Monthly Archives: August 2013

Multiplication Tic Tac Toe

Analytic presentation of all possible Tic-Tac-Toe games

I adapted this tic-tac-toe game from one I saw in a workshop claiming to be a multiplication tic-tac-toe game. It was similar to this multiplication tic-tac-toe game. It was fun enough, but it had no resemblance to a tic-tac-toe board.

I think my version has what it takes to be considered a “tiny math game.” All you really need to play this is paper, pencil, and two tokens (which could be two pieces of paper).

Embedded in the game is practice with multiplication facts, common multiples, and some good old fashion tic-tac-toe strategy, with a twist.

Instructions:

-Make a big Tic-Tac-Toe board, then make a tic-tac-toe board in each of the 9 squares.

-Now fill in the 9 squares with the multiples of 1-9 (see example below).

-Write the numbers 1-9 underneath your board.

-First player places two tokens (pennies in this case) each on one of the 9 numbers at the bottom. Multiplies these together, and places an “X” anywhere that multiple is found on the tic-tac-toe board. (in the example below player one has chosen 6 and 4, and has placed an X on all four “24s”)

-After the first move, players take turns choosing to move only one of the pennies to select their multiple to “X” or “O.” (For example 2nd player could move the “6” to a “3” and put an “O” over every 12 on the board)

-If you win a small tic-tac-toe game, you win that square on the larger board. The goal is to get Tic-Tac-Toe on the large board, by getting three of these smaller boards in a row.

-Also, I like to say any “Cat’s game” is a wildcard spot once it is completely filled in. This allows for player one and two to win simultaneously, which I like because I’m a sucker for win-win situations. 🙂

Notes For the Classroom:

I usually start by handing out this blank Multiplication Tic-Tac-Toe board. Students then take a few minutes to fill out the multiples of one in the top left corner, then multiples of 2 in the top middle, multiples of 3 in top right corner, etc (See example above).

First player places two tokens (pennies in this case) each on one of the 9 numbers. They multiply those two numbers together, and put an “X” anywhere that multiple is found on the tic-tac-toe board. In the example above, the first player has chosen to place the two tokens on 6 and 4, allowing her to place an “X” on the four places where “24.” I call these “quadruple plays,” and tell students to try to get as many of those as possible. Sometimes I have them color code the quadruple plays, and triple plays (like 36 or 9) so they are aware of them. This introduces and/or reenforces the concept of common multiples and factors. Check out my follow up post for more information on this.

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Filed under Elementary, Games

100 Game Theory

This is a great game to introduce game theory at a young age while simultaneously assessing place value and addition concepts.

Race to 100

How to Play:

Two players start from 0 and alternatively add a number from 1 to 10 to the sum. The player who reaches 100 wins.

I usually give students a hundreds chart to help keep track of where they are, as well as a “Race to 100” handout with tables to record what number each person said. Also once they discover that saying “89” guarantees they will be able to say 100, I have them star that number. I ask them to think if there are any other numbers that guarantee a win.

A 3rd grader shows the winning strategy visually on a hundreds chart. He put an X on the numbers he wants to say, and then shaded in the numbers his opponent "him" would be able to say.

A 3rd grader illustrates the winning strategy visually on a hundreds chart. He put an X on the numbers he wants to say, and then shaded in the numbers his opponent “him” would be able to say.

Extensions:

How would the strategy change if it were a race to 99?

How about if we change the numbers that you can add?

This is part of the family of games commonly known as Nim, NRICH has a thorough article and resources for these games called “Meet the Nim Family.”

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Filed under Elementary, Games

Number Bowling

This is a student favorite, simple to start, differentiated, with various levels of success. I’ve done this with grades 2 and up, but my 5th-6th graders have gotten the most out of it.

Most importantly students learn to be very clear in writing their expressions. This activity naturally leads to a discussion about order of operations and mathematical “grammar.” Also, in their pursuit of the strike, students often ask to be introduced to new operations.

Instructions: Begin by rolling a die three times and recording these numbers as your “1st bowl.” You may cross out (knock down) any number that you can write an equation for using those three numbers each only once. For example, if I rolled a 6, 6 and 5, I could knock down the number four by writing: 5=6-6+5, or knock down 1 by writing 1=(6÷6)^5. Notice I used all three numbers, but each only once.

The goal is to knock as many “pins” (numbers) as you can. Knocking all the pins down on your first bowl is called a “Strike.” If you can’t think of any other equations, you may bowl again and try for a “Spare.”

Notes on Implementation:

I’ve created this Number Bowling handout for students to keep track of their games. I’ve also experimented with keeping score, and I think three frames is a good length time for a game. This can get complicated though, since scoring bowling is foreign and not straightforward to many students.

This year, after a few games, I had students write down their “favorite” equations on a notecard. We used these equations during a “strategy session” where we came up with tricks to help knock down more pins. The “tricks” can all be described as using an operation to change a number, or two numbers, into another. For example, 3 can be changed into 6 by using factorial, (3!=6). Some more advanced tricks include using square root, and/or the floor and ceiling function (rounding up or down to nearest integer).

Extensions:

Last year students wondered whether a strike was possible for every combinations. We chose the brute force method of proof :). First students had to figure out how many unique outcomes were possible with 3 dice. For many I assisted them by having them look at this pdf. Obviously rolling 1,6,6 is the same as rolling 6,6,1.  Then whenever a student achieved a strike, we crossed that off the list.

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Filed under Games, Middle School

High Fives in Three Acts

This is my first attempt at publishing a “3-Act Math Lesson.” So it’s not quite polished yet, but it worked really well on the first day of school. Lots of different directions to take it at the end, including paths into rates and design thinking.

Prologue

Act One: High Fives All Around

Students share whatever questions they have about this clip with their neighbor.

Possible Questions

Why is he doing that?

How many people are in the circle?

How long is he doing that for?

How many high fives does he give?

Why would you have a world record for high fives?

(students are really surprised at first)

Act Two: How many high fives did he give?

Students work with their neighbor to come up with an estimate.

Take another look at the video, are there any clues?

Notice that in the clip there is a man keeping time, can you estimate how many times he makes it around the circle in a minute from these clues?

What do we need to know?

-Times around the circle

-Number of people in the circle

I make a table on the board with their estimates for revolutions, people in circle, and total high fives.

Act Three: Watch The Whole Clip

59 people in the circle

4 revolutions

How many high fives is that?

What is the average rate of high fives per second?

Is that more or less than you expected?

Sequel:

Do you think you could beat that record?

How could you better design the attempt to get more high fives?

What’s the upper limit for most high fives in 60 seconds?

Who would be able to high five more people Usain Bolt or LaShawn Merritt (400m World Champion)?

What if we each gave a high five to every student in the class, how many high fives would be given in total?

So many more directions you could go with this!

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Filed under 3-Act, Middle School