6th Grade Writing and Reading Algebraic Expressions Lesson (Free PDF)
This write expressions lesson for 6th Grade covers writing and reading algebraic expressions (Common Core 6.EE.A.2a, 6.EE.A.2b), with a free PDF to print.
An algebraic expression combines numbers, variables, and operations. Key words show the operation: sum means add, less than means subtract, product means multiply, and quotient means divide. A term is a part that is added, a coefficient multiplies a variable, and 3(x + 5) is the product of 3 and a sum.
Grade 6 · Common Core State Standards: 6.EE.A.2a, 6.EE.A.2b
Key facts in this write expressions lesson
- Sum, plus, more than: add. Difference, less than, decreased by: subtract.
- Product and times: multiply; quotient and divided by: divide.
- A term is a part of an expression separated by plus or minus signs.
- A coefficient is the number multiplied by a variable; a constant has no variable.
- Read an expression in parentheses as one quantity.
How do you write expressions from words?
An algebraic expression uses numbers, variables, and operations. A variable is a letter that stands for a number. Key words tell you which operation to use.
Watch the order for less than and decreased by. “8 less than k” means \(k – 8\), not \(8 – k\).
What are terms, coefficients, and factors?
In \(7x + 3\), the terms are \(7x\) and \(3\). The coefficient of \(x\) is 7 and the constant is 3.
How do you read an expression as one thing?
Treat a group in parentheses as one quantity. The expression \(3(x + 5)\) is the product of 3 and the sum \(x + 5\). It is different from \(3x + 5\), which is the sum of \(3x\) and 5.
- Underline the operation words.
- Write each quantity as a number or variable.
- Use parentheses when a sum or difference is multiplied.
- Read the expression back in words to check.
Expressions also model rates. If a bus ride costs \(\$2.50\) for each trip, then \(2.5t\) gives the cost for \(t\) trips. When \(t = 4\), the cost is \(2.5 \times 4 = 10\) dollars. Writing the rule as an expression lets you find the cost for any number of trips without drawing a new picture each time. Always say what the variable stands for, such as “t is the number of trips.” That sentence makes your expression easy to check.
Example: A gym costs $20 to join and $15 per month. For m months the cost is \(15m + 20\). Here \(15m\) is the monthly cost and 20 is the one-time fee.
Write expressions lesson: questions and answers
What is an algebraic expression?
An algebraic expression has numbers, variables, and operations but no equals sign, such as 3n + 2.
What is the difference between a term and a factor?
Terms are added or subtracted, and factors are multiplied. In 3x + 5, the terms are 3x and 5; in 3x, the factors are 3 and x.
How do you write “8 less than k”?
Write k – 8. The number 8 is taken away from k, so k comes first.
What is a coefficient?
A coefficient is the number multiplied by a variable. In 9z + 4, the coefficient is 9.
How do you know when to use parentheses?
Use parentheses when a sum or difference is multiplied by something. Twice the sum of n and 3 is 2(n + 3), not 2n + 3.
How to use this write expressions lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the write expressions lesson as a PDF with the button below and keep it with your notes.
All Grade 6 chapters: Grade 6 math.
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