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Pre-Algebra
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Pre-Algebra
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Pre-Algebra
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Algebra
Problems in this category often have multiple entry points. Beginning pre-algebra 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 6-8

Access to these problems requires a Membership.

Accounting for Age - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given a number trick, explain why the result is always the original number followed by your age. ... more>>

Anh's Code - Annie Fetter
Pre-Algebra, difficulty level 2. Decode the five mathematical operations symbolized in three equations, then evaluate an expression. ... more>>

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

Bank Balances - Stephen Weimar
Pre-Algebra, difficulty level 3. Will Tamil and Nydiyah bank balances ever be exactly the same? ... more>>

Bartering for Bananas - Suzanne Alejandre
Pre-Algebra, difficulty level 4. How many bananas can Byron get with five fish? ... 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>>

Buying Cola - Leon Roland & class
Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy? ... more>>

Cadence - Lillian Ray
Pre-Algebra, difficulty level 3. Determine which friend has the faster cadence. ... more>>

Card Covers - Claire Mead, Annie Fetter
Pre-Algebra, difficulty level 1. Help Ellen, Lora, and Mai determine which purchase will cost them the least amount of money. ... more>>

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

Change Woes - suggested by a Western Oregon University mentor
Pre-Algebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her brother's? ... more>>

Chirp! Chirp! - Annie Fetter
Pre-Algebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute. ... more>>

Choosing Cs - Lisa Lavelle, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the expression c^2 - 2, what is the probability that the result is composite for integers -10 through -2? ... more>>

Citius, Altius, Fortius - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone? ... 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>>

Coding Conundrums - Mary DeYoung & class
Pre-Algebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle. ... 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>>

The Complex Apartment Complex - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above. ... more>>

Counting Chicken Wings - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings. ... more>>

Covered Bridges - Steve Risberg, Suzanne Alejandre
Pre-Algebra, 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. ... 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>>

Distance Driving - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Dividing Daffodils - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils. ... more>>

Dollar Dealing - Suzanne Alejandre and Lillian Ray
Pre-Algebra, difficulty level 2. How much money did Hector and Larissa each have? ... 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>>

Election Day in Prealgpoweria - Steve Risberg, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how many eligible voters are there? ... more>>

Exploring Area - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method. ... more>>

Falling into Sequences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula. ... more>>

The Gates - Suzanne and Richard Alejandre
Pre-Algebra, difficulty level 3. How much time did Suzanne spend walking on "The Gates" pathway? ... more>>

Gearing Up - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

Getting Your Kicks On Route 66 - Cynthia Lanius, Suzanne Alejandre, Richard Tchen
Pre-Algebra, difficulty level 2. If she traveled about 5000 miles, which routes might Lani have driven? ... 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>>

Graphs - Suzanne Alejandre, Annie Fetter
Pre-Algebra, 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 y-axes. ... more>>

Holding Pattern - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How long should the next outbound leg be? ... 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>>

How Far in Space? - Suzanne Alejandre
Pre-Algebra, 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? ... more>>

How Old is Ms. Nelson? - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Integer Images - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use the four equations to figure out which integers the quadrilateral and the circle represent. ... more>>

It's A Secret - Judy Ann Brown
Pre-Algebra, difficulty level 2. In this puzzle, your job is to decode the secret message. ... 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>>

Lucky Lollipops - Suzanne Alejandre & Maria Fung and her students
Pre-Algebra, difficulty level 3. Find the number of lollipops Logan the Leprechaun gives away using his "lucky" method. ... more>>

Measuring Melons - Suzanne Alejandre, Claire Mead
Pre-Algebra, difficulty level 3. Students determine how much each type of fruit weighs. ... 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>>

Milo's Mile - Stephen Weimar, Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use data to describe how the number of minutes it takes Milo to run a mile changes as his speed changes. ... 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>>

Mixing Marbles - Stephen Weimar
Pre-Algebra, difficulty level 3. Find how many marbles each person had at the beginning. ... 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>>

Operating Diagonally - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Think about the effect of multiplication and addition on the numbers in the hundreds chart. ... more>>

Ostrich Llama Count - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

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

Perfect Timing - Steve Risberg & Stephen Weimar
Pre-Algebra, difficulty level 3. Find out what time Eva and Aurora reached the resort. ... more>>

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

Prime Probability - Lisa Lavelle
Pre-Algebra, difficulty level 3. Given the expression n^2 - 5, what is the probability that the result is prime for integers between 2 and 12? ... more>>

Quilting Squares - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design. ... more>>

Riz's Route - Richard Tchen & Steve Risberg
Pre-Algebra, 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? ... more>>

Santa's Little Helpers - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves. ... more>>

Saturday Bike Ride - Judy Ann Brown
Pre-Algebra, 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. ... 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>>

Seesaw - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw? ... 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>>

Stina's Hike - Annie Fetter
Pre-Algebra, difficulty level 2. Choose the graph that best represents Stina's hike. ... 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>>

Timber! - Steve Risberg
Pre-Algebra, difficulty level 3. A tree breaks three-eighths 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? ... more>>

The Tower of Hanoi Puzzle - Roya Salehi
Pre-Algebra, 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? ... more>>

Train Travel - Annie Fetter & Ian Underwood
Pre-Algebra, difficulty level 2. At what time does the end of the train emerge from the tunnel? ... more>>

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