
A line such as a(b + c) packs two steps into one: add inside the parentheses, then multiply by a. With a = 3, b = 2 and c = 4, that is 3 × 6 = 18, not 3 × 2 + 4 = 10.
Getting more out of the page
Have students rewrite each expression with the numbers in place before simplifying, so the work is visible and errors are easier to find. When a student is steady, ask them to pick their own values for a, b and c and predict whether the answer will be larger or smaller than before. Then move on to writing and expanding expressions with the distributive property.