New Version of Number Sense Card Game 123 Switch

Aidil, a teacher from Singapore read about the number sense card game 123 Switch! that I shared a few years ago. Like any good teacher, he tried it out with his students and when it didn't work as planned, he adjusted the rules and game play to make it easier.

Adaptation is probably any teacher's most important skill in today's ever-changing education landscape, so I am excited to share Aidil's improved version:

To prepare my students for the game, I had to go through the basic rules:
Ace = 1
J,Q,K = 10
Joker = 0
Spades, Clubs = Black (Positive Numbers)
Diamond, Hearts = Red (Negative Numbers)

Rules for adding the cards:
Add 2 same coloured cards together,
If they are 2 diffferent coloured cards, the resulting card will take on the colour of the larger numbered card and its magnitude will be the difference of the 2 cards.

Explaining the 123 Switch game to my students took quite a while and there was a lot to digest as the combinations were quite overwhelming for them as they had to work out a proper number sentence and then decide if they are to put 1, 2 or 3 cards down.

Because my students couldn't grasp the rules of the games clearly, a few students lost interest in the game.

After the lesson, I decided to see how I could simplify the game and involve more people. So I came up a variation with your game. Here is how it goes.

You can start a game with 6-9 players.
Deal out all the cards with the jokers included.
The player to the dealers left will start. He will put a card down on the first box.

For example:

B3+ ___ = ____

The second player will put a card in the second box, for example,

B3+ R6 = ____

The third player will then see if he has the card to complete the number sentence, which is R3

Then he will then start of the new number sentence by putting down the first cards.

If he does not have R3, he will choose a card from his pile and put it facing down in the third box. The fourth player will then see if he has R3 and so on. The person that completes the  number sentence correctly collects all the cards on the game board and starts off a new number sentence.

The game ends when a player has no more cards left over and the last pile is won by a player. The player with the most cards in hand wins.

The game ends straightaway when a person collects all the Joker cards.

The third card on the game board must be of magnitude 10 or lower.

If for example, it is a player's turn to put the second card when he has only Black cards bigger than 3 on hand, for example B4

B7+ B4 = B11 (there is no B11 card)

Since he can't put down a card to satisfy the condition for the third box, he will put any card facing down in the second box, forfeiting it

Find the original game here:  I Want to Teach Forever: Easy New Number Sense Card Game: 123 Switch!.

Fixing a Common Problem With My Like Terms Card Game

Jen B, a high school math teacher from Kansas recently wrote me with a dilemma using my Like Terms card game:

My students are playing the game and our biggest problem is getting someone to go out. They use all the draw pile and then the only card left is ,'take 1 card from another player' Sometimes they can go out, sometimes they are at a stand still. What did we do wrong? They are in groups of 3 kids and I only let them create matches of 3 or 4 like terms at a time. It seems like you'll need a discard pile. Please advise us.

What I told her was that I avoided using a discard pile in my original game because my students were not familiar with rummy style (draw, play, discard) gameplay, but you can certainly add it back in.

The other option is to allow students to add individual cards onto other people's piles, which some people allow in rummy type games. So if my opponent has x, 3x and 5x and in my hand I have a lonely 2x, I can add it on to my opponent's group. I would put it with my own cards and I have to announce what I'm adding it on to, so that players aren't just throwing down cards they can't make groups of. In this way, they're still making groups but have the flexibility they need to get out.

After my response, she let me know how she fixed the problem:

For my second class, I added the discard pile back in. My students seemed to be familiar with Rummy and even asked if they could take the top card off the discard pile instead of draw, which I just might do next time.
Adding the discard pile back in solved our problem.

Earlier posts on this game:

• Sample 5e Lesson Plan: a Card Game for Combining Like Terms
• How to Improve the Combining Like Terms Card Game
• Follow-Up: Combining Like Terms card game
• Combining Like Terms Card Game Revisited

Easy New Number Sense Card Game: 123 Switch!

 

Here's another new card game you can use to quick and easily practice adding and subtracting positive and negative integers.  I've dubbed it 123 Switch, and you'll see why in a moment:

You'll need: a deck of cards for each group of 2-4 players, the DIY graphic organizer seen above, and paper for each student to write down (and double check) every simple number sentence that's created.

As with many of the other games I've shared, black cards represent positive integers and red cards represent negatives.  Aces are ones and all other face cards are tens.

1. Each player gets 7 cards.  The remaining cards are a draw pile.
2. For the first turn, the player must create a correct number sentence in the form A + B = C (for example, 6 + (-8) = -2, as in the photo above)
3. For all subsequent turns, players can replace one, two or all three cards to create a correct number sentence.  They should stack the cards on top of each other (so there's always three showing).
4. As in Uno, each player must put down at least one card per turn.  If they can't do so with the cards in their hand, they have to draw cards until they can put down something.
5. The objective is to be the first player to get rid of all of your cards.

Let's say it's my turn to continue the example above, and my hand is the one on the left.  I would have the option of playing one, two or three cards:

One card: Replace just the -8 with my own -8.

Two cards: Replace the 6 and -8 with -6 and 4, which still equals -2.  I could also leave the 6, replace the -8 with 4, and the -2 with 10 (6 + 4 = 10).

Three cards: I could replace all three cards with -6 + 10 = 4

As they play, students should write down every number sentence that's made, and should be encouraged to police each other closely (with your help, of course).  Every group will have had different practice, and can proceed at their own speed.  That would make this quality independent practice for your lesson on this concept. 

Adaptations

1. Designate a wild card.  I'd leave aces as ones and use one of the other face cards.
2. Assign other values to face cards.  See last week's card game idea, Summy, for more.
3. Change the game to subtraction.  This adds a significant layer of difficulty (as I found out when testing this idea out) and could make each game much longer.
4. Give each player more cards.  I tested this out and estimate that one game should take about 5-10 minutes using the default 7 cards.  I don't recommend using less cards, since it reduces the practice your kids would get, but you could give each player 10 cards instead.
5. If you run out of cards in the draw pile, take all of the stacked cards except the top ones.  Shuffle them and put them in a draw pile.

How might you use this in your classroom (or with your kids at home)?  What adaptations might you make to improve this idea?  Share your ideas and feedback in the comments.

Summy: A Math Twist on a Classic Card Game

I love the classic card game of rummy.  Whether it's because the game is so great or I'm just not very original (I prefer to believe the former), I constantly revisit rummy as a basis for creating new learning games.

My latest twist on rummy involves adding positive and negative integers.  It's called Summy (pun most certainly intended):

1. Players are dealt 7 cards.
2. Remaining cards are placed in a draw pile, with the top card turned over to be the "sum total" card and the first in the discard pile.
3. Black = positive integers, red = negative integers.  All face cards are positive or negative 10, depending on their color.
4. During their turn, each player draws one card from either the draw or discard pile, and tries to make groups of 2 cards or more that add up to the sum total.  
5. Players must put down something, so they might have to keep drawing cards until they can.
6. After their turn, players should discard one card from their hand.
7. When one player has no cards left, the game is over.

As I noted when I revisited my combining like terms card game, if your students aren't familiar with the draw-play-discard structure of games like rummy, you might need to adjust or eliminate some rules.  The key here is that instead of making groups according to traditional rummy rules, players are seeking sums that match the sum total.  All other parts of the game are secondary.

Let's use the cards on the left as an example.  If my "sum total" card is (-8), I need to find 2 or more cards in my hand whose sum is (-8).  I could put down a group of 3 using either the jack of diamonds or queen of hearts as (-10):

(-10) + (-5) + 7

That wouldn't be the best play, though.  I would still have a red and black face card in my hand, worth (-10) and 10 respectively.  Since their sum is zero, I can include them in my group as well:

(-10) + (-5) + 7 + (-10) + 10

I'd be left with just the 8 and (-2).  I'd still have to draw a card, and discard one, so I would not have won quite yet, but I'd be well on my way to victory.

One of the most important lessons I learned while tutoring at Mathnasium was that children need number sense to become great at math.  With this game, they're being challenged to think of multiple ways of adding up to the same total, and as their hand changes constantly, so do the possibilities.

Adaptations

1. Eliminate the draw-play-discard structure.  For example, you might simply pick one card as the "sum total," insert it back into the deck, and divide the deck equally among the players.  From there, each player could simultaneously try to make as many groups of 2 or more as quickly as possible.  The player with the most correct groups after 3 minutes is the winner!
2. Use aces as 1 and (-1), or turn them into a wild card.
3. Assign other values to face cards.  Instead of having all face cards equal positive and negative 10, you could assign these values: jacks = 11, queens = 12, kings = 13.

What do you think?  Do you have other ideas to make this better?  Would this idea benefit from a video demonstration?  Share your thoughts in the comments.

Toys & Games Every Kid Should Play With Growing Up

Kids play with all sorts of toys and games as they grow up, and there's certainly value in anything that allows children to engage in free, creative play.  Yet considering the kinds of skills those children will need to excel in school and later in life, all toys & games are not created equal.

With this in mind, the following is a list of items every child should have access to at the earliest age possible:

Tetris

While there's clearly value in students doing all kinds of puzzles and brain games, there's something special about Tetris.

Our kids are too often taught that there's one right way to do things, one right answer to every question.  When they get to college, all the creativity and problem solving skills they need are severely lacking.

That's the beauty of Tetris: you have to think creatively to survive, and you have to do so pretty quickly.  Even better: the problem is different every time you try to solve it!  Get this game into your kids' hands in whatever format they prefer.

If you want an analog alternative, try my Fun and Easy DIY Tetris-Style Magnetic Blocks.

Legos
Speaking of toys that foster creativity, there's nothing better than Legos.  Again, kids should be playing with blocks (no matter the type) from a very young age, but Legos are something very special.  The variety of themes, block types, kits and built-in encouragement from the company to rebuild endlessly combine to form an amazing canvas for creativity.

In addition, children learn how to follow increasingly challenging directions as the sets increase in number of blocks and design complexity.  There's also no shortage of adults inspiring new and awesome ways to use these toys as a learning tool.

Card Games

Teachers who have lamented the slow death of the simple deck of cards as a fun, easy tool for learning need to thank everyone who's helped make poker popular as a spectator sport.  Because of those bracelet-loving folks, cards are still relevant to young people despite being completely and utterly analog.

What that means is that all of the great card-based educational games that have been around for a long time can still be used to engage today's kids.  Check out my list of lesson ideas and games based around cards for some inspiration, but don't forget that most traditional card games have essential skills baked right in.

Board Games
There's no shortage of board games designed primarily for learning, but even games built for fun or the challenge (Monopoly, chess, Settlers of Catan) incorporate a wide range of skills that students need.  Creativity, problem solving, basic math, following directions, even collaboration and cooperation are easy to find.  They're also cheap, readily available, and aren't limited by your access to technology (or restrictions on content therein).

Of course, you can also take this to another level by having kids create their own board games.  There's even companies that will self-publish your board game idea into something very professional looking.

Your Turn!
What other toys & games should ever child be able to play with growing up?  Disagree with anything on this list?  Am I too much of an analog educator in a digital world?  Let's discuss it in the comments.

New Resource for Deal or No Deal Probability Game

Mr. Faris, a reader from the Federated States of Micronesia (shout out to all of my readers around the world!) took my Deal or No Deal probability game and created a spreadsheet that calculates the bankers' offer for you.  In the original card game, the bank offer is based on a randomly drawn card, not on the prize amounts left on the board.  Thus you often get offers that make no sense, which can take away from the game experience.

As he explains: "It calculates the banker's offer for you.  I came up with the formula for the offer by studying data from game shows.  It is very accurate and useful.  One variable I think is used in the real formula which I did not use is whether the expected value has gone up or down since the previous round."  There's also a version of the score cards included as a second worksheet.

Huge thanks to Mr. Faris for sharing this resource!

Download the Deal or No Deal bank offer spreadsheet (via Google Docs)

Original post: Lesson Idea: Probability using Deal or No Deal

Combo Book Giveaway: 2 Books Full of Card Games!

This week's giveaway is what we in Texas call a twofer: one lucky reader will get both Crazy Eights and Other Card Games by Joanna Cole & Stephanie Calmenson AND 101 Best Family Card Games by Alfred Sheinwold.

Card games certainly aren't the hippest things for kids to play with, but I believe they belong on a short list of toys/games that every kid should play with growing up.  Pick just about any card game at random and you'll find that the skills needed to master the games are essential skills for children to master: grouping, ordering, counting, simple math operations, following directions, taking turns, and sportsmanship (among others).

Crazy Eights outlines games in a kid-friendly way; you can simply hand this over and let them have at it.  101 Best is more of a encyclopedia of family-friendly games that a parent or teacher could draw from.  Of course, I'd encourage you to modify and extend the games (or encourage the kids to do so) to broaden their impact.  As with any good resource, it's all in how you use it.

I think these are complimentary resources, so I'm giving them out together.  If you're interested, just email teachforever@gmail.com by 11:59pm CST tonight and let me know how you intend to use these books.  I'll pick the most compelling entry and send them both books!

If you've won anything from me in 2011, sorry, but you're not eligible this time around.  Got to spread the love.

Good luck!

You Can Count on the Sequence Numbers Board Game

The original Sequence Game is a classic mixing traditional cards, a board game, and a little bit of Connect Four.  I'm always looking at old school games for their possible classroom applications, but I didn't see where this one would be directly educational.  Recently, I learned about a new version of the game that you should definitely have in your elementary school classroom (and at home as well).

The Sequence Numbers Game allows students to practice addition and subtraction number facts in the context of an easy to learn game.  The game goes like this: each player/team has a handful of these number facts cards.  The game board, as you can see in the picture, has color-coded numbers that match the cards.  Each turn, you can put one of your chips on the answer to one of the cards in your hand.  The object is to get five chips in a row.

I've played this, and watched some students play it as well, and I think this would be a big hit with kids in grades 2-5.  It would make a great Christmas present for your favorite elementary teacher or student.

Buy Sequence at Amazon.com

Use a Deck of Cards to Set Your Child Up For Future Math Success

It's never too early to start working with your children on counting and grouping, and you can use just about anything.  I'm partial to using a deck of cards, though, because they are so simple to use for this and so many other activities as your child gets older.  This basic activity is designed for young children up to the Kindergarten level.

Give the child the entire deck (minus jokers, rules for Texas Hold 'Em, and other extraneous cards).  Ask them to group by color, suit and number or letter (rank).  Make sure you encourage them to arrange all of the cards into their respective groups.  As they arrange the cards, have them count how many are in each group, and ask about whether the groups are the same size or not.

You might explore this idea visually, having them arrange groups into equally sized rows and columns.  I've seen other teachers have students stack the groups of cards vertically and talk about the relative heights of the stacks.

The possibilities for extending this simple exercise are endless: you could have them group all of the cards bigger or smaller than a certain given number, or shuffle the deck and challenge them to create groups more and more quickly.  You could play any number of traditional card games that covertly teach math skills.

You could even explore ideas such as even and odd numbers, but at some point you're going to get into concepts that are far beyond the Pre-K/K level.  Then again, if your child seems to like this kind of game and is progressing quickly, you should by all means raise the level of difficulty as high as you can.

All in all, you can do this anywhere with no setup, and in a short period of time.  If you're worried about your kids ending up in the World Series of Poker due to their use of regular cards, you can do a lot of these activity with a deck of UNO cards (not to mention by playing the game itself).

Instant Elementary Grouping Game for School or Home Using Cards

Following up on yesterday's simple elementary grouping game, here's a way to use a deck of cards to do more practice on grouping in the classroom, at home, or anywhere you have some table space to lay out cards.  This is appropriate for K-3, (older children having trouble with multiplication and division).

Basically, using different amounts of cards, you'll ask the students "How many groups of ... can you make?" using the numbers given.  You can remix this activity in a variety of games, working your way up from a smaller group or starting with

• Start with all 52 cards, face down.  Groups of 26, 13, 8, 7, 4, 2, 52, 1.
• Remove 4 cards (leaving 48 cards).  Groups of 12, 24, 4, 8, 6, 2, 48, 1.
• Remove 8 cards (leaving 40).  Groups of 10, 20, 40, 1, 5, 8, 2.
• Remove 5 cards (leaving 35).  Groups of 5, 7, 35, 1.
• Remove 10 cards (leaving 25).  Groups of 1, 5.
• Remove 1 card (leaving 24).  Groups of 2, 4, 6, 8, 12, 24.
• Remove 6 cards (leaving 18).  Groups of 3, 6, 9.
• Remove 8 cards (leaving 10).  Groups of 2, 5, 10, 1.

Throughout this activity there's opportunities to ask about multiplication and division facts as well as fractions.  You'll notice the number of groups and order changes in each round; that's on purpose.  I didn't include any group numbers that would leave remainders, which you can of course add depending on the child's aptitude and grade level.

You could replace the deck of cards with basically any other object, but cards are useful for many different types of games and I think are easier to organize and keep track of than block, beads, and other typical counting objects used in schools and at home.

High or Low: From Drinking Game to Learning Opportunity

Let me start this post with a hopefully obvious disclaimer:

Do not, under any circumstances, tell your students (or your colleagues, administrators or anybody else) that this is based on a drinking game.

Let them figure that out for themselves when they're in college, where they'll have a distinct advantage over their classmates because of the probability skills you're going to teach them.

The premise of the drinking game High or Low is to guess whether the next card is higher or lower than the last one dealt. That's basically it (minus the obvious). The only element we're going to add to the game is that students will figure out the exact probability that the next card will be higher, lower or the same suit.

Introduction/Guided Practice:
Explain that you'll be using a regular deck of cards to help students understand some challenging probability problems. Show them the graphic organizer and how to fill it in by "playing" a few sample rounds. Click through for a rough example of what a filled in organizer might look like.

While you're modeling how to play and use the organizer, that's the best opportunity to review the structure of a regular deck of cards, as that's essential knowledge they'll need to play.

I wouldn't try to sell this to your students as a super fun game so much as a different way to practice problems (better than say, doing problems out of a textbook). They might get into the guessing element, but I don't think it will be as engrossing as my Deal or No Deal probability game. Students definitely don't like it when you tell them something is fun when it's not, but they do appreciate the novelty of using cards and just doing classwork differently in general.

Collaborative Practice:
Split your class into small groups, giving each one no more than 10 regular playing cards. Each group would have a different set of cards and probabilities to figure out, which eliminates the problem of students copying answers. That element plus the "game" itself should keep most students focused and invested in the activity. They'll be filling out the organizer and then considering the reflection questions as well.

Wrap-Up:
At the end of the game there's a few reflection questions you might talk about together. Students will probably think this game is pretty easy at the beginning--how hard can it be to guess correctly high or low? I think their results will probably skew towards an even number of correct and incorrect guesses.

You could also give them an exit slip like: "How could we change this game to make it easier? ...harder?" A game of Red or Black?, for example, would elicit some interesting answers.

Things to Consider:

1. Do you want students to leave probabilities as fractions, simplified fractions, or change them to percents as well? The latter would take a bit more time and might require you to give 1 or 2 less cards to each group.
2. How long do you want this activity to take? As is, it should fill a 45-55 minute period, allowing for opening and closing procedures and transitions. If you want to spend less time on this, give students only 4 or 5 cards. You can spend the rest of your class period on similar probability problems from your usual resources or whatever you'd like.
   
3. This should be taught after you've introduced the basics of probability in other ways, as it involves the idea of independent and dependent probability (replacement).
4. Every time I post something about probability, some people like to start an argument over the Monty Hall Problem. I think you could argue either way, but the point of this activity is to provide practice on finding probability in a way similar to typical standardized test questions, and that's all. Let's leave that debate for another time.
5. If you want to add an additional challenge, you can use this activity as a segue to talk about compound probability!
   

Materials to Download:

High or Low card game graphic organizer
Rough example of filled-in graphic organizer

Three Fun Probability Games and Projects

I did a lot of research on probability lesson plans this past year, but I really didn't like a lot of what I found. I found that most of them they just weren't any fun, which in my mind seems to go hand in hand with probability. So here's two new resources I found, an old idea worth revisiting, and advice about setting up your students for success on this topic.

1. Mathwire.com One-Die Toss Activities - This site has a bunch of dice-based probability games. I recommend Pig, Skunk and the Cheerios Experiment (which really should be named after a more unhealthy, toy-promoting cereal), as all of them were successful in class.
2. Design Your Own Game Project [Word doc] - Students design their own carnival-style game, calculate the probabilities involved and reflect on what they learned and created. It's simple to explain but will push your students to really think about probability in this kind of context. The document includes a rubric as well. My students really enjoyed doing this, both in Algebra I & II. If you have the time and resources, you could even have a "Carnival Day" where students would play each other's games. This game was found online and the link had been dead for a long time, but I found a copy in my records.
3. Probability Using "Deal or No Deal" - This is arguably my most popular lesson plan idea ever, but I actually want to make sure you read the opening coin-flipping activity I used before starting the game. Even if you don't use the game itself, you should absolutely open any probability unit with that fun activity.

Setting students up for success with probability

Unlike in the Rio Grande Valley, many students in Boston didn't know the basics of a regular deck of cards. I would imagine that is the case in many areas these days, as kids move farther and farther away from the traditional games you and I might have played in our youth. First, it might help to post this in the room somewhere for your entire unit:

A regular deck of cards has:
52 cards total
26 red (13 diamonds, 13 hearts) and 26 black (13 spades, 13 clubs)
Each of the 4 groups has the cards 2-10, J, Q, K, and A

Probability questions involving playing cards are one of the most common asked on standardized testing in both Massachusetts and Texas (and we all know how much influence the latter has, for better or worse). Your students need to be ready for them, and I think it will make other probability questions easier as well.

You can ask simple questions as a review and check to make sure they're simplifying each fraction, then move on to asking them about independent and dependent events. Your textbook and supplemental material is probably full of these types of questions as well.

Finally, some students will need an actual deck of cards in front of them to understand the questions, which is another good reason to make sure you always have one in your classroom!

On Success, Part 2: New Games & Projects

This is part of a two-week series on my five biggest successes and failures as a teacher this year. This week is focused solely on success.

I'll be the first to admit that I abandoned many successful elements of my past classrooms this year. I also didn't have much experience teaching Algebra II beyond a stint at an alternative school, so I didn't have the wealth of resources as I did for Algebra I. Yet despite these setbacks, I've created a number of new lesson ideas, games and projects this year in both courses.

Algebra I
I'm a near-perfectionist. That is, I am rarely satisfied with my ideas and tweak them every year, no matter how successful they might have been before. Of course, I still go forward and use my unfinished strategies to teach out of necessity. I'm happy that not only did I improve many good lessons, I created new ones to cover a wide range of topics:

1. New Version of "Students Become The Teacher", 9/27/08 (Idea #8 in my book Ten Cheap Lessons)
2. How to Improve the Combining Like Terms Game, 9/27/08
3. 2008 version of the Math in the Real World project, 10/9/08 (Idea #4 from TCL)
4. Basic Geometry Formula Book project, 10/26/08
5. Coordinate Plane Battleship Game: 2008 edition, 11/21/08
6. Linear Functions Mini-Poster project, 12/14/08 (Remix of Idea #1 from TCL)
   
7. Linear Equations Formula Book project, 1/12/09
   
8. Multiplying Polynomials and FOIL review games, 3/4/09

Algebra II
I had a much harder time coming up with ideas for Algebra II, as I have not deconstructed and planned out the clearest explanations for the much more complex concepts I have to teach. I'm starting to feel comfortable in breaking things down now, and building interesting projects and games around the topics.

1. See #1 & #3 above.
2. Transformations of Exponential and Logarithmic Functions project, 1/27/09
3. Transforming Logarithmic Functions Bingo, 2/8/09
4. Straightforward Example Posters, 3/10/09

There's still much more to come in both subjects, as I feel my creative juices are flowing quite well these days. I get so much satisfaction when I hear from readers that they used my idea in class or that it inspired them to create something.

In a Sentence
Keep improving your teaching, no matter how long you've been doing it.

How to Improve the Combining Like Terms Card Game

I recently received this comment on my original post Sample 5e Lesson Plan: a Card Game for Combining Like Terms:

Please help me understand how do I make the scores MEANINGFUL to the students at the end (other than saying that we just learned how to combine like terms). cchou1@lausd.net

This is a completely valid concern, one that I haven't addressed well enough. One possibility is to make the game a short one, playing one round only and stripping down the structure to the bare minimum. Then you immediately start doing straight practice of combining like terms during the very same class period, telling students only to follow the grouping rules used in the game, and that their answers will look like their "scores" for the game.

Of course, I don't see the world through rose-colored glasses, and I realize that idea may not be the most meaningful way to wrap up this activity. The other most obvious answer is to assign numerical values to a, b, and c and have students plug in those values after simplifying their respective expressions. I think most Algebra I teachers cover evaluating expressions for a given variable just before they move on to combining like terms, so it could be a good way to tie those two topics together. Students get a tangible numerical score, and it could help them understand the concept of variables as well.

I worry though that the evaluating approach would confuse or distract students from what they can combine and how they do so because they would be wrapped up in calculating a numerical result. Perhaps the solution is to keep the original "scores" intact and follow the game with a simple graphic organizer that reviews what they learned and connects it to the big picture. For example [with prospective student answers in brackets and italics like this]:

In this game, we learned that:

An "a" could only be combined with... [ a].
A "b" could only be combined with... [ b ].
A "c" could only be combined with... [ c ].
An "a²" could only be combined with... [ a² ].
A "b²" could only be combined with... [ b² ].
A "c²" could only be combined with... [ c² ].
Numbers without a variable could only be combined with... [other numbers without a variable].
When I had a group of 3 or 4 cards, combining them meant that I had to... [add up the coefficients].
Like terms are terms that have the same [variable] and the same [exponent].
if I have like terms in a problem, I have to... [combine them]!

Finally, one last perspective on the original question. I think there's a lot of inherent meaning in this activity as is. I created the game because I wanted my students to remember what combining like terms looks like, and what a simplified expression might look like. This is why I've never assigned values to the variables. To a typical student, it is a weird, cryptic thing, all these letters and numbers arranged in this way. Our job is to demystify and decode these expressions so that our kids are not confused or intimidated by them, especially considering that they get more complex as we progress through the subject. The fact that they combine their terms mostly independently, and could complete all the statements in my sample graphic organizer above, is infinitely more meaningful and memorable than it would have been if I had done a traditional, straightforward lesson on the topic. The game, and the resulting "scores" they get are very meaningful for everything that comes afterward.

If you think you might want to use some form of this card game, please be sure to read two other follow-up posts I wrote about the game designed to make it work better in your classes:

Follow-Up: Combining Like Terms card game
Combining Like Terms Card Game Revisited

Lesson Idea: Probability using Deal or No Deal

No matter what I'm doing or where I am, I'm constantly making literal and mental notes of ideas I can use to improve my teaching. Sometime last year, while wandering around an educational toy store in the mall for just this reason, I mentioned to my friend Dave (a fellow teacher) how I thought the game show Deal or No Deal would be a great way to teach probability. At its heart, the show is about figuring out your chances of getting a better deal by playing on or taking the bank's offer--in other words, your probability of getting the better deal. Dave thought this was a great idea, and we returned to our perusing.

Several weeks later, Dave told me he had shared the idea with math teachers at his school, who used it in class to great success. It was apparently a huge hit. While I'm all about sharing my ideas and helping students beyond my classroom, I was a little miffed, because I hadn't actually used the idea with my students! I had forgotten all about it until Dave's reminder, and so I made a resolution to reap the benefits of my own idea this year.

Building Background

The first thing I did was introduce probability the day before the game. I started with a question: "Every time I flip a coin, I have a 50/50 chance of landing on heads or tails. So if I flip it 50 times, I should get 25 heads and 25 tails, right?" This kicks off a discussion about theoretical probability, which we then tested. Small groups flipped a coin 50 times and tallied heads and tails. Then we came back together and compared their data (experimental probability) to our theoretical probability. I also used a deck of cards to show several examples of probability (especially the idea of replacement) as well as compound probability. This would provide a foundation for our game the next day.

Adapting the Game

I already had an idea of how to adapt the game for my purposes, but I thought I would buy the Deal or No Deal card game that I had seen severely discounted at local Target stores (about $7). I thought it would give me some ideas and at the very least neat prop (the briefcase) to use, but basically everything I needed was there in the game. The only thing I needed to add was a graphic organizer where we would calculate the probability of getting a better deal by saying "no deal" after each bank offer.

The card game has a 4 decks:

1. Briefcase cards are numbered 1-26
   
2. Round cards show how many briefcases to open each round (why they couldn't just write it down as a list is a mystery)
3. Bank offer cards to provide a random offer each round
   
4. Cash cards to hide under the Briefcase cards

The game play is simple:

1. Take one briefcase to hold onto which could be yours at the end of the game.
   
2. Each round, players open a diminishing number of briefcases, starting with six in Round One and ending with one in Round Nine.
3. After the briefcases are opened, the bank makes an offer, and the player can accept it (deal) and the game is over, or reject it (no deal) and keep playing.
4. If the player rejects all bank offers, they will be left with their briefcase and one other, and choose which they will open. Whatever they choose is the amount they win.

As I said, I only needed to add students finding the probability of getting a better deal if they rejected the bank offer. So I created a simple graphic organizer combining the enclosed game sheets and a table that looked like this:

Students would write in the results of each round, like so:

Round	Bank Offer	# of briefcases left with more money than Bank Offer	Probability of winning more than Bank Offer	Deal or No Deal?
1	$100,000	5	5/20 = .25 = 25%	No Deal

I used magnets to hold the briefcase cards and cash cards underneath on the board (you could also use a hanging pocket display with clear pockets, the kind you often see in elementary classrooms). I would play Howie (I considered, but did not purchase, a bald cap), there wouldn't be any models to open the cases, and the class would play as a whole group.

Playing the Game

After picking a student to start us off by claiming "our" case, I had students pick each other "popcorn style" to choose the briefcases to open each round. When it came time for the bank offer, I pretended to get calls and text messages from the bank on my cell phone. We would figure out the probability, fill in the graphic organizer like the example above, and decide whether to take the deal. Most classes wanted to play at least a few rounds no matter what before they started to argue over taking the deal or not (especially once the million dollars came off the board). In those cases, we voted.

The game took about 40 minutes to play through, and in a couple of classes we had enough time for an extremely rushed second game. Students only needed their graphic organizers and a calculator to help convert fractions to decimals and percents (since probability is shown in all three ways).

It was exciting to see the kids really get into it--the roars of disappointment when the big money came off the board, or the huge cheers when $0.01 or $25 came off. They laughed at my phony conversation with the bankers, and nearly everyone was engaged all day. It was a rousing success.

Thinking Ahead

I would have liked to give them maybe five probability word problems for homework as an informal assessment. We are working on the measurement project I posted earlier this week, and their focus should be on that. Instead, we will have an alternative assessment on Monday. In keeping with my no-multiple-choice-test policy, I am thinking we will create mini-posters (Idea #1 in my book Ten Cheap Lessons) for this and the rest of this unit.

If we had more time, I would like have students create their own probability game, or adapt an existing game to include probability calculations. This would encourage higher order thinking and make it more memorable for the long term, as well as provide a game they could later play for review.

As I look to next year, I'm also looking for ways to incorporate compound probability into our game or post-game follow up, since those questions often pop up on standardized tests.

If you like this idea and the others posted here on I Want to Teach Forever, please check out my new book, Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom. It's available now at Lulu.com and coming soon to bookstores everywhere. As always, please contact me with your feedback and questions. Thank you!

I just published my first book: Ten Cheap Lessons!!

I have been known to make grand declarations of things I plan on doing, only to do just the opposite a short time later. After months of excuses and stalling, I made a new year's resolution to sit down and write a book. I had the idea for a teacher resource book a long time ago, and I thought it would be the easier of the two planned books I wanted to do (the other being a memoir of my time here in the RGV). It would prove to me (and future publishers) that I was up to the task, and was something I wanted to do anyway. When I wrote out self-imposed deadlines for the month of January, I didn't know if I would follow through. Indeed, I almost gave up in the first week, when the crushing exhaustion of going back to school after winter break was making an already monumental task seemingly impossible.

Yet I persevered, and the product of my months of work is Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom. It is available now, for about $12 for the paperback or $6 to download immediately. I have put my heart and soul into this, and I can't tell you what it would mean to me to know that my book could help me have a far-reaching effect on the education of children I've never met.

Regular readers of I Want to Teach Forever will see some ideas originally published here, as well as many I've been saving for Ten Cheap Lessons. I hope that the book and the website grow together, so that I can have the opportunity to meet more great teachers and collaborate on great new ideas with them. If you read the book and would be interested in having me present a workshop or speak at a conference, please email me, as I would love the opportunity. You know I'll do a good job--I couldn't live with myself if I didn't provide quality professional development.

Thank you to everyone who visits this website, and for all of the positive feedback I've gotten over the past six months. Stay tuned to teachforever.com for updates and opportunities to learn more about it. Enjoy:

Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom

Adding and Subtracting Integers Card Game

Last year my students had their usual struggles with adding and subtracting integers at the beginning of the year (this is not just a middle school problem). So I used a game I found online called Twenty Five, where students would draw from a regular deck of cards and add them to a pile, trying to reach a target sum of 25. Red cards were negative and black cards were positive, and each new card would be added to all the ones put on the pile before it. Presumably students were writing down each addition problem they did. It was a waste of time: it was hard to monitor whether students were adding correctly during the game, and difficult for students to keep track of and add up 10, 15 or 20 numbers quickly.

Since then I have been laboring over an idea for my own game, since I believe this would help my students internalize an essential skill. I came up with a complete game, but it was too complicated for classroom use (based on my experience with Like Terms); too many rules and steps to get caught up in would leave the core activity lost in the fray. It could be suited for an advanced class, block schedule or playing at home. In a regular 45-55 minute class, things need to be simpler.

I actually eschewed any game this year and focused on the number line as a simpler tool for students to use to add and subtract integers correctly. What dawned on me last weekend was that the number line was the missing piece to the puzzle. Here now, for the first time ever, is Plus/Minus.

Materials

1. Standard 52-card deck of playing cards
2. Paper and pencils.
3. 2 objects to mark a goal and starting location

Setup

1. Students draw a number line on a piece of paper, at least from -10 to 10 with room for more.
2. Have 2 objects (maybe candy the winner can eat afterwards?) to mark the location of the goal and the current location of the players
3. No cards are dealt. There is a face down draw pile and face up pile for each card drawn.

Game Play

1. Flip the top card from the draw pile. This is the goal. Black card are positive whole numbers and red cards are negative (aces are 1 and all other face cards are 10). The starting point is zero.
2. Each student takes a turn flipping the next card from the draw pile. They add that number to 0 and move to the resulting location. If they reach the goal number, they win. If not, their turn is over and each player takes a turn moving back and forth on the number line until someone reaches the goal.
3. After one or several games (depending on time) , switch to subtracting all numbers.

While They Play

Students must write down each simple addition or subtraction problem they are doing throughout each game. This is what you can check and grade immediately as you are monitoring the game. Follow up with homework for practice.

Extension/Assessment

At the end of this lesson, use a mini-poster where students have to show an example, write out how to do it (what the rule is) and most importantly include the correct answer. Hang the best ones up on the wall (as you should always do with good examples of student work).

When To Play

This would be a good game to play after a day where you had introduced the concepts or when you were reteaching. I think that the number line makes this concept easy to understand with little upfront work, but that is an assumption on my part. Use it whenever you feel it is appropriate.

Combining Like Terms Card Game Revisited

The Like Terms card game has been the most popular idea posted here, accounting for half of this blog's traffic since its inception. The truth is though, like most good ideas, it still needs work. I have been wracking my brain to find ways to simplify the game after watching many of my students get caught up in the rules and procedures because they don't have experience playing traditional card games (like rummy, upon which Like Terms was originally based).

My solution is to cut out all but the essential parts: the deck of "Like Terms" cards, having students create groups of 3-4 like terms, and adding or subtracting them (simplifying) when the game is over.

Simplified Rules for Like Terms

1. Deal 7 cards.
2. Players lay out their hand face up in front of them for all to see and arrange them into groups of like terms.
3. Each player draws one card and tries to make a set of 3-4 like terms.
4. Repeat until one player has a group of complete sets.
5. The winner adds all of their terms together, but the losers add complete sets and subtract incomplete ones.

This setup also allows you to add a few new cards to the deck to create some new twists:

1. "Killer" cards - Add cards that don't have any like terms in the rest of the deck, essentially ending a player's chances of winning since you can't complete a set. Maybe there's two like terms, but a third or fourth matching card doesn't exist (i.e. z², x²y², a⁴, etc)
2. Skip, reverse and wild cards - My students may not know rummy, but they do know Uno, so you could add these to the deck as well.
3. "Steal" cards - Action cards that allow players to steal one card from any other player that they need to complete a group, making the game a bit more competitive.

I think the original score sheet would actually work better with this version of the game as well.

If you have tried the original Like Terms card game in class or try out this new version, please email me or leave a comment. I want to continually improve the ideas posted on this site and I need your feedback to help me and the other teachers reading teachforever.com!

Follow-Up: Combining like terms card game

I tested out the Like Terms card game in class today with fairly positive results. It took me a few periods to work out the best way to introduce the game and explain the rules, requiring a lot of adjustment on the fly, but by the end of the day things were going swimmingly.

I made a false assumption that many students had played a variation of rummy or any card games where you take a card, make a play, and discard. However, beyond Uno or poker, many students were unfamiliar with this style of game. Thus, I had students following the rules to make groups of 3 or 4 like terms (which is good) but through varying methods of obtaining cards.

As far as knowing which cards go together (and thus which terms can be combined), I think there was no problem--that part of the objective was clear even in classes where the rules of the game were confusing. What was lacking in the classes earlier in the day was a better explanation on how to score the game--taking the tally of each group of cards and turning it into a longer expression.

I realized that I needed to walk everyone through a turn or two to get things started. At first, I would explain the rules myself, showing examples from the decks and referring to the Like Terms rules and scoring guide I had written before arranging them into groups or having the cards dealt. This was a significant mistake on my part that gave some students in earlier classes quite a bit of confusion.

Later in the day, I made sure the groups were formed and cards were dealt before I explained anything. Then I had the first person in each group complete a turn along with me walking the whole group through it, so each group saw a clear example and knew how to proceed. I held off on the scoring until a few groups had ended the game, and using the score tracking sheet I had printed on the back of the directions, wrote out a full example to show them when and what to add or subtract.

To clear up the morning confusion and review for everyone who did get it, I filled out a score sheet with 2 sample scores, one from a winning hand and one from a losing one, and will ask them to total up the scores properly to start tomorrow's class. I told students all day that as long as they understood and remember the main idea of the game--which terms are like terms and how to simplify expressions containing them--it doesn't matter if the rules of the game themselves were confusing.

So if you plan on doing something like this, be sure to:

1. Arrange students into groups and distribute cards first.
2. Walk students through the first turn (or more if needed).
3. Understand that it may take time for students to grasp the rules of the game (but probably not the concept).
4. Constantly monitor and be prepared to walk groups through the game procedures to get them to the point where they can play on their own.
5. I recommend having groups play through no more than 2 full games.
6. Design a closing activity, even as simple as 1-5 sample questions on the overhead, to end the lesson.
7. Follow up the next day with a filled out sample score sheet (you can borrow ones from students that are correct and cover the totals OR take one that is incorrect and have the students identify the mistakes) and related simplification activities (we will be doing the ever-present "Find the perimeter of the polygon" where the sides are labeled with algebraic expressions.

***More about the sample 5e lesson plan on combining like terms***

Sample 5e Lesson Plan: a Card Game for Combining Like Terms

A few weeks ago I discussed learning the 5e instructional model at a workshop this summer, but neglected to include the sample 5e lesson plan I had created using the model.

I started with an unfinished idea I had last year for teaching simplifying equations using a card game where the cards would be algebraic terms. My sister and I used to play rummy, spit and every other card game during summers at home when we were young. (We also used to play board games like Monopoly, but it inevitably ended badly). Reflecting on these memories as this summer started, I came up with "Like Terms".

Like Terms

Like Terms is played like rummy, but with a special deck of cards made up of sets of like terms: a, 2a... through 10a and so on for b, c, a², b², c² and the integers 1-10.

The game follows the normal rules of rummy:

• Each player is dealt 7 cards.
• The remaining cards are placed face down--this is the draw pile.
• The top card is flipped over to a new pile--this is the discard pile.
• Each player draws a card, looks for a 3 or 4 card set of like terms, and places that face up on the table in front of them if they have it (7a, 3a and a or 6c², 2c², 4c², and 10c² would be two playable hands).
  
• Whether they have something to play or not, they must then discard one card to end their turn.
  
• Play continues until someone discards their last card and has no cards left.
• The winner adds everything they placed on the table together. Everyone else subtracts what's in their hand from what they had placed on the table.

At this point in the real game of rummy, players would tally their score based on a point system. You could assign points to each variable in this game, I suppose, but I think that defeats the purpose. I would rather have the "scores" look like 15a² + 16b² + 9b + 6c + 7 for the winner and -5b² - a - 6c - 11 for the loser and jump directly to giving students problems where they have to simplify expressions.

If you only explained the rules of Like Terms and told your students they would use only the game rules to solve math problems afterwards, it would make a sometimes boring and easily forgettable operation fun and easy to remember.

How to make a deck of cards for Like Terms the easy way:

• Use white 3x5 index cards and at least 4 different colors of highlighters or flip chart markers (so the terms won't bleed through). Each term gets a different color (a and a2 are blue, b and b2 are red, etc), OR...
• Use colored index cards for the sets and one marker that won't bleed through, OR...
• Cut up scratch paper and use trusty blue, black and red pens, OR...
• If you want to really get fancy, you can get card stock and print out cards on the computer.

Whichever method you choose, remember that you'll need multiple decks since a typical game should be 4 players (max 6).

How to use this in your classroom

I designed this with my 9th grade Algebra I students in mind, because they usually come to me unable to simplify expressions. This little problem, like so many little problems, gets compounded as we move into more complicated equations and make things infinitely more difficult than it needs to be. This is appropriate for the first few weeks of school when you're working on review, basic skills and procedures.

Some teachers may find this more appropriate for middle school, and I'd be interested to see how this would fare in a Pre-Algebra classroom. If you try it please share your results!

Here is the full sample lesson plan based on the 5e model to help you plan a complete lesson around this activity.

UPDATE 9/3/07: Since I will be using this lesson in class this week, I am adding 2 documents I will be handing out to my students as a one page back and front handout:

1. Like Terms rules and scoring - Simplified for student consumption.
   
2. Like Terms score sheet - This is a simple graphic organizer that they can hand in or you can refer to while monitoring the games so you can identify problems (and/or give them a grade for participation). I had to reformat this document for Google Docs, because it didn't like the tables I used for the score sheets or the columns I used to fit 2 on the same page. You might have to cut and paste to save paper. Or, email me at teachforeverATgmailDOTcom and I can send you the original document in OpenOffice, Word or PDF format.

Please leave comments or email me with feedback.

UPDATE #2 7/22/11: Check out Combining Like Terms Game Revisited for an alternate version of this game. I've expanded upon this lesson idea and many more in my book Ten Cheap Lessons: Second Edition.