Tag Archives: Liberal Arts Math

Mad Math, or Math Libs

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car

Did you ever play Mad Libs? I loved to play this game on long car rides when I was a kid. You could get books of them in the drug store, and best of all, your parents didn’t mind spending the money to get you a whole package, because it was “educational”!

Now the game has a new online incarnation: http://www.madlibs.com/, and you can even find an app to play it.

In Mad Libs there is a leader, who asks everyone else to give them words to fill in the blanks — but the leader does not tell the rest of the group the story until all the blanks have been filled in! Once the blanks are all filled in, the leader reads the story to much hilarity.

I created my own story, with a twist — it has numbers at the end that students also have to fill in. When my students finish reading out the story, they also read out and do the problems they have created. The particular problems you’ll see below involve factoring, but could be changed to suit any topic. The great thing about this game is that it brings in topics from English (interdisciplinary!) and story telling. It gets students laughing and more ready to do the problems, and it allows students to create their own problems.

Mad Math: Factoring Frenzy

 Directions

  • The group leader does not show the group this piece of paper!
  • The leader asks each person in the group in turn to contribute a word, letter or number until all the blanks are filled in, including the number blanks for the factoring problems.
  • If a person gets stuck on a word, they can use one of the ones on the board.
  • Then the leader reads the story and the group works out the problems.

My ___________ subway ride started when a giant  ___________   _____________ up from the subway               adjective                                                                    animal         verb ending in –ed               

and into the ____ train.  People were  ___________, but I got a ___________, so I was ___________.

                  letter                                    verb ending in –ing               noun                                adjective

When I got to school, my ___________ professor would not ___________my excuse and said that if

                                                       adjective                                        verb

was late one more time, I would get a ____. What a ___________ day! Luckily, I found out that if I could

                                                               letter                    adjective

do these ___________ factoring problems, everything would be ___________!

                   adjective                                                                                 adjective

Factor:                             Caution: one of the problems is not factorable!

 

  1. x2 + 3x – ___                                             2.  x2 –  ___x + 25                                 3.  x2 + 12x +  ___

an integer between 3 and 5          an  integer between 9 and 11      a perfect square betw 30 &40

 4. x2 – ___                                                16x2 –  ___                                6. x2 +  ___

any perfect square                              an odd perfect square                              any perfect square 

Bonus: change the problem that is not factorable into one that is.

The word file here: mad-math-example gives you a better copy, plus some signs I made up to put around the room so that students would know what an adjective, adverb and noun were.

I invented this game at a What’s Your Game Plan workshop, with the help of Joe Bisz, Carlos Hernandez and Francesco Crocc. Much thanks, you guys!

Bizz Buzz for Base Systems

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numbers

A simple game for learning base systems illustrates many of the connections between game based learning and other pedagogies. This game can be played in a liberal arts or mathematics for elementary education class. The game is a variant of Bizz Buzz, often played as a drinking game.

Students sit in a circle and count off – one, two three, four. The fifth person, instead of saying five, says “bizz.” The count continues – one, two, three, four, bizz-bizz, one, two, three, four, bizz-bizz-bizz, one, two, three, four, bizz-bizz-bizz-bizz. After this (four bizzes), the count changes — one, two, three, four, buzz.

This is a base 5 counting game, with 105, or 5, represented by bizz, and 1005, or 25, represented by buzz. The game typically engenders much laughter as students who are not quite paying attention say 5 instead of bizz, or bizz instead of buzz. Students help each other to say the right word, “Say bizz!” they call out to the confused fifth person. But the game is not too hard, and soon everyone gets the hang of it.

Explicit connections can then be made between the game and the notation for base 5. For example, the seventh person is bizz + two = 125 in base 5. The connection can also be made to base 5 manipulatives — units, 5-unit rods, and 25-unit squares.

The game can later be played in a different base, to extend the difficulty level and to deepen understanding. I like to ask my students “how would you play this in base 7?” and they can quickly come up with the new rules.

The Spread of a Rumor or Virus

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rumor

This game introduces students to the concept of exponential growth. It can be played as the spread of a rumor, or the spread of a virus, and works well in an algebra or modeling course, in a quantitative reasoning course, or a liberal arts mathematics class.

Each student gets a card, labeled “Round 0 ____, Round 1 ____, etc.” On one student’s card, there is a yes next to round 0, while on the rest of the cards, there is a no. The student with a yes is the student who “knows” the rumor or who has the virus.

Students are instructed to stand up and mill around. In each round, they must look at one other person’s card. If that person’s card has a yes, the student who did not have a yes now has one, while everyone else writes no – without saying anything about which they have on their card. After enough rounds so that everyone has a yes (for a class of 35, this is usually about 6 rounds), students sit down and a chart is made of how many had a yes at each round. Connections are then made to doubling, and to powers of 2, which then leads to a discussion of exponential growth.

Note that the growth modeled here is actually logistic, since there is a limit to the number who will have the rumor or virus, but if the game is played only up to a certain number of rounds, it mimics plain exponential growth nicely – as does the spread of a rumor or virus in a large population. The game can later be played with different growth factors, such as introducing some amount of immunity (a person only gets the virus after being exposed twice, or three times) or increased virulence (each person shows two or three people their card, on each round).

The Spread of a Rumor can be seen as a simulation, rather than a game, although the distinction between a simulation and a game is often only a matter of semantics. However, for serious 18-year olds, it can be problematic to be seen “playing” – whereas older students and future teachers do not seem to mind as much.  I usually introduce this one without saying the word “game.”