Math Forum - Problems Library - Pre-Algebra, Algebra: Equations

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Pre-Algebra
operations with numbers
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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 6-8

Access to these problems requires a Membership.

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

The Big Picture! - Judy Ann Brown
Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area. ... more>>

Boxes of Stationery - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery? ... more>>

Building Fences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence. ... more>>

Car Rental Quandary - Judy Ann Brown
Pre-Algebra, difficulty level 3. Compare the car rental deals using the given information. ... more>>

Club Competition - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition. ... more>>

Coin Count - Roya Salehi and Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank. ... more>>

Commuting Conundrum - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar. ... more>>

A Cranberry Craving - Claire Mead, Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use the pattern to find out how many cranberries Carissa ate on Thanksgiving Thursday. ... more>>

Dishwasher Discounts - Pat Hagan
Pre-Algebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal. ... more>>

Ducky Promenade - Leon Roland & class (poetry by Annie Fetter)
Pre-Algebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem. ... more>>

Duke is Missing - Judy Ann Brown
Pre-Algebra, 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? ... more>>

The Graduating Class - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class. ... more>>

A Holiday Gift for Grandmother Brown - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the cost of the dishwasher and the contribution from each of five children. ... more>>

Join Us for a Quarter-pound Burger - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with fractions and percents to help plan this cookout. ... more>>

Kaytee's Contest - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use clues to figure out how much Kaytee's cows weigh. ... more>>

Lemonade Fun - Maria Fung and her students
Pre-Algebra, difficulty level 2. How many cups of each size lemonade did Jose and Nick sell? ... more>>

Membership Boom! - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school. ... more>>

Mirror Musing - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is. ... more>>

The Most Appealing Nose Contest - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to determine the amount of money raised for the Humane Society by the Student Council. ... more>>

The Nutty Squirrel - Alice Miller
Pre-Algebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel? ... more>>

Olympic Temperature - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Peeling Potatoes - Terry Trotter
Pre-Algebra, difficulty level 2. How many potatoes did Annie and Steve have to peel? ... more>>

Pi Day Treats - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... more>>

Seating Arrangements - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Shapes Rock - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides. ... more>>

Sharing Birthday Cake - Ian Underwood
Pre-Algebra, 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. ... more>>

Spring Garden Planning - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden. ... more>>

A Stellar Garden - Bill Marthinsen
Pre-Algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden. ... more>>

Study Hall Games - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Three-dimensional Television - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook. ... more>>

Unknown Numbers - Suzanne Alejandre and Lillian Ray
Pre-Algebra, difficulty level 2. Use the four equations to figure out which numbers the quadrilateral and the circle represent. ... more>>

Valley Springs Snow Cream - Kelly Crisp
Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream. ... more>>

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