Exponents

Using multiplication and addition try to create the target number using the least number of ones. For example… to get to the number 12, you could do (1+1+1+1)*(1+1+1) or (1+1+1+1+1)*(1+1)+1+1 but the first solution is better since it uses only seven ones. This is good for elementary school.

Now we’ll try it using addition and exponents, but not multiplication. Which pair of operators is fastest? This is good for older students.

Give your students practice working with bases and exponents while in pursuit of the answers to bigger questions. In this video you will explore three such… including the infamous Polignac Conjecture:

Polignac Conjecture – Sometimes mathematicians make strong conjectures that can be disproven easily by tenacious middle school students. This is true of the humiliating Polignac Conjecture.

Give your students practice working with Pythagoras. One of MathPickle’s best classroom puzzles. In the newest version Theseus always starts in the upper left and the minotaur is always lurking in the lower left. If Theseus fails to find the Minotaur he dies is ignominy – lost in the labyrinth!

Downloadable this file with the last two pages printable.

Rainbow Squares is a challenge inspired by Henri Picciotto. Each rainbow arc needs to be anchored at two integers that sum to a square. Here we have tried to find a solution for 1-10, but have failed because the last two numbers, 2 and 3, do not sum to a square. Is this possible?

Downloadable Rainbow Square puzzle-sheets here.

1-10 did not work. It was impossible. However, 1-26 does work. Complete the two puzzles on the left. Spoiler alert: the next page will give the answers.

Solution to the previous slide.

Another pair of puzzles with the solution on the next page...

Solution to the previous slide.

Here I've failed with 1-60 because the remaining numbers, 21 and 22, do not add to a square. Even though there are over 4 million solutions to this it took me more than an hour to find one! Computers are reliably good at these kind of brute force searches. I choose not to tell students how good computers are because everyone wants to feel awesome when they solve something difficult - not be told that a computer found 4 million solutions in one second. It is a matter of our human pride 😉

Prime Number Catacombs

Jump in and explore this dangerous cave system with any group of students learning binary notation.

Give your students practice working with the addition of square roots and Pythagoras.

Download printable puzzles here.

Ballast Puzzles have students identify two warships that can be made to float and one that will sink no matter what exponential measures are taken to try to save her.

Scientific Notation Notrivia

(MathPickle, 2010)

Practice Scientific Notation with in a trivia game. Each question will ask you to place an unknown length in relationship to two other known lengths. Have a mini-competition in class...

The game on the left is where you should start. It is for the microscopic world. Then move on to the human world (middle), and finally to the world of the big universe (right).