Words to expressions
Twice a number is 2x, half of it x/2 and the next whole number x + 1. Then two operations in the order the words give them and, at the end, brackets: twice the sum of a number and 3 is 2(x + 3).
Start over?
Teaching guide: algebraic expressions from Grade 6 to Grade 8
Algebraic expressions use letters for unknown numbers, so that a description in words becomes a short expression. They open the door to secondary school algebra and to the step PISA calls formulate: turning a situation into an expression or an equation. This free algebraic expressions worksheet generator makes A4 worksheets for every step, from Grade 6 to Grade 8, with answers that give each expression and work out each calculation.
- For
- Elementary 6th · Middle & High 7th, 8th (ages 11-13)
- Subject
- Mathematics › Algebra
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Expressions to words
Read 2x − 3 and choose between "twice a number minus 3", "twice the difference between a number and 3" and "3 minus twice a number", with the same numbers so that only the structure counts.
Substitution
Replace the letters with their values and follow the order of operations. Negative values go in brackets: when x = −3, −x² = −(−3)² = −9.
Terms
The coefficient, letters and degree of each term, also when the coefficient is −1 or a fraction, or when the term is a number on its own (degree 0).
Collecting like terms
Group the terms with the same letters and powers and add their coefficients. At level 3, expand the brackets first.
Forming equations
Problems about numbers, ages, prices, perimeters and sharing: students write the equation and solve it. The answers show the equation and every step to the solution.
Frequently asked questions about algebraic expressions worksheets
Which grades are these worksheets for?
For Grade 6, where a letter first stands for an unknown number, and for Grades 7 and 8 (Years 7 to 9), where algebraic expressions are a topic of their own. Level 1 of each type suits Grades 6 and 7; level 3 (brackets, two letters, problems with fractions) is for Grade 8.
Is there more than one right answer?
The same expression can be written in several ways: x + 2x and 3x, or 2(x + 3) and 2x + 6, are equivalent. The answers give the expression as the words build it and, where it helps, simplified too. In the multiple-choice exercises, the wrong descriptions always give different expressions, whatever the value of x.
How do you substitute negative numbers?
Write the value in brackets in place of the letter and follow the order of operations: brackets, then powers, then multiplication and division, then addition and subtraction. The answers show every step, for example 3·(−2)² − 1 = 3·4 − 1 = 11.
What kind of problems are there?
Number problems (twice a number plus 7, consecutive numbers), ages, prices, the perimeter of a rectangle, sharing and coins. Each problem says what x stands for, so the whole class uses the same unknown, and the equation always has a whole-number solution.
What other worksheets go well with these?
Before them, the order of operations and integer operations prepare substitution. After them, linear equations and polynomials carry on from here, and number sequences lead to the nth term. Find every resource under maths worksheets.
How do I print only the answers?
Press Print and choose "Answer key", or "Worksheet and answer key" to get both. You can also save it as a PDF from your browser's print dialog. The worksheets are made in your browser and no data is sent anywhere.
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