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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.
-
The Professors' Primes
- Terry Trotter
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Algebra, difficulty level 2. Find the product of three prime numbers that three professors pick.
... more>>
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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.
... more>>
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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.
... more>>
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Radical Rectangle
- Steve Risberg
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Algebra, difficulty level 2. Solve a quadratic equation to find the area of a rectangle, expressing
your answer in simplified radical form.
... more>>
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Reciprocals
- Steve Risberg
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Algebra, difficulty level 3. Explore the numeric difference between numbers and their reciprocals.
... more>>
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Reverse It!
- Annie Fetter Steve Risberg
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Algebra, difficulty level 1. Find a two-digit number such that when you reverse the digits and add
the new number to the original one, the sum is 154.
... more>>
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Rocket Science
- Steve Risberg
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Algebra, difficulty level 1. Given the initial velocity of a model rocket, determine at what time
the rocket attains a certain height.
... more>>
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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.
... more>>
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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?
... more>>
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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?
... more>>
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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.
... more>>
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Sam and Teri's Bank Accounts
- Terry Trotter
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Algebra, difficulty level 1. Sam and Teri have bank accounts. Sam always withdraws money; Teri always saves it. When will they have equal balances, or will they?
... more>>
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School Spirit
- Steve Risberg
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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>>
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September Squares
- Cynthia Lanius and Steve Risberg
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Algebra, difficulty level 2. Use a variable to explain how you can be given the sum of four dates
that form a block on a calendar and determine what the four dates must be.
... more>>
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A Sequence of Numbers
- Asher Walkover
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Algebra, difficulty level 2. Find the second number in a Fibonacci-like series.
... more>>
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Shanell's Holiday Treats
- Terry Trotter
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Algebra, difficulty level 3. Given some data about purchasing fancy nuts for cooking, find the total cost of buying one pound of each type.
... more>>
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Ships Ahoy!
- Terry Trotter
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Algebra, difficulty level 1. One-third of a fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were later lost in a storm. The 24 remaining ships sailed home. How many ships were there before the engagement?
... more>>
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Skeeball Showdown
- Steve Risberg
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Algebra, difficulty level 3. Kira and Daquan each play a game of Skeeball to see who gets the
higher score. Given descriptions of their results in relation to each
other, determine the final score of their match and how many balls
each player rolled.
... more>>
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A Space Diagonal
- Terry Trotter, MATHCOUNTS
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Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
... more>>
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Spell It Out
- Steve Risberg Annie Fetter
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Algebra, difficulty level 2. A word-find problem exploring how sets of points that form lines can
be described by written sentences. An introduction to linear equations
that sets the stage for the standard y = mx + b form.
... more>>
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The Spider and the Fly
- J. A. H. Hunter
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Algebra, difficulty level 2. A spider presents a challenge to a fly: solve a math problem and escape!
... more>>
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The Spiral on the Can
- Ethel Breuche
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Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can.
... more>>
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Splash!
- Steve Risberg
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Algebra, difficulty level 1. How many throws did it take each student to sink Mr. Rashanul in the
dunking booth at the carnival?
... more>>
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Splitting a Square
- Terry Trotter
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Algebra, difficulty level 3. A square is drawn on a coordinate plane with vertices P(1, 0), Q(2, 0), R(2, 1) and S(1, 1). A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1. What's the equation of the "cutting" line?
... more>>
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The Sprats
- Terry Trotter & Lisa Lavelle
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Algebra, difficulty level 2. The Sprats go out to dinner three times, and at each meal they order a different combination of two of their three favorite dishes. Given the bill for each meal, determine how much the Sprats' favorites cost individually.
... more>>
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The Straggler Shakes Hands
- Melissa Kennedy, Susan Rose, Ethel Breuche
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Algebra, difficulty level 3. There were one hundred forty-one handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers.
... more>>
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Studying the Standings
- Steve Risberg
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Algebra, difficulty level 3. Write and solve a system of equations to determine how many points the
Potters have in the World Tiddlywinks League standings.
... more>>
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Sums, Quotients, and Remainders
- Terry Trotter
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Algebra, difficulty level 3. Given the sum of two numbers and information about the quotient and
remainder when they are divided, find the larger number, then
solve the same sort of problem in a general case.
... more>>
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A Surprising Sequence
- Steve Risberg
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Algebra, difficulty level 2. In a Fibonacci sequence, the first number is 1 and the tenth number is
111. Find the second number.
... more>>
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Susita's Savings Account
- Terry Trotter
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Algebra, difficulty level 2. Find the original balance in Susita's savings account.
... more>>
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A Tale of Two Intercepts
- Terry Trotter
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Algebra, difficulty level 3. Find the distance between two y-intercepts.
... more>>
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Taxi!
- Steve Risberg
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Algebra, difficulty level 1. Taxi fares in Lineville are based on a linear equation. Given the
costs and distances of two rides, find the equation and use it to
answer several questions.
... more>>
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Teeter-Toddlers
- Steve Risberg
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Algebra, difficulty level 1. Two kids of different weights balance on a seesaw. How far from the
center is each one sitting?
... more>>
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Teeter Trio
- Steve Risberg
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Algebra, difficulty level 1. Find a function that expresses where a child sits on a seesaw in terms
of her weight.
... more>>
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Teeter Troop
- Steve Risberg
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Algebra, difficulty level 3. Four animals are balancing a seesaw. Can you determine how much each
one weighs?
... more>>
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Tele-Plus
- Terry Trotter
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Algebra, difficulty level 1. Find the cost of one phone that is part of a three-in-one communications package deal.
... more>>
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Tennis Anyone?
- Ethel Breuche
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Algebra, difficulty level 1. Use algebra, inequalities, and ratios to find the greatest number of matches a player could have won before the weekend to achieve the win ratio of .503 after the weekend.
... more>>
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That's Interesting!
- Steve Risberg
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Algebra, difficulty level 3. Two men follow different strategies for saving money. Who winds up
with more?
... more>>
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That's Some Sequence!
- Terry Trotter
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Algebra, difficulty level 4. Find the product of 3 terms of an unusual sequence.
... more>>
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The Coordinate Carousel
- Steve Risberg
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Algebra, difficulty level 3. Mrs. Nomial is watching her daughters on the carousel and notices
something interesting. Determine how far away from the edge of the
carousel she is standing.
... more>>
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The Great Northern Triathlon
- Steve Risberg
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Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the
given information to determine how fast he snowshoes.
... more>>
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Three Consecutive Integers
- Annie Fetter
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Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers.
... more>>
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The Three Jelly Bean Jars
- Terry Trotter
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Algebra, difficulty level 2. Three brothers buy jelly beans. The jelly beans are in jars that are three different sizes. How many jelly beans does each brother buy?
... more>>
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Throw It Down!
- Steve Risberg
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Algebra, difficulty level 3. Kelvin leaps high to dunk a basketball. How long are his hands high
enough above the rim for him to dunk?
... more>>
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Tiffany's Triumphs
- Terry Trotter
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Algebra, difficulty level 1. Given the number of games that Tiffany has played so far and the number that she has won, how many games would she have to win in a row to get her winning percentage up to 60%?
... more>>
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Time Trial Triumphs
- Steve Risberg, Terry Trotter, and Annie Fetter
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Algebra, difficulty level 2. At 9:05 a.m. Ernesto starts riding at a speed of 440 yards per
minute. At 9:20 a.m. Johnny starts riding, but he's going 20% faster
than his little brother. At what time, to the nearest minute, will
Johnny catch Ernesto?
... more>>
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To B or Not To B
- Steve Risberg
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Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the
ratio of B's to total letters in the nth term.
... more>>
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To Grandmother's House We Go
- Ethel Breuche
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Algebra, difficulty level 4. Red Riding Hood goes to visit Grandmother for the holidays at the same time that Grandmother heads out to visit Red. What is the ratio of their speeds?
... more>>
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Touchdown Toddlers
- Terry Trotter
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Algebra, difficulty level 2. Two little boys run an unusual race on a professional football field, and everybody comes out a winner!
... more>>
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Triangle Probability
- Annie Fetter
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Algebra, difficulty level 3. A point is randomly selected from within a triangle with vertices at (0,0), (0,4) and (6,0). What is the probability that the x-coordinate of the selected point is less than the y-coordinate?
... more>>
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