Give a relationship a precise form
Turn a phrase into an expression, rewrite it without changing its value, and evaluate it for a given input. Choose a focused set with room to show the reasoning.
Choose a worksheetThree ways to work with one expression
Understand every step
Connect a relationship in words with the variables, operations and grouping that express it.
Algebraic expressions
A printable guide to the language of algebra. Connect words with addition, subtraction, products, quotients, equality and grouping, with examples that explain operand order.
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Algebraic expressions
Translate words into algebra with ten questions per worksheet. Select easy, medium and hard phrases, including grouping, fractions and powers, and print an explained answer key.
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Expand grouped products and collect like terms. Explain why each new expression is equivalent.
Algebraic expressions
Print ten combining-like-terms questions and a separate worked key. Choose original one-variable practice or a progressive English lesson with two-variable grouping, distribution, error analysis, and perimeter.
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Algebraic expressions
Print 10 distributive property expressions. Choose grouped three- or four-term forms, signed factors and coefficient ranges, with worked answers.
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Use the given value for each variable, then calculate with parentheses and exact arithmetic.
Algebraic expressions
Substitute a given value and evaluate expressions with one variable. Choose addition, subtraction, grouped products or exact division, with whole-number or signed integer inputs.
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Algebraic expressions
Evaluate expressions using two distinct variable values. Select sums, grouped multiplication and exact-division forms with whole numbers or integers, plus an explained answer key.
Preview and downloadThe expression 3x + 5 can describe a starting amount of 5 plus three equal groups of size x. It does not tell us one numerical result until a value of x is supplied.
An equation makes a statement that two expressions are equal. In this collection, the task is to write, simplify or evaluate an expression. When a question supplies x = 4, that is a given input to use in the calculation.
“Seven less than n” means n − 7. “Seven minus n” means 7 − n. Try n = 10: the first expression is 3, while the second is −3. The words describe different relationships.
Likewise, twice the sum of n and 7 means 2(n + 7). Twice n plus 7 means 2n + 7. Parentheses show which entire quantity is multiplied.
Simplifying 5x + 2x − 4 gives 7x − 4, an equivalent expression valid for every input. Evaluating it at x = 3 gives 17, a number for that particular input.
Like terms have the same variable part. Combine their coefficients and keep constants separate. To expand −2(x − 5), multiply both terms by −2, giving −2x + 10.
Choose by readiness
These Grade 5–6 entry points use prerequisites rather than a particular national curriculum. Hard writing levels, fractional coefficients and negative inputs may be appropriate later.
Use the phrase guide to discuss operation order and the meaning of grouped quantities.
Open this starting point →Begin with short one-variable phrases after the four operations are familiar.
Open this starting point →Use whole-number inputs in short expressions; signed coefficients still require careful arithmetic.
Open this starting point →Combine like terms with smaller coefficient magnitudes before adding more terms and groups.
Open this starting point →Practice one distribution at a time, including negative factors.
Open this starting point →Match each variable with its own value, then calculate with positive and negative integers.
Open this starting point →Practice a variable as the dividend or divisor, with whole-number inputs chosen for exact division.
Open this starting point →Keep track of both inputs, negative divisors and the other terms in the expression.
Open this starting point →Model one example aloud, let the learner explain another, then use a ten-question sheet. Review the kind of error before adding difficulty: a reversed phrase, a missed sign and an arithmetic slip need different follow-up.
Use the separate key to discuss equivalent forms and intermediate steps. Create a new set with the same settings after revisiting the idea.
