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Browse all Algebra Problems of the Week

Participation in the Algebra Problems of the Week allows teachers and students to address the NCTM Problem Solving Standard for Grades 9-12, enabling students to build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; and monitor and reflect on the process of mathematical problem solving.

For background information elsewhere on our site, explore the High School Algebra area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Basic Algebra in our Internet Mathematics Library.


Access to these problems requires a Membership.

2002 Is Sum Year! - Terry Trotter
Algebra, difficulty level 4. Find an arithmetic sequence the sum of whose terms is 2002. ... more>>

A 2-for-1 Lunch - Marsha Hurwitz
Algebra, difficulty level 2. Two boys had lunch on a two-for-one coupon, plus taxes and tips. What was their percent of savings on the transaction? ... more>>

The ABC's of Exponents - Steve Risberg
Algebra, difficulty level 3. Solve a system of equations involving exponents. ... more>>

'Ace' Trotter - Terry Trotter
Algebra, difficulty level 1. A problem from the sports world regarding free-throw percentages. ... more>>

Adrienne's Axel - Leslie Hogben
Algebra, difficulty level 2. Adrienne, an algebraically inclined figure skater, figures an interesting problem for us. ... more>>

The Ages of Sigma - Terry Trotter
Algebra, difficulty level 1. Find the ages of the three artists who make up the latest singing sensation: Sigma. ... more>>

All Wet - Linda Benton
Algebra, difficulty level 3. Solve simultaneous equations, find area, and use the Pythagorean theorem and percentages to find the spraying distance needed for a circular sprinkler in a rectangular yard. ... more>>

Alvin's Theorem - Terry Trotter
Algebra, difficulty level 2. Alvin notices that the difference between any two consecutive square numbers can also be expressed as the sum of consecutive integers. Can you use algebra to show that this pattern is always true? ... more>>

Ancestors - Steve Risberg
Algebra, difficulty level 2. Find how many ancestors Gene had from various generations going back in time. ... more>>

Ant Race - Terry Trotter
Algebra, difficulty level 1. Two ants race to a piece of food. Your task is to figure out how far apart they were when the race started. ... more>>

Apple Orchard - Steve Risberg
Algebra, difficulty level 2. How many of each kind of apple did the Nomial family pick? ... more>>

Approval Method of Voting - Ethel Breuche
Algebra, difficulty level 3. In the country of Algpoweria, eligible voters can cast their votes for two candidates. Based on the clues given, find how many votes each candidate received and the number of eligible voters. ... more>>

Are We There Yet? - Terry Trotter
Algebra, difficulty level 1. Given what fractions of a car trip have been completed at two different times, can you predict when the trip will end? ... more>>

Are You Positive? - Steve Risberg
Algebra, difficulty level 3. Find all values of x that make a rational expression have a positive value. ... more>>

Are You Ready for Some Football? - Steve Risberg
Algebra, difficulty level 2. The Algenauts football team racked up 229 yards rushing in their first game. Given descriptions of how many yards each of the players ran for in relation to each other, determine the exact yardage each one had. ... more>>

As the Crow Flies - Terry Trotter
Algebra, difficulty level 1. A percentage of crows sitting on a telephone line leaves, then returns. Find how many crows are present at the end. ... more>>

At Least This Many - Terry Trotter
Algebra, difficulty level 2. Using two data points from the NBA statistics chart, form an equation (y = mx + b style), then use it to predict other data points. ... more>>

An "Average" Problem - Terry Trotter
Algebra, difficulty level 2. Three test grades are removed from a set of scores. You are given the new set's average and a ratio involving the scores removed. What scores have been removed? ... more>>

Baffling Brother - Steve Risberg
Algebra, difficulty level 2. Brandon wows his sister by having her choose a secret number and make a series of calculations, then telling her what her final answer is. Can you use variables and algebra to explain how Brandon did it? ... more>>

Battle of the Bands - Terry Trotter
Algebra, difficulty level 3. Students at Rahkenrole High School vote to decide which band should play at the end-of-year dance. After some students change their minds about which band to vote for, the result is a tie. Can you figure out how many students voted? ... more>>

Blowin' in the Wind - Steve Weimar Steve Risberg
Algebra, difficulty level 3. A plane flies a round-trip on a calm day and then flies the same trip on a windy day. How do the flying times compare? ... more>>

The Bouncing Ball - Steve Risberg
Algebra, difficulty level 1. A ball is dropped from 27 feet and bounces back to 2/3 of the height from which it fell. Find and use a formula to calculate the height of the nth bounce. ... more>>

Bowling Buddies - Steve Risberg
Algebra, difficulty level 2. Four friends go bowling and have a small contest. From the clues given about their scores, can you determine who won the contest? ... more>>

Bowl-O-Rama! - Steve Risberg
Algebra, difficulty level 1. Given information about the number of games two people bowled and how much each paid, determine the cost of bowling at Bowl-O-Rama. ... more>>

Boxes of Cereal - Steve Weimar
Algebra, difficulty level 2. Lily and Mikey consume their boxes of cereal at different rates. Use the hints to determine how much cereal is in each child's box. ... more>>

The Box Supper - Terry Trotter
Algebra, difficulty level 3. Find the amount of money that Judy Ann's "beau" paid at the box supper auction for her box of delicious food. ... more>>

Break the Code! - Steve Risberg
Algebra, difficulty level 1. Can you factor the polynomials and use the factors to decipher the secret message? ... more>>

Bugs Bunny's Money - Terry Trotter
Algebra, difficulty level 2. Find how much Mr. Bugs Bunny is carrying in a money bag, given clues such as the ratio of coins that are pennies and the percentage of coins that are dimes. ... more>>

Building a Bakery - Steve Risberg
Algebra, difficulty level 3. Find the best place to build the bakery so that the delivery miles to the stores are minimized. ... more>>

Bull's-eye Probability - Ethel Breuche
Algebra, difficulty level 3. Find the probability of hitting a circular target board closer to the center. ... more>>

Burger Inflation? - Annie Fetter, Terry Trotter, Steve Risberg, and Steve Weimar
Algebra, difficulty level 2. Given the affect of inflation, is a national-chain hamburger cheaper or more costly than it was in 1970? ... more>>

Buried Treasure - Steve Risberg
Algebra, difficulty level 3. The pirate Algebeard has drawn an unusual treasure map. Can you determine where his treasure is buried? ... more>>

Buy This Tune! - Terry and NCTM's WLME
Algebra, difficulty level 2. Using data about buying habits of music lovers from 1990 and 1996, predict the results for 2000 and compare those predictions to the actual data. ... more>>

Calendar Calculations - Steve Risberg
Algebra, difficulty level 1. Write variable expressions for dates in a calendar pattern and use your expressions to explore a numeric relationship among those dates. ... more>>

Calling Long Distance - Terry Trotter
Algebra, difficulty level 1. Use simple equations to compare two telephone calling plans. ... more>>

Capture the Flag! - Steve Risberg
Algebra, difficulty level 4. Help the Algebra and Geometry classes at Mathland High find the equation of a perpendicular bisector to fairly divide the woods for their game of Capture the Flag. ... more>>

Carlita's CD Collection - Terry Trotter, Steve Risberg
Algebra, difficulty level 2. Carlita describes how many CD's are in her collection in a rather mathematical way. Can you figure out how many there are? ... more>>

Cheap Sunglasses - Steve Risberg
Algebra, difficulty level 2. Help Gilbert figure out if his idea for making cheap sunglasses with filter film will work. ... more>>

Cherokee Creek Checkers Club - Terry Trotter
Algebra, difficulty level 1. Until one month ago, the Checkers Club had won 40 of 90 matches so far this year. But last month they won 3 of every 5 games they played. How many games did they play last month if their overall winning percentage is now 52%? ... more>>

The Chip Swap Game - Ethel Breuche
Algebra, difficulty level 4. The object of this game is to swap the positions of the different colored chips. Count the number of moves and, as you increase the number of chips, find the general formula. ... more>>

Choosing Charity - Steve Risberg
Algebra, difficulty level 2. A company donates to a relief fund by giving a certain amount plus an additional amount for each employee who decides to donate. Given two data points, find the linear equation that defines the company's part of the total donation. ... more>>

The Christmas Gifts - Terry Trotter
Algebra, difficulty level 2. A grandfather doles out his annual Christmas gifts to his beloved grandchildren in a most unusual way - mathematical, of course. ... more>>

A Coat of Golden Angels - Terry Trotter
Algebra, difficulty level 1. Show how to do scientific notation problems on an 8-digit, four-function calculator. ... more>>

The Continued Fraction - Ethel Breuche
Algebra, difficulty level 4. Find the value of a given continued fraction. ... more>>

Copying Conundrum - Annie Fetter
Algebra, difficulty level 1. Using a copy machine, copy an 8 x 10 inch picture at 80%. Then copy the copy at 80%, and repeat this until you have 5 copies of the original. What's the largest dimension now? What's a formula you could use? ... more>>

Count Your Change - Steve Risberg & Terry Trotter
Algebra, difficulty level 3. I have three times as many nickels as dimes in my pocket. If the number of coins is reversed, by what percent will the value of the money in my pocket increase? ... more>>

Crossed Wires - Steve Risberg
Algebra, difficulty level 3. Guy wires support two poles of different heights. Find the height of their intersection and explore what happens as the distance between the poles changes. ... more>>

The Custom of Customs - Ethel Breuche
Algebra, difficulty level 2. Two wine merchants enter Paris with their merchandise. They need to pay custom duties. Each pays with francs and with some casks of wine. What is each cask of wine worth and what is the duty on each cask? ... more>>

A Day at the Fairs - Terry Trotter via Kraitchik & Chuquet
Algebra, difficulty level 2. A merchant went selling and buying at three city fairs. Did he make a profit or take a loss? ... more>>

Diego's Building Block - Terry Trotter
Algebra, difficulty level 3. Find the surface area of a rectangular prism, given the volume and information about the dimensions. ... more>>

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