# 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 = bh12
- interest: I = prt
- distance: d = rt

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## 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

- Two more than a number

- Eight less than the number of flowers

- The cost of twelve books

- The number of hours in k days

- Twice the cost of a pen

- Timmy's age twenty years ago

- Three fourths of my pencils

- A third of the students

- Three degrees less than the current temperature

- The number of legs on n sheep

- The price of a car discounted by $200

- The total number of dogs and cats

- The product of the length and the width

- The sum of the base and the height

- 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

- Twice the number of chairs

- The product of a number and seven

- The value of n nickels, in cents

- The value of n nickels, in dollars

- All but five of the people

- some amount less than 20

- The number of calories in a banana and an apple combined

- The ratio of boys to students

- The difference between the larger and the smaller number

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

- One fifth of my score

- Ralph's age thirty-five years ago

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

- The price of an item, after 5% inflation

- 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

- The area of a rectangle, if the length is 5

- The perimeter of a rectangle, if the width is 10

- The distance traveled by a car in 20 hours

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

- The area of a triangle with base of length 12

- The perimeter of a rectangle, if the length is 18

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

- The difference between the length and the width of a rectangle

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

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

- Two less than the perimeter of a rectangle

- n more than the area of a rectangle

## Algebraic Expressions Worksheet #1.3: Answer Key

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