New Dice Game: Variation on "Race to 100"

There's a K-6 class (20 kids total) at my kid's school and I know their teacher Jen is always looking for activities that are adaptable for this wide age range. Plus, she's game for just about anything! That's why, when I came up with a variation on the "Race to 100" hundreds chart game the other day I just knew her class would be the perfect testing ground.

Race to 100 (or whatever other number you choose) is essentially adding or multiplying three dice then flipping a coin to determine whether you have to halve that number (tails) or double it (heads).  When I tried out the basic rules w/ my 9yo she got bored quickly which made me wonder what *could* keep a kid interested in playing?

It was fun to hear this afternoon how Jen's class took the game and ran with it -- so many different rules and variations!

Below is Jen's write-up on her class blog (password protected) of all the wonderful adaptations her class came up with on their first "roll" through the game.  She's going to do this again next week some time, so stay tuned for the update!

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1. Historically, dice is the plural of die, but in modern standard English,dice is both the singular and the plural: throw the dice could mean a reference to two or more dice, or to just one. In fact, the singular die (rather than dice) is increasingly uncommon.

Today the kids played variations of dice/coin flipping games.  I gave them a basic idea of how they COULD play and it was up to them to come up with the rules that fit their ability.

The Basics:  Choose three dice.  Add or multiply them in any order.  Flip a coin.  Heads means double your answer.  Tails means half your answer.  Add your score.  First one to 100 wins.

They had choices in dice as well:  your typical 6-sided dice, 10 sided dice, 12 sided dice, and we had one 20-sided dice.  As I walked around, here are some of the rules they made up:

K and B were multiplying a 6-sided dice, a 10-sided dice, and a 20-sided dice.  They flipped the coin:  doubled their total if heads flipped, halved their total if tails flipped.  The originally planned to play to 1000, but changed is to 3000 after B won too quickly.

A and O were adding a 12-sided dice, a 12-sided dice and a 6-sided dice.  They decided that if heads flipped on the coin, they would add 1.  If tails flipped, they would subtract 10.  They added a rule that said you should subtract 20 if your dice total was more than 10.  They played to 100.

M and C were adding their two 12-sided dice.  For the coin, heads meant +10 and tails meant -10.

Z and E added 2 6-sided dice and then multiplied their answer by a “multiple of 10″ dice.  They played to 1000.  Coin flips:  heads +10, tails -10

S and L added 3 dice (2 six sided dice and one “multiple of 10″ dice).  Coin flips:  heads x2, tails divide by 2.  They decided to play to 900.  L was having bad luck though.  When I asked how, they told me that he kept having to divide his answer because he kept flipping tails!!!

L, E, and A were playing with three dice, but the third dice, a “multiple of 10 dice” only came into play if someone flipped heads.  Apparently on E’s first turn, “she got to add 90 to her score!!!!”

The Littles played as well, rolling and adding 2 6-sided dice.  Flipping coins with heads meaning +1 and tails meaning -1.  They played to 100 and used a hundreds chart to keep track of their score.

Knowing Numbers & UNO Update

I've been watching my six-year-old daughter explore math all fall and now into the winter.  At the same time, I have also been reading books about how K-2 kids learn math, and growing my own 'math eyes' (as Maria Drukova of Moebius Noodles and Natural Math says). 

It's been fascinating to watch my kid's understanding of numbers develop over the last six months, even with a somewhat hands-off approach. She started this summer with a lot of comparing and measuring.  Then she started asking lots of questions about numbers and shapes, mostly on her own time.  Sometimes I'd be there during the process, as in this line of questioning about dividing a number in half.  Other times I'd run across the results of her thinking later in the day, as with a geometric study she initiated with some tangrams. 

There's a book I've been reading, a few pages in bed each night before I turn off the light.  It's called Games for Math: Playful Ways to Help Your Child Learn Math from Kindergarten to Third Grade, written by Peggy Kaye.

In this book, Peggy shares all sorts of fun math games that require no more than some paper, a pencil, some dice to roll, tape, egg cartons, beans...you get the picture.  The best thing about this book, besides the very easy-to-implement, high-interest games is how she puts the games into context with stories about working with specific children.  I really, really like 'hearing' her have math conversations with children; the activities are pretty simple but the important thing is how she models mathematical reasoning and problem solving strategies while she plays the games with each child.  

My favorite games so far are Star Count and Lots of Boxes.  Both involve a pen, some paper, and a die to roll and both focus on understanding groupings of  numbers as a way of practicing counting and introducing multiplication at the same time.  My kid has been asking questions that show she is thinking multiplicitively, but she is not quite ready for or interested in sitting down to discover the patterns in the multiplication chart, so these games are perfect for her right now.  Also, How Many Boxes is also a great introduction to perimeter and area since it is played on graph paper. 

A couple weeks ago the kid surprised me with some spontaneous backward counting from 100.  It was wonderful listening to her find enjoyment in figuring out the pattern, but I didn't really understand the importance of this new skill until last night.  That's when I read a section where Peggy Kaye talks about the kinds of number skills kids need to have to learn how to add and subtract.  These include:

- Counting forward from one (I keep trying to remember to start counting from zero, but starting at one is just too ingrained)
-  Counting forward from a number other than one, like five and going from there
- Counting backward from ten or twenty or one hundred
- Counting backward from a random number
- Skip counting twos, threes, fives, tens...

My kid has been spontaneously skip counting since the early summer, and counting forward for longer than that.  In terms of the girl's new penchant for counting backward, it seems this new skill of hers is really important for mastering subtraction, something we haven't done a lot of.

What she and I do do is a lot of adding numbers together with daily UNO games but, just today, the whole 'adding up the UNO score' activity seemed like it had lost it's challenge.  When I lose, she whisks the cards over to her space, spots the tens easily and without prompting, adds up 10's and 20's without pause, and takes the extra cards and finds a final total.  Sensing a turning point, I suddenly had an idea for another way to challenge her.  Here's my new thing:

Instead of adding up the numbers, take all the cards you've won from your opponent and use them as digits.  The object?  Make the absolutely largest number you can.  A five and a one can make 15 or 51, for example.  Or, there's this hand I lost to her this afternoon:

Ha!  It's probably the largest UNO score EVER!!  And, it's a great way to introduce hundreds, thousands and millions as well as 'which number is biggest' on the grandest possible scale.  The cards become great manipulatives, so once she gets comfortable reading the numbers I've made (while modeling my thinking process), she'll get a chance to figure out how to move them around to make 'the biggest number' she can.

But back to counting backwards.  I don't really understand my child.  She is quite independent in her learning, and often resistant to formal instruction.  But she really likes it when I give her spelling tests!?  And, today, when we were at the library, she asked me to give her a math test.  Um, okay.

I eventually obliged and put together a list of equations.  As I've said, we haven't done much in the way of subtraction, so this little test was actually a good way to assess where she is right now.  Plus, with my new understanding of counting backwards?  Wouldn't you know it -- there she was counting backward to figure out the answers!

She also wanted some multiplication problems so I used a strategy from Peggy Kaye's Star Count game to illustrate each problem.  "Two groups of two", "three groups of four", "five groups of one" are the way we say it.  She got her answers by counting the dots, but I can imagine if she keeps this up we might be ready for coloring in the patterns in the multiplication chart by spring.  I really want to do square and triangular numbers with her using visuals but, as always, I just need to be prepared to jump in with it when there's an opening.

In closing, as I was in the process of wrapping up this post, the kid wanted another math test.  I learned a lot from seeing how she answered the questions.  Next time I'll put the addition, subtraction and multiplication problems in their own sections, not all mixed together.  But the biggest thing is that I'm going to get the Cuisenaire rods out again so we can solve the subtraction problems together for a while. 30-2 was just a little too big of a 'problem' for her, but if we can look at it with the rods I think the idea will click into place without much fuss.  My final lesson?  Math is definitely a morning thing.  No more math at 5pm!

[Edit, 1/26/12: Here's what happened the very next day with the subtraction and the counting backward.  When it rains, it pours.]

Survival Math -or- How Cuisenaire Rods Contribute to Independent Living



From South to North: Our House, Bloomington, Park,
Nashville, Columbus (IN), Ohio (see the archway?)

Darling girl is an early riser and a morning learner.  Every day she rises, recites her list of questions and plans, and sets it all in motion.  This morning the dear child drew herself a map.

Soon after, she was really, really frightfully intent on writing number sentences.  All before my first cup of caffeine.  Normally I'd just let her chatter away and let it all wash over me (it was only 7am after all) but today the tide was just too strong.  I didn't really understand why there was such a need to do all this before breakfast but sometimes you just need to act first and ask questions later. 

She had already started her 'math lesson' by writing down 1+1=2.  Then 2+2, 3+3, 5+5.  At some point she said, "Every time I add, the numbers get bigger!"  The answer to 5+5 was doubled, which was doubled again.  80+80 gave her some pause, but by then I had drunk my tea and decided we might as well get out those Cuisenaire rods again. 

I wasn't completely sure if she was ready to move on to labeling each rod with a unit number or, for that matter, if I really understood how to use the rods to represent addition, or if we were going in the 'right' sequence of learning with these things.  But why let any of that stop me?

I said, "First, can you just put the rods in order from smallest to biggest?"  Done.  "Okay, let's look at your first number sentence, one plus one.  Here are two of the white blocks.  Which block is the same length as two white blocks?"

She picks up the red rod.  I say, "Okay, how many whites makes a red?  So when you write 'two plus two' this is what it looks like.  Which rod equals four whites or two reds?"  She pulls the purple rod to match.

 

 Then I had a bright idea:  "Can you figure out how many white blocks make an orange?  What other ways can you combine the rods to make ten?"  Girl interrupts my line of thought, "I want to make a line of a hundred!" She knows that ten tens make one hundred so she starts stacking them together to make sure she has ten of them before she lines them up.  I persist, "How many more ways can you make a ten?"

 

She wanted to see how long a line the ten tens would make when lined up end to end. 

This is how long it was and there are apparently many different ways to combine the rods to make ten.  We didn't get to all of them, I'm sure.  Then she wanted to see what a line 200 units long would be...



"Look Mama!  I'm 110 units long!"

Overall, my biggest takeaway from this morning is that, although she has enough questions to keep us busy for now, I need to do some more research on the best way to use Cuisenaire rods -- quick!

Later in the day I did find out why she was so intent on doing math this morning.  It's actually a secret so if you see her don't let on that you know.  "Mama," she said, "You know why I've been wanting a longer math lesson and have been so interested in maps and money?  Because T. [a good friend] and I were wondering what would happen if you [the mommies] stopped loving us and those things would be important to know."

Apparently, she and her great friend T. have hatched a sort of secret survival plan for an undefined point in the future when "our mommies don't love us any more."  They've decided they need to know how to do math, figure out how to work with money, and know how to survive in the outdoors.  After I assured her repeatedly that I will ALWAYS love her, we went to the library to get some books about how to identify and cook with edible plants. 

She said, "Don't tell T. that I told you.  And even if you never stop loving me, it's still helpful information to know."

"I won't tell," I replied, "But it's probably good that I do know so I can help you find the information you need. Learning all this will be really helpful when you grow up and live on your own."

"But I'm going to live with you forever."

White...Red...Light Green...Purple...Cuisenaire Rods!

I pulled out the cuisenaire rods yesterday.  The set had been sitting on a shelf for almost a year.  If you don't know what they are the best I can say right now is that, essentially, they are unit blocks of specific colors designed to (at least at first) help kids develop number sense as well as strengthen conceptual understanding of addition, subtraction, multiplication and division. 

The girl immediately remembered the long ago time when we played a 'trick' of putting the first four (white, red, light green, purple) behind our backs.  One of us would tell the other which color to bring forward, and every time we'd be right!   I can tell I'm going to do a little more research on how to use these things, but I know from what I've seen so far is that the first thing you do is focus on the attributes of each color in relationship to each other before assigning a unit number.  Here's how things developed today:



Girl: "I'm going to put them biggest to smallest..."  Mama: "Say it with me!  Orange, blue, brown, black...  Okay now, with our eyes closed!  Orange, blue, brown...Yay we did it!  Now smallest to biggest, white, red, light green, purple..."



Mama: "Hey look!  A blue with a white makes an orange.  Oh, and a red with a black makes an orange, too!"  Girl: "Let me do it."

Girl: "It's divided here."  Mama: "Oh, I see it, on the diagonal.  Let's put a block down to show where it is."

Girl: "I want to pull them apart."  Mama: "Look, they're in the same order!"

Girl: "Now I want to make a design."

What she figured out is that to make this design work you had to skip colors: orange + 2, blue, (skip brown), black, (skip green), yellow, etc.

So many more things to do with these -- I can't wait!!