Digit Sum Game

The digit sum game is for two players, or two teams, if you want to have a team collaborate to come up with their play. Players/teams take turns picking a digit from 1-9. Once picked, a digit cannot be used … Continue reading

Box method for multiplying polynomials


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In algebra, most students are taught FOIL for multiplying binomials. It is an application of the distributive law of multiplication, but specifically limited to multiplying binomials. For example, What if we are multiplying more than two binomials, or polynomials that … Continue reading

Casting out nines


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A whole number is divisible by nine if the sum of n's digits is divisible by nine. In fact, we can make the stronger statement that the remainder when we divide by 9 is the same as remainder when the … Continue reading

Human binary computer


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As part of introducing binary arithmetic in the classroom, I use volunteers to create a human digital computer. We start with simple operations, and work our way up. Getting physically involved and watching your classmates makes it interesting, but I … Continue reading

Mechanical sorting

I found this among the many gems in Mathematics: A Human Endeavor. The trick uses sixteen special numbered cards. Each card has a combination of holes and slots. These are used to sort the cards by inserting a paper clip … Continue reading

Divergent sums


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By time you complete high school math, you've probably encountered the idea of convergent sums, such as The idea is often presented with a story such as Zeno's paradox about Achilles and the tortoise. As the number of summed terms … Continue reading

Numbers, big and small


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Number Two: Why not use your knowledge of the future to play the stock markets? We could make trillions. Dr. Evil: Why make a trillion when we could make... billions? The modern world presents us with numbers of unimaginable scale. … Continue reading

Sam Loyd's Paradoxical Dissection


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Print this pdf, and cut out the four pieces. Can you arrange them into a square? How about a rectangle? What's up with that? … Continue reading

Arrows

In the grid below, you can click or shift-click arrows. Can you fully describe what happens (or doesn't happen) when you click/shift-click an arrow? Is it possible to get all four corners pointing in different directions? Is it possible to … Continue reading

Super-elasticity and infinite series


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Physics problems are often greatly simplified for new students. We assume negligible friction and perfectly elastic collisions. In some problems, the assumption of negligible friction might be reasonable. But students have a harder time understanding what perfectly elastic looks like. … Continue reading