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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.
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Home-Made Valentine Card
- Terry Trotter
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Algebra, difficulty level 2. Reuben expresses his affection for his girlfriend by making his own Valentine's Day card, described mathematically.
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Homer Jones
- Terry Trotter
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Algebra, difficulty level 3. Find the area of a certain triangle laid out on a baseball field.
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How High Is Enough?
- Terry Trotter
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Algebra, difficulty level 3. A right triangle is formed by stretching flexible elastic "legs" sufficiently high. How high must that be?
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Humphrey's Great Escape
- Bill Graham
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Algebra, difficulty level 3. Calculate Humphrey's running speed as he tries to outrun a train across a trestle.
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Humphrey's Phone Number
- Bill Graham
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Algebra, difficulty level 3. Figure out Humphrey's 10-digit phone number given various clues about the divisibility of parts of his number.
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Illuminating Lines
- Annie Fetter
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Algebra, difficulty level 2. Match up statements, equations, and sets of points on coordinate planes.
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It's the Law!
- Terry Trotter
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Algebra, difficulty level 3. Explain the two most important laws of exponents, as a good teacher or book might do.
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Jack and Jill Go Jogging
- Terry Trotter
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Algebra, difficulty level 2. Two famous Mother Goose characters take up aerobics, running at some numerical speeds while exercising. How fast can each one jog?
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Jimmy's Hits
- Terry Trotter & Annie Fetter
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Algebra, difficulty level 2. Given information about how many doubles, homers, and singles, figure out how many total hits Jimmy had during his record-breaking season.
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Judy and Jen's Garden Problem
- Terry Trotter
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Algebra, difficulty level 2. Judy and her daughter Jen make up math problems while working in their vegetable garden.
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Kristina's Code
- Suzanne Alejandre & Steve Weimar
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Algebra, difficulty level 1. Use the four equations that Kristina wrote to figure out her two unknown numbers.
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The Length of Larry's Rectangle
- Larry Sue
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Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him?
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Lettuce for Sale
- Ethel Breuche
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Algebra, difficulty level 1. Using a linear equation, determine the number of heads of lettuce sold on Monday.
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Lieutenant Stone's Troops
- Terry Trotter
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Algebra, difficulty level 2. Find the number of soldiers, performing in a formal military ceremony, who were marching in various rectangular arrangements.
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Louis And Boris Get Even
- Ethel Breuche
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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?
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Lucie and Daryl's Bike Ride
- Terry Trotter
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Algebra, difficulty level 2. A sister and brother who ride bikes provide us with a math challenge concerning distance, rate, and time.
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Marsha's Triangle
- Marsha Hurwitz
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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).
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Maxwell's Mowing
- Terry Trotter
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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?
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The Mensa Toy Store
- Terry Trotter
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Algebra, difficulty level 2. The prices are strange in this store. Can you decipher them?
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Midpoint Magic
- Terry Trotter
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Algebra, difficulty level 4. Connecting the midpoints of a general quadrilateral yields a special new four-sided figure. What is it?
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Milly Miffin's Muffins
- J. A. H. Hunter
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Algebra, difficulty level 2. Milly Miffin et al. are muffin makers extraordinaires, and they make muffins mathematically, too. The question is, how many?
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Missing Angle Mystery
- Terry Trotter
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Algebra, difficulty level 2. Help Detective Sam Spade solve a robbery of valuable polygons from Mrs. Hempstead's famous collection.
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Motorcycle Daredevil
- Terry Trotter
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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.
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Mr. Cramer's Cousins
- Terry Trotter
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Algebra, difficulty level 3. Find the ages of two young men by using Cramer's Rule to solve a system of linear equations.
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Mr. Green's Birthday
- Ethel Breuche
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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?
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Music Survey
- Ethel Breuche
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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?
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My Bag of Marbles
- Terry Trotter
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Algebra, difficulty level 2. Find the probability of drawing a blue marble after additional marbles have been placed in a bag.
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My Grandfather's Clock
- Ethel Breuche
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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?
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My Three Dogs
- Terry Trotter
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Algebra, difficulty level 2. Given information about the weights of three pairs of dogs, figure out the dogs' individual weights.
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Number, Please!
- Terry Trotter
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Algebra, difficulty level 4. Given two telephone calling plans, find the point at which the monthly bills would be the same.
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The Operations Grid
- Annie Fetter
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Algebra, difficulty level 2. Use variables to explore whether this grid works for the four basic operations.
... more>>
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Painting Partners
- Terry Trotter
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Algebra, difficulty level 1. Two house painters combine their skills and talents to make short order of a painting job.
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Paper and the Moon
- Ethel Breuche
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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.
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Partners in Pizza
- Terry Trotter
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Algebra, difficulty level 2. Three friends share the cost of a pizza. How much does each contribute?
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Peanuts and Cashews
- Terry Trotter
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Algebra, difficulty level 1. Find the proper mixture of nuts that have a certain price rate to be sold in the nut store.
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Perfect Apples
- Melissa Kennedy
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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?
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Phone-O-Graph Phollies
- Bill Graham
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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.
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Porky Pig's Popcorn Diet
- Terry Trotter
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Algebra, difficulty level 4. Porky is put on a special diet plan so that he can enjoy his favorite snack: POPCORN!
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Presidential Approval Rating
- Ethel Breuche
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Algebra, difficulty level 3. Students were given a questionnaire. Only 60 percent of the students answered, and of those 55 percent said they approved of the President. What is the maximum number of students who approved of the President?
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The Price of Pollo
- Terry Trotter
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Algebra, difficulty level 2. Use a linear equation model to predict a future price of fried chicken.
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Probability on the Board
- Ethel Breuche
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Algebra, difficulty level 3. On a 6 x 6 grid, what is the probability that a marker starting at (0,0) will pass through (3,3) when moved either north or
east?
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A Product-Plus-1
- Terry Trotter
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Algebra, difficulty level 3. The product of any four consecutive integers, increased by one, is always a square number. Give at least three instances of that statement and prove that this will always occur by finding an algebraic expression for that "square number."
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The Professors' Ages
- Terry Trotter
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Algebra, difficulty level 3. Find the professors' ages to complete the requested calculation.
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The Professors' Primes
- Terry Trotter
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Algebra, difficulty level 2. Find the product of three prime numbers that three professors pick.
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Profits and Lots
- Terry Trotter
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Algebra, difficulty level 1. A person buys some land, keeps some for himself, divides the rest into lots, and sells them, thus making a profit.
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Pythagoras and Y2K
- Terry Trotter
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Algebra, difficulty level 4. Find Pythagorean triples for which this special year, Y2K (2000), is one of the three numbers in the triple.
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Romance by Rowboat
- Terry Trotter
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Algebra, difficulty level 1. Romance on the river motivates a nice upstream-downstream sort of problem.
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Round the World on a Wire
- Terry Trotter
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Algebra, difficulty level 2. A wire is wrapped around the equator of the earth. Then extra wire is spliced in. Can you walk under the slack that results?
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Row, Row, Row Your Boat
- Ethel Breuche
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Algebra, difficulty level 2. Cassie and Mat are sinking fast on their raft. How fast must Cassie bail so that they don't have to swim to shore?
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Sam and Teri Revisited
- Terry Trotter
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Algebra, difficulty level 3. A bank account deposit-withdrawal problem with a difference.
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