Algebraic Expressions (Grade 6)

Examples, solutions, videos, and lessons to help Grade 6 students learn how to use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Common Core: 6.EE.6

Suggested Learning Targets

• I can use variables to represent numbers.
• I can write expressions to solve real-world problems.
• I can recognize that a variable can represent an unknown number, or, depending on the scenario/situation, any number in a specific set.
• I can relate variables to a context.
• I can write expressions when solving a real-world or mathematical problem.
  

Constructing Expressions (6.EE.6)
Examples:

1. I have x pencils. You have 10 more pencils than me. What is an expression for the number or pencils you have?
2. Nathan has 8 times as many goldfish as Akko, who has G goldfish. How many goldfish does Nathan have?
   
3. You have m mandarin oranges to divide equally among 9 people. How many oranges will each person get?
   
4. For a political campaign, you are gathering signatures. You get paid $30/day plus $3/signature. What’s an expression for the amount you earn in a day in which you gather s signatures?
   
5. The temperature of a liquid is 200 degrees and is dropping 2 degrees per minute. What is an expression for the temperature after m minutes?

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Translating words into algebraic expressions
Translate words and expressions into algebraic expressions involving variables.

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Writing Algebraic Expressions
This video discusses writing algebraic expressions by turning words into math using real-world examples, or word problems.
Examples:

1. From the time of her 13th to 14th birthday, Sarah gained 10 lbs. If she weighed x lbs. on her 13th birthday, how much does she weigh on her 14th birthday?
   
2. On her 14th birthday, Sarah compared her weight to the weight of her older brother and found that he weighed twice as much. Write an expression for the weight of Sarah’s older brother.
   
3. A certain skyscraper in New York City is z feet. Write an expression for the height of the skyscraper in inches.

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Writing Algebraic Expressions
Examples:

1. The surface of a table is a rectangle with width w inches and length l inches. Write an expression for the area of the surface of the table.
   
2. 5 inches were cut off both width and length of the table. Write an expression for the area of the surface of the table after being cut.
   
3. A family of 6 is going out to the movies. The price of a ticket is different for children and adults. The price for an adult ticket is x, while the price of a child’s ticket is y. If there are 2 adults and 4 children, how much does the family pay for tickets?

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Write an algebraic expression
Write an algebraic expressions for a give phrase or sentence.

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Creating Algebraic Expressions from Word Problems
Example:
At a garage sale hardcover books sold for $1.05 and paperback books sold for $0.85.
a) Create an algebraic expression for the total income.
b) Evaluate the expression if 8 hardcover and 15 paperback books are sold.

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