SamizdatMath

Cuisenaire Rods and Algebra, you ask? Yes, Cuisenaire Rods AND Algebra go together! Like beans and cornbread, rods and algebra go together! Rods and algebra go hand in hand like bagels and lox. Like cornbeef and cabbage. Like pot cakes and molasses! Like liver onions, so do Cuisenaire Rods and Algebra! Like wieners and sauerkraut, you need to use Cuisenaire Rods and Algebra! Has this convinced you? Okay, here's how it works: one of the things that consistently trips up our algebra students in

Here's the problem: There are 100 seats on an airplane and 100 people waiting to get on. The first person loses their boarding pass, so they take a random seat on the plane. If the next person finds their seat occupied, they take another random seat. If their seat is free, they sit in it. Question: What is the probability that the 100th person on the plane will sit in their assigned seat? Oh, sure, you can look up the answer and come up with some convoluted or excessively mathematical explanati

This is an approach to teaching the geometric concepts of complementary, supplementary and exemplary (also known as conjugal) angles through groupwork and problem solving using non-standard examples. This makes this activity different from anything else you’re likely to see anywhere. Why is this? Because most curricula treat this important topic as one where students see some examples, solve some lame-o problems related to them, and then more on. No thought is given about how to make this intere

This is an activity that teaches students to classify acute, obtuse, straight and right angles using semaphore flag signals. Why semaphore flag signals? Because they're fun, interesting and "real." And also, they're a good example of how to teach a concept beyond the "prototypes." What do I mean by this? Well, do an image search on "right angle" and you'll see that the examples that show up are "textbook prototypes." That is, they all have a side resting on the horizontal, the other on the verti

Here’s a nice little “take home” activity that develops both visual spatial skills, mathematical vocabulary AND it's really fun! Here’s how it works: print out the puzzles and challenge booklet on card stock (or laminate before cutting out...) and have your kids cut them out. The kids cut out the “clue cards” and have kids write clues about the different puzzles. Then they can share their cards and look at one another’s clue cards, find the shape it is describing and use the puzzle pieces to “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

Teach your students the importance of ratios and unit rates.

This is a collection of ten different four-step mysteries where students have to work backwards (if you'll pardon the pun...) Instead of just taking a number and rounding it off to the nearest hundredth, tenth and unit (which is just soooooo boring and unproductive), the student is given the following clues about a "mystery number" • When rounded off to the nearest unit, the number is 0. This indicates that the number could be anywhere between 0 and .499 - it the number was .5 or above, it w

This is the same as Number Logic Puzzles Silly Creatures with a winter theme, which should really motivate your students! This is a fun little booklet that your students can put together in about 3 minutes and we’ll really give them some fun working logically - and because this is something you purchased from me, your kids will also have a chance to make their own puzzles to share with one another. Ain’t that cool? Comes in b//w and color booklets - the color booklets have been formatted to g

This is a winter themed variation of Silly Creatures Number Logic Puzzles, a fun little booklet that your students can put together in about 3 minutes and features 2 kinds of objects to decipher. This version involves three different objects to interpret, which will really give them something fun to do and most likely fry their brains by working logically - and because this is something you purchased from me, your kids will also have a chance to make their own puzzles to share with one another.

Note: this is the same as the "winter theme three part number logic puzzles," but with "silly icons" instead of "winter icons." This is a sequel to Silly Creatures Number Logic Puzzles, a fun little booklet that your students can put together in about 3 minutes and features 2 kinds of objects to decipher. This version involves three different objects to interpret, which will really give them something fun to do and most likely fry their brains by working logically - and because this is somethin

Here’s a set of puzzles that will promote the use of “backwards thinking.” That is, the technique is to look at where you want to “end” and then work backwards step by step in order to get to the beginning. Some people refer to this as “guess and check,” but that is incorrect: that technique involves putting in possible solutions and then starting from the beginning to see if the solution is correct. Eh, no, that’s not quite the way it works.In working backwards, you get to the beginning by work

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

This is an investigation where your students design, cut out and fold different networks in order to determine which ones will become a cube. Students are introduced to the concept of a network, learn how it can be used to form different types of polyhedra, and then investigate different ways (there are 11) to create a 2-D net that can be folded into a cube. Students then take the "working" and "non-working" nets and sort them onto a sheet, then compare their properties. There is also an activi

This is an activity I’ve done with my 5th, 6th and 7th graders to help them understand the importance of “thinking” before rounding off a number. You know, some of us (not you, of course) teach rounding as a “rule” and our students blindly go off rounding numbers without thinking about the implication of doing so. These two activities are designed to impress upon your students that when they round off a number, they should do it with a certain amount of forethought, because if they blindly follo

This is an activity that I used as a kind of “warm-up” to a unit on fractions with my 5th graders; I wanted to relate fractions to ratios, as well as see what the classes had remembered from the previous year. I gave out this activity, put the students in dyads (that’s groups of 2, for those of you who have forgotten their Greek, it means students work in pairs of 2.) They complete the activity sheet and then write up a summary of their findings, which they post on a wall. You can use this acti

Did I ever tell you that I design amazing assessments? Everybody says so: they are the best assessments you've ever seen. The other assessments you've seen? They're a disaster. Sad. This is a percent assessment that is unlike any that you have ever done. First, it requires your students to use scissors! Second, there are very few "clean" numbers (that is, exact numbers) because, well, life is NEVER exact! Third, it assesses on concepts and skill AND problem solving, so your students have to in

These are four puzzles that explore the issue of parity, which has to do with the "evenness" and "oddness" of a number. The first two puzzles involve "visual parity," which has to do with how two colors or shapes "match" up to one another. The second two are puzzles that involve numerical parity, neither of which has a solution due to the nature of odd and even numbers. They come in poster form, or you can print them out 4 to a sheet a leave them around for your students to puzzle over. Include

Note: There is now a video tutorial that goes with this activity: Division With Remainders: Just Do It (RIGHT!) Your students are "learning" about division, and if you're using a really, really cruddy curriculum, then they probably all sound like this: "I have 24 blah blah blahs which I'm packing into cases of (choose some divisor of 24.) How many cases will I be able to make. This, my friends, is a lackadaisical and churlish approach to teaching students about solving problems with division.