# findingEMU

### Building Enduring Mathematical Understanding, one lesson at a time.

When I was taking Math Ed. classes in college we had to choose one manipulative and describe all of the different ways they could be used in the classroom. I chose Legos, and came up with quite a list of activities. Many of them involved using Legos as replacements for other manipulatives, therefore allowing you to spend less by “just” buying Legos. I guess I was frugal even back then ๐ (Of course, that was before I knew just how EXPENSIVE Legos are!) Almost all of the Legos at our house are “claimed” by my son, and those that are left belong to his sister, so I have yet to use them in the classroom. (I did “sneak” some Duplos to school when they were younger, but those are all now in storage.)

Anyways, I originally developed the idea of “Math Cards” just for the “Find Your Match” activity listed below, but it has morphed into much more. See what other ideas you can think of!

The first incarnation of Math Cards involved having students pick a slip from a bucket when they arrive in class and find their partner for the day based on their card. Now, the cards are not identical (this is middle school math, after all) but “match” in some way. Maybe they are equivalent. Maybe one card is the solution to the equation on another. Maybe they are different representations of the same linear relationship. The sky’s the limit on what you can create. Here are some I have made for this year.

I also have “Find Your Match Trios” cards where groups of three will “find each other.”

Each year, I would print out the sheet and cut it up for the class to use. I would create new “cards” for different concepts to add to my collection. (I have quite an assortment for 6th Grade, where we have a two period block with the students.) The next year I would find the file, print it out, cut it up . . .
I found that students would “cheat” (in my opinion) by putting their “answer” on the back of their slip and THEN finding their match, but in reality the “game” involves NO talking, and students are holding up their card and looking at other cards (analyzing them mentally) to find their match. The idea is that they will have to “do the math” for every other student’s card until they find their match.

Sooo, my brilliant idea was, hey, I can have these laminated and reuse them for years and they also won’t write on them! I took it up a notch and glued them on construction papers before having them laminated. Color coding made them easier to keep in sets. I had a TA first semester last year and it kept her busy quite often. Here are some of the finished products:

THEN, other uses started flowing into my brain. Below are “two more ways” that I have been using the cards, but within those two categories are MANY more uses ๐

Math Greetings
I have mentioned this briefly in other posts: First Day and Magnets, and I plan to do a more in depth post on it in the future. As students enter the room, they are required to “do math” in some way. I can put a set (or part of a set) in a “bucket,” have a student draw a card and “do it.” Sometimes it means solving the equation, sometimes it means changing the fraction to a decimal, sometimes it means finding the slope for the near relationship, sometimes it means just doing the arithmetic on the card. Again, the possibilities are endless.

Some cards are just numerical values (fractions, decimals, percents, square roots, cube roots) so I combine the cards with student magnets and they plot the values on a number line.

I have also combined the cards with dice.
-Draw a card with an algebraic expression, roll a die, evaluate the expression for that value of the variable.
-Draw a card with an algebraic expression, roll a die, set the expression equal to the value and solve.
-Draw a card with a fraction, roll a die, multiply (or divide!)

This year I plan to add some more “twists.”
-Set out a 4 by 4 grid of cards. Students find a match, I take the cards and place out two new ends.
-Pick two “ax + b” cards: set equal and solve, just add them together, or multiply together.

I really value the brief 1-on-1 with each student. It allows me a quick assessment of where they are at on a particular skill or concept. Often 2-4 students are “answering” their Math Greeting at the same time, so it really keeps me on my toes! Sometimes it really opens my eyes as to the general level of understanding that remained after 23 hours, and this may alter my plans for the day ๐

Review Games
At the end of each Unit, I often have a variety of different activities that rotate among groups of students. Many of these end up involving the cards in some way.
-Math Race: Flip a card from a stack, race to answer it, keep the card if you “win” OR everyone writes down their answer, earn one point for getting it right and one for being first (IF you are correct.)
-Match Game: Lay out cards upside down. Flip pairs and try to find a match.
-Go Fish: Students play the game while “fishing” for cards that match the ends in their hands.
ANY of the Math Greetings activities can be modified slightly as well.

Final Thoughts
Most of the time I am quite intentional in the problems I choose. For instance, for the scientific notation set in the first image, there are only two different mantissas (had to look that up) so plenty of opportunities to demonstrate conceptual errors. The Exponent Rules set provides for the same “opportunity for error.” Does 2^20 รท 2^5 = 2^4? Students who think so will “find the wrong match.” However, in the factoring/multiplying set, I could have done a better job just switching two values so that the “a and c” in the quadratic are the same. I once turned my brain into mush coming up with sets of five values where each card matched with two other cards having the same mean, but also matched with two different cards having the same median. It made for a good discussion of outliers!

Once I figure out the “tech side of things” I do plan to post links to them on a page here on this blog, but for now, feel free to come with your own ideas!

Part of Enduring Mathematical Understanding comes through practice, and Math Cards certainly provide that opportunity. However, deeper understanding comes from dialogue. “Find Your Match” is often followed up by questions regarding “why” two particular cards are a match. It’s always interesting to hear the conclusions!