We are going to talk today about place value and how we can, even starting at kindergarten, build a solid understanding of place value and regrouping. Here we go!
We are going to play Race to 1,000 starting in kindergarten, yes race to 1,000, and yes kindergarten. Well, not at the first week, but by the end of the year we can expect all the children to know how to play Race to 1,000 - this is place value regrouping at its best. There are several games, Race to 100, Race to 200, Race to 500, Race to a Dollar, Race to 1,000, basically any variation you can think of. They all have the same basic rules, they are played with three players, one player is the banker and has all the blocks, and then there are two players and they are racing to see who can get to 100 first, or whichever goal number is set. That’s it, one is a banker and two are having a race.
The directions for Race to 100: students are in groups of three, the banker has twenty-five 1-blocks, twenty-five 10-blocks, and one 100-block. There is a die labeled with 10, 12, 8, 15, 5 and 11. Doesn’t have to be exactly those numbers, you can vary it, but you want an average of about 10 when you are racing to 100, so there are about ten rolls of the die before there is a winner. If the numbers of the die are too large, the game ends too quickly, if they are too small, the students will get bored before there is a winner.
The first player will roll the die and the banker then will distribute the blocks, the second player does the same - that’s it! They take turns rolling the die and the banker gives them the blocks. But, here is the key, when a player has ten 1-blocks, then they will give them back to the banker and the banker will give them one 10-block. That’s what they do, over and over and over. You will soon hear them counting by tens at a young age, “I have 10, I have 20, I have 30, I have 40, I have 50!” They are counting by tens and then they will add the ones on, “I have 51, 52, 53”, they are keeping track of it at a young age. The winner is the first person to trade in ten of the 10-blocks for the 100-block! The winner usually then becomes the next banker and then when they play the third round, the third player is the banker. It takes about three games for a math period and this is the assignment for that day, it is not something else that you do when you finish your assignment, this is the assignment. And, by the way, you don’t have to limit this to kindergarten, I’m just saying that kindergarteners understand it and love it.
Race to 500, the same game, except the banker has a bunch of 100-blocks, maybe nine or ten. The first person to have 500 is the winner. The only change is the number on the die. The rolls for this game need to be larger numbers, 50, 60, 40, 65, 35, and 52, for example. You will see the average is around 50, you want to keep with the rule of approximately ten rolls before there is a winner.
Race to 1,000, oh my goodness, do students love this! They love that 1,000 block. It’s the same game, just increasing the numbers, you can write 100 on one side of the die, 120, 102, 85, 58, and 110 for example. You will enjoy seeing the little argument between the student who rolls 120 and the banker who gives them 102, they have to solve it and figure it out. We are working on the placement and regrouping - but they understand it at a young age, it's all about trading in the smaller numeral for the bigger and all the way down the line until they get to the 1,000 block.
The same rules apply when you race to $1.00, except it is a little more difficult to know that you trade five pennies for a nickel and two nickels for a dime and then nickels and dimes for quarters or half-dollars and then two half-dollars for a $1.00, but they do get it. They can learn this, even at a very young age, they can learn the rules for money.
The rules change when you play Go for Broke, instead of racing to get to 100, you are racing to have nothing left. You give each player a 100-block and whatever they roll, they have to give it back to the banker. Well, if each player has a 100-block and they roll an 8, they have to give the banker back the 100-block, the Banker would then give them ten-10-blocks, but then they player would need to take one of the 10-blocks and trade that in with the banker for ten 1-blocks, only then would they be able to give the Banker the 8 blocks that were rolled on the die. It is more difficult, it is harder, but obviously subtraction is harder at schools than addition, so of course it is harder. You will hear funny things from students like “I don’t want to go broke”, they like the hanging on more than they do going broke - but it really sets the stage for explaining addition, subtraction and regrouping when you come to that in the curriculum.
Once children have a firm grasp of place value and regrouping, they understand our computation explanations! You do not need to limit the young children to add and subtract, they can learn the beginning of multiplication and beginning division at a young age. 369 divided by 3, imagine knowing how to do that in the first grade, you get three 100-blocks, six 10-blocks and nine 1-blocks and divide the blocks into three piles, instead of wasting a bunch of time trying to explain all of that, they get it because they know the place value regrouping and we have built a solid foundation for them
Please do not hold children back! Here is a 40-year-old story, I was a Math Coordinator for a school district and we placed base ten blocks into every first grade classroom. They were fairly new at that time, and no teachers had them. I went into every first grade classroom, there were 50 of them, three times during the year to help the teachers with implementing them. I walk in the room and ask the teacher, “Hey, where do you keep your blocks”, and they would point over in a corner and I would go over, look and say,”Huh, where are the 1,000-blocks?”. The teacher would put their hand over their mouths and have a look and say, “this is the first grade”. “Yes, I know this is the first grade, but where are the 1,000-blocks?”, the teachers would answer a little louder, but still in a whisper, “This is first grade, so they are up in the cupboards”. Then I would have to go get something to stand on, climb up, move the boxes out of the way and get the 1,000-blocks out of the cupboard. You think… well, that is an old story, but this actually happened to me recently, very recently, the only difference this time was it was a special education class. Same thing, walk in the room, “Where are the 1,000-blocks?”, “This is special ed”, “Yes, I know, so where are the 1,000-blocks?”, “but this is special ed”. And then again, within this last year, a first grade teacher told me that “Children can’t even handle 100 in first grade”. So, this is part of what we have inherited? I’m just saying, please do not hold back our students.
Students can learn far more than we ever, ever expected. Lets take a first grade problem, 374 + 267. Triple digit addition?!? We must be crazy! But once your students have played these Race Games it will be so intuitive to them. Your student will simply grab four 1-blocks, seven 10-blocks, and three 100-blocks. For the next number, they will grab seven 1-blocks, six 10-blocks, and two 100-blocks. When they add them together, they build the first number, then they build the second number, then they put them all into one pile. Once they put them together, they will realize they ended up with eleven 1-blocks and you can say to them, “What do you do when you have eleven 1’s?” Oh, we will have to trade some of them in for a 10-block. That’s how they learned the regrouping, they learned it while playing the game. And that is true for all that we do to add, subtract, multiply and divide, when grouping and regrouping is necessary, they get it. Please don’t hold them back, students love a challenge and proving they know more and more.
Our team would love to hear from you, especially if you have any stories, such as the kindergartner saying, “Well, I don’t want to go broke!”
