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Algebra

Problems in this category often have multiple entry points. Beginning prealgebra students are encouraged to start using variables, expressions, and equations, but sometimes it might not be their original approach to solve the problem.
Some of these problems are also in the following subcategories:
 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: Algebra
FAQ: Word Problems
Resources from our Teacher2Teacher service:
FAQ: Algebra Help
NCTM Standards:
Algebra Standard for Grades 68
Access to these problems requires a Membership.

Accounting for Age
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given a number trick, explain why the result is always the original number followed by your age.
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Anh's Code
 Annie Fetter

PreAlgebra, difficulty level 2. Decode the five mathematical operations symbolized in three equations, then evaluate an expression.
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Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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Bank Balances
 Stephen Weimar

PreAlgebra, difficulty level 3. Will Tamil and Nydiyah bank balances ever be exactly the same?
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Bartering for Bananas
 Suzanne Alejandre

PreAlgebra, difficulty level 4. How many bananas can Byron get with five fish?
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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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Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
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Cadence
 Lillian Ray

PreAlgebra, difficulty level 3. Determine which friend has the faster cadence.
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Card Covers
 Claire Mead, Annie Fetter

PreAlgebra, difficulty level 1. Help Ellen, Lora, and Mai determine which purchase will cost them the
least amount of
money.
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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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Change Woes
 suggested by a Western Oregon University mentor

PreAlgebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her
brother's?
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Chirp! Chirp!
 Annie Fetter

PreAlgebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute.
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Choosing Cs
 Lisa Lavelle, Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the expression c^2  2, what is the probability that the result
is composite for integers 10 through 2?
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Citius, Altius, Fortius
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Would recordholding speed skaters and runners break the speed limit in a residential zone?
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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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Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
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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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The Complex Apartment Complex
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
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Counting Chicken Wings
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings.
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Covered Bridges
 Steve Risberg, Suzanne Alejandre

PreAlgebra, difficulty level 2. If the sum of three nephews' ages is equal to the driving time of
their trip, find the age of the
youngest nephew.
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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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Distance Driving
 Judy Ann Brown

PreAlgebra, difficulty level 3. Write an expression that will help you determine how long it will take the car to travel any given number of kilometers.
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Dividing Daffodils
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help us plant our garden of daffodils.
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Dollar Dealing
 Suzanne Alejandre and Lillian Ray

PreAlgebra, difficulty level 2. How much money did Hector and Larissa each have?
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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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Election Day in Prealgpoweria
 Steve Risberg, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how
many eligible voters are there?
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Exploring Area
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method.
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Falling into Sequences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula.
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The Gates
 Suzanne and Richard Alejandre

PreAlgebra, difficulty level 3. How much time did Suzanne spend walking on "The Gates" pathway?
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Gearing Up
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
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Getting Your Kicks On Route 66
 Cynthia Lanius, Suzanne Alejandre, Richard Tchen

PreAlgebra, difficulty level 2. If she traveled about 5000 miles, which routes might Lani have driven?
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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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Graphs
 Suzanne Alejandre, Annie Fetter

PreAlgebra, difficulty level 3. Match the descriptions to the graphs. Explain how to find one of the points on each graph and give the labels for the x and yaxes.
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Holding Pattern
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How long should the next outbound leg be?
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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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How Far in Space?
 Suzanne Alejandre

PreAlgebra, difficulty level 1. By the time the Space Shuttle Discovery had undocked from it in
August, 2005, how far
had the International Space Station traveled while orbiting the Earth?
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How Old is Ms. Nelson?
 Judy Ann Brown

PreAlgebra, difficulty level 2. Ms. Nelson claims that she is three times as old as her little sister. However, six years ago she was five times as old as her sister was. How old is Ms. Nelson?
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Integer Images
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Use the four equations to figure out which integers the quadrilateral
and the circle
represent.
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It's A Secret
 Judy Ann Brown

PreAlgebra, difficulty level 2. In this puzzle, your job is to decode the secret message.
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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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Lucky Lollipops
 Suzanne Alejandre & Maria Fung and her students

PreAlgebra, difficulty level 3. Find the number of lollipops Logan the Leprechaun gives away using his "lucky" method.
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Measuring Melons
 Suzanne Alejandre, Claire Mead

PreAlgebra, difficulty level 3. Students determine how much each type of fruit weighs.
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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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Milo's Mile
 Stephen Weimar, Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 2. Use data to describe how the number of minutes it takes Milo to run a
mile changes as his
speed changes.
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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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Mixing Marbles
 Stephen Weimar

PreAlgebra, difficulty level 3. Find how many marbles each person had at the beginning.
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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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Operating Diagonally
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Think about the effect of multiplication and addition on the numbers in the hundreds chart.
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Ostrich Llama Count
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Given the combined number of heads and legs of ostriches and llamas, help Raul and Esteban figure out how many ostriches and how many llamas there are.
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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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Perfect Timing
 Steve Risberg & Stephen Weimar

PreAlgebra, difficulty level 3. Find out what time Eva and Aurora reached the resort.
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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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Prime Probability
 Lisa Lavelle

PreAlgebra, difficulty level 3. Given the expression n^2  5, what is the probability that the result is prime for integers between 2 and 12?
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Quilting Squares
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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Riz's Route
 Richard Tchen & Steve Risberg

PreAlgebra, difficulty level 3. Where is Riz standing when he realizes it would be the same distance to
continue walking
on the longer path as it would be to turn around and take the shortcut?
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Santa's Little Helpers
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves.
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Saturday Bike Ride
 Judy Ann Brown

PreAlgebra, difficulty level 2. Now that spring has arrived, Ali and Maya decide to dust off their bikes and go for a Saturday ride. Help find what time they will meet.
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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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Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
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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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Stina's Hike
 Annie Fetter

PreAlgebra, difficulty level 2. Choose the graph that best represents Stina's hike.
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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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Timber!
 Steve Risberg

PreAlgebra, difficulty level 3. A tree breaks threeeighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree?
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The Tower of Hanoi Puzzle
 Roya Salehi

PreAlgebra, difficulty level 4. Tower of Hanoi: What is the minimum number of moves it will take to transfer 25 disks from one post to another?
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Train Travel
 Annie Fetter & Ian Underwood

PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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Tunnel Time
 Annie Fetter, Ian Underwood, Suzanne Alejandre

PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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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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