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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.

That's Interesting! - Steve Risberg
Algebra, difficulty level 3. Two men follow different strategies for saving money. Who winds up with more? ... more>>

That's Some Sequence! - Terry Trotter
Algebra, difficulty level 4. Find the product of 3 terms of an unusual sequence. ... more>>

The Coordinate Carousel - Steve Risberg
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>>

The Great Northern Triathlon - Steve Risberg
Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the given information to determine how fast he snowshoes. ... more>>

Three Consecutive Integers - Annie Fetter
Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers. ... more>>

The Three Jelly Bean Jars - Terry Trotter
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>>

Throw It Down! - Steve Risberg
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>>

Tiffany's Triumphs - Terry Trotter
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>>

Time Trial Triumphs - Steve Risberg, Terry Trotter, and Annie Fetter
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>>

To B or Not To B - Steve Risberg
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>>

To Grandmother's House We Go - Ethel Breuche
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>>

Touchdown Toddlers - Terry Trotter
Algebra, difficulty level 2. Two little boys run an unusual race on a professional football field, and everybody comes out a winner! ... more>>

Triangle Possibilities - Steve Risberg
Algebra, difficulty level 2. Given information about side lengths of a triangle, determine possible dimensions. ... more>>

Triangle Probability - Annie Fetter
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>>

A Triangle's Area - Canadian Open Math Challenge 1999 via Tim Lang
Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area. ... more>>

Triangular Number Identities - Terry Trotter
Algebra, difficulty level 3. Prove two famous theorems of ancient number theory: the sum of any two consecutive triangular numbers is a square number, and the product of 8 and any triangular number, increased by 1, is a square number. ... more>>

Tribonacci - Terry Trotter
Algebra, difficulty level 3. Find the second and third terms of a "Tribonacci" sequence. ... more>>

Tribonacci Tribulation - Steve Risberg
Algebra, difficulty level 2. Given data describing a tribonacci sequence, find a missing number in the sequence. ... more>>

Trick-or-Treat Box - Terry Trotter
Algebra, difficulty level 1. Harvey and his classmates make trick-or-treat boxes in math class and use a special formula to find the volumes. ... more>>

Two by Canoe - Annie Fetter
Algebra, difficulty level 3. Figure out what time Tashawn and Forrest need to start back downstream after paddling upstream for two days if they need to meet Forrest's mother at 4 pm on the third day. ... more>>

Two for Two - Annie Fetter
Algebra, difficulty level 3. Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? ... more>>

Two for Two More - Annie Fetter
Algebra, difficulty level 3. Two numbers have a ratio of 4:3. The greater number is 60 more than 8 times their difference. What could the two numbers be? ... more>>

Two Ladders - Terry Trotter
Algebra, difficulty level 2. Find the lengths of two ladders, then find their "differences." ... more>>

The Unhappy Carpenter - Ethel Breuche
Algebra, difficulty level 1. A carpenter agrees to be paid a certain amount of money when she works, and to repay money on the days she doesn't work. Find the number of days she worked if she earned $77.00. ... more>>

Up the Down Elevator - Ethel Breuche
Algebra, difficulty level 2. Juanita has to use a freight elevator to deliver packages but can use the passenger elevator to return. What is her average speed for the entire trip? ... more>>

Valentine Candy - Ethel Breuche
Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twenty-five-cent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit? ... more>>

The Variable Rectangle - Terry Trotter and Friends
Algebra, difficulty level 1. Increase a rectangle's width and decrease its length each by 1 and the area is decreased by 4. But decrease its width by 1 and increase its length by 2, and the area is increased by 16. What's the area of the original rectangle? ... more>>

A Variable Triangle - Steve Risberg
Algebra, difficulty level 4. Given a triangle with side lengths of x + 2, x + 3, and 11, what can we conclude about x? ... more>>

Vexing Variables - Steve Risberg
Algebra, difficulty level 3. Use two algebraic statements involving three variables to find the numeric value of the ratio of two of those variables. ... more>>

Voter Turnout - Steve Risberg
Algebra, difficulty level 2. A group of students collected data on voter turnout for the recent election and plotted graphs broken down by age groups. Can you match each age group with its graph? ... more>>

Walter's Weird Wages - Terry Trotter
Algebra, difficulty level 2. Walter's eccentric parents give their son his housework wages in a strange way. Can you determine how much he receives? ... more>>

The Way the Crazy Crow Flies - Janet Bowers
Algebra, difficulty level 3. A crazy crow flies back and forth between two trains that are approaching each other on parallel tracks. How far does the crow fly? ... more>>

Weighing Kittens - Terry Trotter
Algebra, difficulty level 2. Given some facts, figure out how many ounces each of seven kittens weighs. ... more>>

The Weight of Bart's Brick - Terry Trotter
Algebra, difficulty level 1. Bart was asked by his construction foreman about the weight of a brick. Bart's answer befuddled his boss. (But not you.) ... more>>

What's My Angle? - Terry Trotter
Algebra, difficulty level 3. Using concepts of vertical angles and supplementary angles, solve two quadratic expressions to find the measure of a given angle. ... more>>

What's My Line? - Terry Trotter
Algebra, difficulty level 1. Given a set of eight points in the Cartesian plane, find the three that are collinear. ... more>>

What's the Difference? - Steve Risberg
Algebra, difficulty level 3. Does multiplying a number by four always give you a greater number than you started with? ... more>>

What's the Point? - Steve Risberg
Algebra, difficulty level 3. Find all points on a given line such that they are a specified distance from two points in the plane. ... more>>

What's the Score? - Terry Trotter
Algebra, difficulty level 2. Find the final score of the football game between the Falcons and the Bears. ... more>>

What's the Temperature - Annie Fetter
Algebra, difficulty level 1. At what temperature do you get the same answer, regardless of whether you use the Fahrenheit or the Celsius scale? ... more>>

What's what? - Terry Trotter (author unknown)
Algebra, difficulty level 2. A poetical puzzle to ponder about: "What is WHAT?" ... more>>

What Time Is It? - Steve Risberg
Algebra, difficulty level 3. Determine the angle between the hands of a clock at certain times, and find the times that generate a particular angle. ... more>>

Winter Gold - Terry Trotter
Algebra, difficulty level 2. Given some clues, figure out how many gold medals were won by each country. ... more>>

The World's Meanest Math Teacher - Bill Graham
Algebra, difficulty level 3. Students seated around a circular table are being systematically eliminated. What's the rule to follow to be the last one eliminated? ... more>>

Wreck Tangle - Steve Risberg
Algebra, difficulty level 2. When the width of a given rectangle is tripled and the length is doubled, the perimeter increases by 92 cm. Find the area of the original rectangle. ... more>>

X Marks the Spot - Terry Trotter
Algebra, difficulty level 3. A Spanish pirate buries his treasure on an island in a very mathematical manner. Can you locate the "X" spot? ... more>>

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