SamizdatMath

This is a set of 90 puzzles (30 at each level) of Advanced "Square Knot" Puzzles focused on practicing problems solving for 1st through 3rd graders using addition and subtraction. The format is the same as other square knot puzzles, with larger numbers. Why you should try these: One of the things that we should be emphasizing from the very earliest of ages is mathematics as problem solving. This is more than writing a bunch of word problems: problem solving is about using various techniques for

Do you want to know what the problem is with all that math you think you're "teaching?" It's missing something, and no, it's not "standards," or "aims" or "concision" or cryptocurrency. No, it's missing something far more important. Your math is missing "ambiguity." Let's look at how your textbook is probably teaching area and perimeter. It probably states the definition, and then gives a bunch of cruddy problems where you calculate the area and perimeter of a bunch of rectangles and then moves

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

There is no cutesy kids or animals in this activity; it focuses on the math without distraction. This is an activity where children practicing using the "count up" and "count down" activity to make change from whole dollar amounts ($1, $2, $3, and in denominations up to $20.) It is designed to replicate the "real life" experience of giving change when the buyer has a non-whole dollar total. It also gives students practice in making change using coins, or combinations of bills and coins. The goa

This is the one and only collection of "MadHard" 'puzzlas' that I have been collecting, editing and finally, answering for more than a decade. Each one is designed to test the mathematical meddle of your kids, from 3rd through 8th grade. Are they hard? Oh, some are sooooo hard that they even stumped mathematicians! Others are a little less hard, but they're all pretty unique and fun and the contexts are nothing like you've ever seen before. Here are some examples: • A cute baby dressed as a tac

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 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

Here's a very uncomfortable fact: it takes 4 pounds of potatoes to make 1 pound of potato chips. That means that for every 1 pound bag of potato chips you eat, 3 pounds of potatoes have to be thrown away. What a waste of food! This is a series of activities that looks at the hidden world of food waste. It includes a look at how much food is wasted as it is "processed" into finished products like french fries and potato chips. It also includes mathematical activities where students calculate how

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%

This is a set of activities designed to introduce students to a technique for finding the number of paths on a matrix from corner to another. In the beginning problems, students are permitted to use any technique they like, including the "brute force" method of tracing each and every path. Fortunately, for the first couple of problems, this is too confusing, but as the grid gets larger and larger, there are more and more paths to trace, which can get very confusing. From here, a new technique i

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 the most carefully and completely documented use of the "The Handshake Problem" (also known as the "Glass Clink Problem") that you can find. It spans 5 days worth of lessons, homework assignments, enrichment and an assessment. The beauty of the "handshake problem" is that it can be looked at as a way to represent a problem visually through the use of points and connecting edges, but it can be investigated as a sequence of triangular numbers. This is then be compared to other types of seq

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

Let's do the math: there are 10, count 'em, 10 different investigations here, all wrapped up in one neat package. They are themed around the applications of percents. Each one highlights a different feature of percents that your students should know about in order to be good consumers and astute citizens of this democracy. Here is what you'll get: • It's a Deal: Many stores offer "buy one, get the second half off." This activity looks at what the percentage off in each case, and asks students

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....)