Mathematics
Grade 6
15 min
Write variable expressions: word problems
Write variable expressions: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify keywords in word problems that indicate mathematical operations.
Choose appropriate variables to represent unknown quantities.
Translate simple one-step word phrases into algebraic expressions.
Translate multi-step word problems into algebraic expressions.
Understand the difference between a numerical expression and a variable expression.
Check if a written expression accurately represents the given word problem.
Ever wonder how mathematicians turn everyday sentences into powerful math tools? 🤔 It's like decoding a secret message!
In this lesson, you'll learn how to transform word problems into mathematical expressions using variables. This skill is crucial for solving real-world problems and building a strong foundation for future al...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, usually a letter (like x, y, or n), that represents an unknown number or a quantity that can change.In the phrase 'a number increased by 5', 'a number' can be represented by the variable 'n'.
Algebraic ExpressionA mathematical phrase that contains numbers, variables, and operation symbols (like +, -, ×, ÷), but does NOT have an equals sign.`3x + 5` is an algebraic expression.
TermA single number, a single variable, or a product/quotient of numbers and variables. Terms are separated by addition or subtraction signs.In the expression `4y - 7`, `4y` is a term and `7` is a term.
CoefficientThe numerical factor (the number) that is multiplied by a variable in a term.In the term `6z`, `6` is the coefficient.
ConstantA term in...
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Core Formulas
Addition Keywords
`a + b`
Use for words like 'sum', 'total', 'added to', 'more than', 'increased by', 'plus'.
Subtraction Keywords
`a - b`
Use for words like 'difference', 'less than', 'subtracted from', 'decreased by', 'minus', 'fewer than'. Be careful with the order for 'less than' and 'subtracted from'.
Multiplication Keywords
`a \times b` or `ab`
Use for words like 'product', 'times', 'multiplied by', 'of' (especially with fractions/percentages), 'twice', 'triple'.
Division Keywords
`a \div b` or `\frac{a}{b}`
Use for words like 'quotient', 'di...
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Challenging
Which word problem could be represented by the expression `2c + 5`?
A.The total cost of 5 items that each cost `c` dollars.
B.The total cost of one item for $2 and another for `c` plus $5.
C.The total cost of 2 items that each cost `c` dollars, plus a $5 fee.
D.The total cost of 5 items that each cost $2, plus a fee of `c` dollars.
Challenging
A taxi service charges a $3 flat fee plus $2 for every mile driven. Which expression represents the total cost for a ride of `m` miles?
A.3m + 2
B.3(m + 2)
C.5m
D.2m + 3
Challenging
The problem is 'Triple the difference between a number `n` and 4'. A student writes `3n - 4`. This is incorrect. Why?
A.The student confused 'triple' with 'three more than'.
B.The coefficient should be placed after the variable.
C.The student did not use parentheses to group 'the difference' before multiplying.
D.The order of subtraction is wrong.
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