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Algebraic Expressions Worksheets 1

Lesson Plans > Mathematics > Algebra > Expressions
 

Algebraic Expressions Worksheets 1

One of the key abilities that a good Algebra student must have is the ability to take an English language statement and convert it into an equation. Before that, however, students must be able to convert phrases into algebraic expressions, since an equation is nothing more than two expressions separated by an equality.

This is a capability that some Algebra books focus on near the beginning of the book, but then don't really review or practice until all of a sudden students are expected to put together complex expressions into equations in word problems. For this reason, I've developed several worksheets for my students, which start with the simplest expressions and gradually increase in complexity. 

Giving one or two of these worksheets each week helps keep the students fresh and practiced. Plus, since none of these problems take very long to do, students can easily pull out a worksheet and putter away at it during the "down" moments of class.

In this first set of worksheets, there are no compound expressions such as "two more than twice a number." Therefore, these are excellent for students just beginning to work with variables. I require my students to write out what each variable represents, and I am very particular about how they write it. For instance, if a problem talks about "Vinnie's age," and a student writes, "v = Vinnie," I say to them, "So Vinnie is a number, huh?" Since Vinnie is, in fact, a person rather than a number, v cannot be Vinnie. The student must write "v = Vinnie's age," since his age is the number which v represents.

The biggest challenge students are likely to face in these worksheets is the phrase "less than," which students have a tendency to interpret backwards: "seven less than n" is n - 7, rather than 7 - n. Usually I'll say to a student, "What is two less than 10?" and when they say "Eight," they'll immediately see that the direction is reversed.

The third worksheet in this set introduces some basic formulas students can use:

  • rectangle area: A = lw
  • rectangle perimeter: P = 2l + 2w
  • triangle perimeter: P = a + b + c
  • triangle area: A =
    1
    2
    bh
  • interest: I = prt
  • distance: d = rt

More Like This

Lesson by Mr. Twitchell

Handouts/Worksheets

Algebraic Expressions Worksheet #1.1

For each phrase below, pick a variable to represent the unknown. State what the variable represents, and then write the phrase as an algebraic expression.

Example:     Vinnie's age in four years
Solution:      v = Vinnie's age; v + 4

  1. Two more than a number

     
  2. Eight less than the number of flowers

     
  3. The cost of twelve books

     
  4. The number of hours in k days

     
  5. Twice the cost of a pen

     
  6. Timmy's age twenty years ago

     
  7. Three fourths of my pencils

     
  8. A third of the students

     
  9. Three degrees less than the current temperature

     
  10. The number of legs on n sheep

     
  11. The price of a car discounted by $200

     
  12. The total number of dogs and cats

     
  13. The product of the length and the width

     
  14. The sum of the base and the height

     
  15. The difference between a number and five

     

Algebraic Expressions Worksheet #1.1: Answer Key

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Algebraic Expressions Worksheet #1.2

For each phrase below, pick a variable to represent the unknown. State what the variable represents, and then write the phrase as an algebraic expression.

Example:     Edna's age n years ago
Solution:      e = Edna's age; n = number of years ago; e - n

  1. Twice the number of chairs

     
  2. The product of a number and seven

     
  3. The value of n nickels, in cents

     
  4. The value of n nickels, in dollars

     
  5. All but five of the people

     
  6. some amount less than 20

     
  7. The number of calories in a banana and an apple combined

     
  8. The ratio of boys to students

     
  9. The difference between the larger and the smaller number

     
  10. The total value of Sid's nickels and Willis's dimes, in cents

     
  11. One fifth of my score

     
  12. Ralph's age thirty-five years ago

     
  13. Izzie's age in months, if she is n years old

     
  14. The price of an item, after 5% inflation

     
  15. Seventeen less than my score

     

Algebraic Expressions Worksheet #1.2: Answer Key

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Algebraic Expressions Worksheet #1.3

For each phrase below, pick variables to represent the unknowns. State what the variables represents, and then write the phrase as an algebraic expression.

Example:     The perimeter of a triangle with one side equal to 5
Solution:      a = a side; b = another side; a + b + 5

  1. The area of a rectangle, if the length is 5

     
  2. The perimeter of a rectangle, if the width is 10

     
  3. The distance traveled by a car in 20 hours

     
  4. The interest earned if the principal is $1000, and the rate is 0.03

     
  5. The area of a triangle with base of length 12

     
  6. The perimeter of a rectangle, if the length is 18

     
  7. The perimeter of a triangle, if two sides have lengths 12 and 13

     
  8. The difference between the length and the width of a rectangle

     
  9. The interest on a five-year loan, if the rate is 0.05.

     
  10. the distance traveled by a rocket which travels at a speed of 1200 mph

     
  11. Two less than the perimeter of a rectangle

     
  12. n more than the area of a rectangle

     

Algebraic Expressions Worksheet #1.3: Answer Key

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