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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.

Johnny's Orchards - Terry Trotter
Algebra, difficulty level 3. Johnny Appleseed plants three rectangular orchards of various shapes. If each orchard holds the same number of seeds, how many seeds did he plant? ... more>>

The Joke - Steve Risberg
Algebra, difficulty level 1. A joke circulates the Internet via email, with each recipient forwarding it on to 8 friends. Find a formula to represent the number of emails sent out at any stage of the forwarding, and use your formula to answer some questions. ... more>>

Judy and Jen's Garden Problem - Terry Trotter
Algebra, difficulty level 2. Judy and her daughter Jen make up math problems while working in their vegetable garden. ... more>>

Kristina's Code - Suzanne Alejandre & Steve Weimar
Algebra, difficulty level 1. Use the four equations that Kristina wrote to figure out her two unknown numbers. ... more>>

Laser Tag - Steve Risberg
Algebra, difficulty level 3. Help Karsten determine where he needs to shoot his laser in order to hit his friend Jorge in a game of laser tag. ... more>>

The Length of Larry's Rectangle - Larry Sue
Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him? ... more>>

Let It Snow! - Steve Risberg
Algebra, difficulty level 3. Use the given statements to determine how many clear days there were in a recent span of snowy days. ... more>>

Letter Jackets - Steve Risberg
Algebra, difficulty level 4. A company makes jackets that show support for your school. Given information on the time needed to make each of two models and the profit earned for selling them, determine how many of each the company should make each day to maximize the profit. ... more>>

Lettuce for Sale - Ethel Breuche
Algebra, difficulty level 1. Using a linear equation, determine the number of heads of lettuce sold on Monday. ... more>>

Lieutenant Stone's Troops - Terry Trotter
Algebra, difficulty level 2. Find the number of soldiers, performing in a formal military ceremony, who were marching in various rectangular arrangements. ... more>>

Line Logic - Steve Risberg
Algebra, difficulty level 1. Given five statements, find an equation of a line that makes four of the statements true and one false. ... more>>

Lost in Mathland - Steve Risberg
Algebra, difficulty level 2. Zach and Zeke get separated while hiking in Mathland, where roads are named with equations. Zeke is at the intersection of three roads - can you help Zach determine where he is? ... more>>

Louis And Boris Get Even - Ethel Breuche
Algebra, difficulty level 2. After taking their respective hormone pills, Louis is growing and Boris is shrinking. How long will it take before they become the same height? ... more>>

Lucie and Daryl's Bike Ride - Terry Trotter
Algebra, difficulty level 2. A sister and brother who ride bikes provide us with a math challenge concerning distance, rate, and time. ... more>>

Make the Save! - Steve Risberg
Algebra, difficulty level 1. A hockey goalie has saved 112 out of 131 shots so far this season. How many consecutive shots does she need to save to raise her save percentage to .900? ... more>>

Making Triangles - Steve Risberg
Algebra, difficulty level 4. The lengths of three segments are represented by (n + 2)^2, 9, and n(n + 5). Determine for what values of 'n' these three segments can be used to form a triangle. ... more>>

Many or Money? - Steve Risberg
Algebra, difficulty level 3. Help the Student Council decide how much to charge for tickets to the concert. ... more>>

Marathon Mitch - Terry Trotter
Algebra, difficulty level 2. Mitch runs a road race and increases speed twice during the race. Given his total finishing time, determine his standard running rate. ... more>>

Marsha's Triangle - Marsha Hurwitz
Algebra, difficulty level 3. Find the area of an isosceles triangle whose two legs are on the x and y axes and whose hypotenuse passes through the point (c,d). ... more>>

Math Club Mystery - Steve Risberg
Algebra, difficulty level 2. Given information about the total number of people, ticket prices, and money spent, determine how many students, teachers, and parents went on the Math Club field trip. ... more>>

Math on the Midway - Steve Risberg
Algebra, difficulty level 1. Can you win the carnival midway math game by finding a pattern in the numbers? ... more>>

Maxwell's Mowing - Terry Trotter
Algebra, difficulty level 1. Maxwell mows rectangular lawns by mowing around the rectangle, leaving a smaller rectangle. If the lawn is 200 feet by 120 feet, how wide a swath has he mowed so far if his mower runs out of gas 1/4 of the way through? ... more>>

The Mensa Toy Store - Terry Trotter
Algebra, difficulty level 2. The prices are strange in this store. Can you decipher them? ... more>>

Midpoint Magic - Terry Trotter
Algebra, difficulty level 4. Connecting the midpoints of a general quadrilateral yields a special new four-sided figure. What is it? ... more>>

Milly Miffin's Muffins - J. A. H. Hunter
Algebra, difficulty level 2. Milly Miffin et al. are muffin makers extraordinaires, and they make muffins mathematically, too. The question is, how many? ... more>>

Mind Reading - Annie Fetter
Algebra, difficulty level 1. Use variables to show how a number-based "magic trick" works. ... more>>

Missing Angle Mystery - Terry Trotter
Algebra, difficulty level 2. Help Detective Sam Spade solve a robbery of valuable polygons from Mrs. Hempstead's famous collection. ... more>>

Motorcycle Daredevil - Terry Trotter
Algebra, difficulty level 4. A motorcycle stunt person needs some math equation work to calculate her most daring feat: jumping between ramps at high speeds. ... more>>

Mr. Cramer's Cousins - Terry Trotter
Algebra, difficulty level 3. Find the ages of two young men by using Cramer's Rule to solve a system of linear equations. ... more>>

Mr. Fachtore's Gardens - Steve Risberg
Algebra, difficulty level 1. Mr. Fachtore has decided to plant two gardens this year - one rectangular and one square. Given algebraic expressions for the areas of the gardens, find algebraic expressions for their dimensions. ... more>>

Mr. Green's Birthday - Ethel Breuche
Algebra, difficulty level 1. Mr. Green has a birthday but will not tell his age directly. Can you figure out his age based on the clues? ... more>>

Music Survey - Ethel Breuche
Algebra, difficulty level 2. Students were surveyed about their favorite music groups. Some liked Hole, others U2, and still others Third Eye Blind. Given all the clues, how many students were surveyed, how many preferred only U2, and how many liked exactly two of the groups? ... more>>

My Bag of Marbles - Terry Trotter
Algebra, difficulty level 2. Find the probability of drawing a blue marble after additional marbles have been placed in a bag. ... more>>

My Grandfather's Clock - Ethel Breuche
Algebra, difficulty level 3. Listening to the chimes, what would be the longest time I would have to wait to be sure of exactly what time it was? ... more>>

The Mystery Quadrilateral - Annie Fetter & Dr. Math
Algebra, difficulty level 2. Three consecutive sides of a quadrilateral are 2, 6, 9, and x. If the diagonals are perpendicular, what's x? ... more>>

My Three Dogs - Terry Trotter
Algebra, difficulty level 2. Given information about the weights of three pairs of dogs, figure out the dogs' individual weights. ... more>>

Number, Please! - Terry Trotter
Algebra, difficulty level 4. Given two telephone calling plans, find the point at which the monthly bills would be the same. ... more>>

The Operations Grid - Annie Fetter
Algebra, difficulty level 2. Use variables to explore whether this grid works for the four basic operations. ... more>>

Operation Warm-up - Annie Fetter
Algebra, difficulty level 2. Find all possible ordered pairs that are solutions to four given equations. ... more>>

Painting Partners - Terry Trotter
Algebra, difficulty level 1. Two house painters combine their skills and talents to make short order of a painting job. ... more>>

Paper and the Moon - Ethel Breuche
Algebra, difficulty level 4. Students need to express their answers in scientific notation and know how to work in the metric system as well as do conversions to answer this paper-tearing problem. ... more>>

Parakeets on Parade - Terry Trotter
Algebra, difficulty level 2. A flock of parakeets flies a round trip to the feeding ground and back. Given the total time and distance of the round trip, and the speed of the wind in each direction, find the flying speed of the parakeets. ... more>>

Partners in Pizza - Terry Trotter
Algebra, difficulty level 2. Three friends share the cost of a pizza. How much does each contribute? ... more>>

Peanuts and Cashews - Terry Trotter
Algebra, difficulty level 1. Find the proper mixture of nuts that have a certain price rate to be sold in the nut store. ... more>>

Perfect Apples - Melissa Kennedy
Algebra, difficulty level 2. Of 6000 apples, we have some that are too small, some too green, and others that are bruised. How many are perfect apples? ... more>>

Phone-O-Graph Phollies - Bill Graham
Algebra, difficulty level 2. Students are asked to use algebra to compare three telephone calling plans to determine at what number of calls each plan would be preferable. ... more>>

A Phone-y Deal? - Steve Risberg
Algebra, difficulty level 2. Compare two cell phone pricing plans to determine for how many minutes of calls per month each one is the better deal. ... more>>

Pizza Puzzle - Steve Risberg
Algebra, difficulty level 1. Given two pricing examples, determine a general equation for the cost of a Giordano's Giant gourmet pizza. ... more>>

Polynomial Power - Steve Risberg
Algebra, difficulty level 3. Given the value of one variable expression, can you use it to find the value of others? ... more>>

Polynomial Puzzler - Steve Risberg
Algebra, difficulty level 2. Given four polynomials, find an expression that uses each of them once, involves multiplication, addition and subtraction, and results in a given binomial when simplified. ... more>>

Poolish Pride? - Steve Risberg
Algebra, difficulty level 3. Two competitive brothers build rectangular pools of similar shape but different size. Given some information relating the lengths and widths, find the area of the larger pool. ... more>>

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