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Equations

The problems included here often can be solved using multiple methods, but students can be encouraged to try an algebraic approach which includes equations.
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Algebra and Expressions
The closest match in our Ask Dr. Math archives:
Middle School: Equations
NCTM Standards:
Algebra Standard for Grades 68
Access to these problems requires a Membership.

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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The Big Picture!
 Judy Ann Brown

PreAlgebra, difficulty level 3. A picture is enlarged to four times its area.
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Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
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Building Fences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
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Car Rental Quandary
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the car rental deals using the given information.
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Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
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Coin Count
 Roya Salehi and Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank.
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Commuting Conundrum
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
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A Cranberry Craving
 Claire Mead, Suzanne Alejandre

PreAlgebra, difficulty level 2. Use the pattern to find out how many cranberries Carissa ate on
Thanksgiving Thursday.
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Dishwasher Discounts
 Pat Hagan

PreAlgebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal.
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Ducky Promenade
 Leon Roland & class (poetry by Annie Fetter)

PreAlgebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
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Duke is Missing
 Judy Ann Brown

PreAlgebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke?
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The Graduating Class
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class.
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A Holiday Gift for Grandmother Brown
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the cost of the dishwasher and the contribution from each of five children.
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Join Us for a Quarterpound Burger
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Work with fractions and percents to help plan this cookout.
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Kaytee's Contest
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Use clues to figure out how much Kaytee's cows weigh.
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Lemonade Fun
 Maria Fung and her students

PreAlgebra, difficulty level 2. How many cups of each size lemonade did Jose and Nick sell?
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Membership Boom!
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school.
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Mirror Musing
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
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The Most Appealing Nose Contest
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the amount of money raised for the Humane Society by the Student Council.
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The Nutty Squirrel
 Alice Miller

PreAlgebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel?
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Olympic Temperature
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the difference in temperatures between Sydney, Australia at 14 degrees Celsius and Swarthmore, Pennsylvania, U.S.A. at 63 degrees Fahrenheit.
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Peeling Potatoes
 Terry Trotter

PreAlgebra, difficulty level 2. How many potatoes did Annie and Steve have to peel?
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Pi Day Treats
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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Seating Arrangements
 Judy Ann Brown

PreAlgebra, difficulty level 3. Four new students arrive in Mrs. Brown's homeroom. After a few minutes she turns to them and says, "There are 1680 ways
that you can sit in the empty seats." How many empty seats are there in the room?
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Shapes Rock
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
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Sharing Birthday Cake
 Ian Underwood

PreAlgebra, difficulty level 2. Ian and his father have the same birthday, and share a cake based on the ratio of their ages. Determine when Ian will get certain amounts of cake.
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Spring Garden Planning
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
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A Stellar Garden
 Bill Marthinsen

PreAlgebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
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Study Hall Games
 Judy Ann Brown

PreAlgebra, difficulty level 4. I polled the students to find out which of the three games in my closet they might like to play. Then I created a math problem using the results of the poll.
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Threedimensional Television
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
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Unknown Numbers
 Suzanne Alejandre and Lillian Ray

PreAlgebra, difficulty level 2. Use the four equations to figure out which numbers the quadrilateral
and the circle
represent.
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Valley Springs Snow Cream
 Kelly Crisp

PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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