SamizdatMath

On September 18th, 2015, New York City standup comedian Matt Little recorded a video of a rat dragging a slice of pizza down the stairs at the First Avenue L train station in Manhattan. On September 21st, Little uploaded the video to his Instagram and YouTube accounts with a bemusing description comparing the rodent to Master Splinter from the Teenage Mutant Ninja Turtles (shown below). Within the first 24 hours, the video garnered over two million views. This is an investigation into the perime

This activity is based on the documented lies told by the Former President of the United States (FoPUS), Donald Trump. Donald Trump is unique in that all his lies were counted and documented by various news outlets, including The Washington Post. This has inspired me to develop an activity to investigate mathematics. In this case, it is the milestone that Trump reached on January 10, 2018, when Trump told his 2,000th lie, as documented by The Washington Post. Update: The Washington Post now re

Back in the 1980s (before most of you were born), the A & W hamburger restaurant chain tried to go head to head with McDonalds' new "quarter pounder" by creating and marketing a "⅓ pound hamburger." It was a spectacular flop. A research company hired to find the source of the problem found out that half of the people surveyed thought that there was less meat in a ⅓ lb. burger than a ¼ lb. burger because, well, "3 is less than 4." The burger was renamed the "Big Papi" and continued to be sold b

This is a seven part investigation into the carbon footprint of different kinds of food and diets. Investigation #1: What We Emit When We Eat: This is a list of 20 different foods, including meats, dairy, vegetables and grains and the amount of carbon released during their production. Students calculate the equivalent in miles driven by a car, as well as the amount of carbon released per ounce. Investigation #2: Students investigate the carbon footprint of three different meals. The first is a s

This is the best investigation you can find anywhere which links exponential growth with paper folding. It includes background information about the investigation, and uses charts and tables to keep track of how tall a piece of paper would be if you folded it in half up to 60 times. The activity works with both customary and metric units and has answer keys for both. This investigation also looks at the formula that was derived by Britney Gallivan, a high school junior who actually proved that

This is an old problem I saw almost 20 years ago: suppose you took two dice and rubbed off the pips (dots) from the faces, and instead put on numbers. How would you number it in such a way that you can roll the two dice and make all the numbers from 1 to 36? This is a wonderful problem to study combinations, patterns and general problem solving techniques. It is "hard" in that you can't calculate your way through it, and the solution evolves slowly as you work through the problem. But the soluti

Here is an interesting fact: did you know that most castles built during the middle ages were made from wood? It's a true fact! But you're probably thinking: wait, if most castles were made of wood, how come when you google the word "castle," all you see are stone edifices? The answer is: survivor bias! Think about it: you build a wood castle, and over the years, what's the thing that threatens it most? FIRE! So all those wood castles burnt to the ground over the last thousand years, while the

This is the fastest and easiest coin practice game you will ever image: print out the coin cards twice, cut and shuffle. Place between two partners. One card is turned over and the two partners call "salute." They each put a card on their own forehead, then add their partner's card to the one showing between them. They call out the answer, then they have to figure out what card is on their own heads based on that information. Comes in basic, hard, muy hard and mas hard!

This is a "bingo" style game where players have to get 5 in a row. Sound pretty boring, right? Well, it ain't. Here's why: instead of just being a "one to one" correspondence game where the teacher calls out some bogus fraction (like, uh, 4/5 = ? %), this is a game where students choose from 4 numbers, create a fraction and then convert that into a percent, and then choose whatever square fulfills that percentage. Except the squares are not all exact percentages: most of them are "between 20%

Howdy you all! You know, one of the things I love about people who don't know much about math is that they think that there's always one right answer to a math question. Well, there isn't: the reality is that most math questions (even seemingly simple ones like "how much is 2 + 2?") have answers like "well, it depends." In the case of "how much is 2 + 2, it depends on the base system you're working in: if it was base 3, then the answer would be 11 (1 group of 3 and 1 remainder), or it it was bas

Did you ever notice how many different types of paper towels they have for sale in the market? It’s not bad enough that there are like 5 different brands, but within each brand there are different types: printed, quilted, “choose a size,” and let’s not forget single ply versus double ply. When you figure that you’ll probably go through one of these rolls each week (maybe even more, if your family is anything like mine) and then year in year out, it’s going to be a lot of money! So I decided to

My school uses Connected Math for it’s 6th grade math curriculum; it’s pretty bad in many ways, but on the other hand, it is much better than all the other 6th grade math curricula I’ve seen, which are complete and unadulterated junk (I’m looking directly at you, Go Math!!) The 6th grade unit on rates and ratios has some pretty good activities in it, but I think the use of gummy worms is pretty lame, because, well, I am a believer in the separation between crappy food and educational matter

This activity uses a classic Abbot & Costello comedy routine to explain the concept of comparing numbers using ratios. This short video, which is available on YouTube, is about 5 minutes long and features a routine by Abbot and Costello where they compare the age of two people using the difference in their age (40 and 10) to create a ratio ("I am 4 times older than the 10 year old) and then re-calculates the ratio after 5 has been added to create 45:15, which is 3:1 when simplified. There is an

This is a very fun and motivating activity that can be done in 1 - 2 class periods, along with homework. It tells the story of an intern at a website who figures out a way to "hack" his burrito to almost twice the size by ordering "half-portions" of items like red and black beans, chicken and beef, and white and brown rice. The activity looks at how hacking each ingredient adds to the weight of the burrito through the number of additional ounces and how those additional ounces can be written as

First of all, let’s get one thing out of the way: Archimedes never used the Greek letter “pi” when he used it to calculate the area and circumference of a circle. No, never; so just by reading this blurb you've learned something new! The point of this activity is threefold: the first is to show that as you double the diameter of a circle, the area of that circle would quadruple. That’s a very important concept, because many of your students have only experienced relationships where if

You've seen photos of these store bloopers around the web, and say to yourself, "you know, this would be great to use in my class...." but you never have the photo, and you never have the time to photoshop out the brands, fix the colors, crop the image and collect it all in one place. Well, it's all been done for you, and only for the magic price of $4.95, which is nothing when you consider there are 20 different "math fails" that range from simple counting (how many nuggets are printed on that

There are three crates. The first contains only apples; the second contains only oranges, and the third contains a combination of apples and oranges. Unfortunately, all the labels on the crates are incorrect. You can take only one piece of fruit from a crate, and may not look inside while you do it. From which crate would you take a piece of fruit to find out where to put the correct labels? A man who owned a winery recently passed away. In his will, he left 21 barrels, seven of which are fille

It's yet another puzzla from the labs of SamizdatMath: believe it or not, this problem originated in Germany, where a convention of mathematicians was convening. A local newspaper called up a dozen of the mathematicians and asked them this question. Out of the 12 mathematicians, only one of them got it correct (the others either got it wrong, or insisted they couldn't do it because it wasn't in their particular field....)

Jacob Lawrence was perhaps the preeminent painter of the Harlem Renaissance. During his lifetime, he produced among the most striking works that depicted everything from the northern migration of African Americans during the 1920s, to the daily life of the community in Harlem. His paintings incorporate many mathematical ideas, including patterns and geometry, as well as ratio and proportion. This activity makes use of a portion of his 1945 painting The Shoemaker to analyze Lawrence's use of dist