Recommended Investigations

The Last Digit: Given a number raised to a large power, find the ones digit of the expansion.

36 Divisibility: Explore some numbers divisible by 36.

Planning Cruises: Determine three different length cruises that will leave on the same day.

Minimizing Products: Find two positive integers with a given sum and who have the smallest product.

Difference of Squares: Find positive integers which can be written as sum or difference of squares.

Fibonacci Extended: Find the relationship between two terms of a Fibonacci sequence.

Squares and Differences: Determine the relationship of the squares of three consecutive integers.

Want to be a Millionaire?: If a bank doubles your money, how long will it take to become a millionaire.

Average Score: Using test scores and their average, find the missing test scores.

Negative Exponents: Explore the relationship of positive and negative exponents.

Consuming Candy: Determine the cost of packages of gummy bears, caramels, and jaw breakers.

Willing Money: Determine the amount of inheritance each family member receives.

Fair Time: Set up a schedule so that each person plays basketball for the same amount of time.

Salary Schedule: How many total days did a man work?

Scoring the Winning Goal: How many games did the Maple Leafs win, lose, or tie?

Collecting Stamps: Determine how many stamps Jessica has.

Inventory Supplies: How many packages of colored pens is an art-supply store selling?

Consecutive Sum: Given the sum of consecutive numbers, find the least of these numbers.

OOPS! I Subtracted: You know what you get when you multiply and subtract, but what two numbers did you start with?

Greatest Product: Find the greatest possible product of two natural numbers who have a particular sum.

Keeping Pace: How fast do two joggers run?

Save the Princess: Help Princess Stunning find a particular perfect square number.

Blocked Off: Determine how many blocks Jeff has.

Almost a Square: What rectangle can you form that is close to a square?

Choose an Elevator: Determine which of two elevators reaches the lobby first.

Multiples of 72: What is the relationship between two divisors and their product, sum, difference, and quotient?

Three Daughters: Determine the age of each daughter.

Perfecting 90: How can 90 become a perfect square? a perfect cube?

The Frog Race: Two frogs have a race. Determine which frog wins the race.

Double Trouble: Find a number that fits this description.

Hypatia's Triumph: Take on the Egyptian Hypatia's challenge about sums of squares.

Proper Patterns: Given some of the proper factors of a number, what could the number be?

Pages with Digits: How many pages are in the book?

Super Soccer: How many full size soccer teams and how many "short formation" soccer teams will Supertown field?

Double Exponents: Find the power of 2 that is equivalent to a given expression.

Same Base Multiples and Exponents: Find the power of 4 that is equivalent to a given expression.

Four Number Challenge: Does the absolute value of four numbers always lead to zero?

Submit your idea for an investigation to InterMath.