Mathematics
Grade 6
15 min
Write an equation from words (Tutorial Only)
Write an equation from words (Tutorial Only)
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify keywords that represent mathematical operations (addition, subtraction, multiplication, division).
Recognize words that indicate an equality sign in a word problem.
Choose an appropriate variable to represent an unknown quantity in a word problem.
Translate simple word sentences into one-variable algebraic expressions.
Construct a one-variable equation that accurately represents a given word problem.
Differentiate between an algebraic expression and an algebraic equation.
Have you ever tried to describe a math problem using only words? 🤔 It's like solving a puzzle where words become numbers and symbols!
In this lesson, you'll learn how to turn everyday language into powerful mathematical equations. This skill is super important becaus...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA letter (like x, y, or n) used to represent an unknown number or quantity in a mathematical problem.In the sentence 'A number plus five is twelve,' 'a number' can be represented by the variable 'x'.
EquationA mathematical statement that shows two expressions are equal, using an 'equals' sign (=).x + 5 = 12 is an equation because it states that 'x + 5' is equal to '12'.
ExpressionA mathematical phrase that contains numbers, variables, and operation signs, but does NOT have an equals sign.x + 5 is an expression. It describes a quantity but doesn't state its value.
CoefficientA number multiplied by a variable.In the expression '3x', the number '3' is the coefficient. It means &...
3
Core Formulas
Rule 1: Translating Addition and Subtraction Keywords
Identify words that mean addition (+) or subtraction (-).
Use '+' for words like 'sum', 'total', 'more than', 'increased by', 'added to'. Use '-' for words like 'difference', 'less than', 'decreased by', 'subtracted from'. Be careful with 'less than' – the order often reverses!
Rule 2: Translating Multiplication and Division Keywords
Identify words that mean multiplication ($\times$ or juxtaposition) or division ($\div$ or /).
Use '$\times$' or write numbers next to variables (e.g., 3x) for words like 'product', 'times', 'of', 'twice', 'multiplied by...
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A student translated 'six less than one-third of a number is one' as `6 - (n/3) = 1`. What is the primary error in their translation?
A.They used division instead of multiplication for 'one-third'.
B.They reversed the terms in the subtraction.
C.They wrote an equation instead of an expression.
D.They should have used parentheses around `6 - n`.
Challenging
The equation `(x + 6) / 2 = 11` represents a word problem. Which of the following word problems could it represent?
A.Six more than half a number is eleven.
B.Half of a number is added to six, giving eleven.
C.number is added to six, and the result is multiplied by two to get eleven.
D.When the sum of a number and six is divided by two, the result is eleven.
Challenging
Consider the equations: (1) `2x + 10 = 30` and (2) `2(x + 10) = 30`. Which statement accurately describes the difference in the word problems they represent?
A.Equation (1) represents 'ten more than twice a number,' while equation (2) represents 'twice the sum of a number and ten.'
B.Equation (1) represents 'twice the sum of a number and ten,' while equation (2) represents 'ten more than twice a number.'
C.Both equations represent 'ten more than twice a number.'
D.Both equations represent 'twice the sum of a number and ten.'
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free