Decimal Place Value, Decimal Estimation Strategy Game
I developed this activity a course of years ago. The first versions involved whole numbers, where players drew cards and used ones and tens to make 100 (I actually have a similar activity that uses cubes and rods to make a flat; it’s called “Close to a Flat.”) In this activity, players select numbers and place them in different place values to get as close to 1 as possible.
The game can be played with a set of 0 - 9 digit cards (which are attached for your pleasure), or you can use a ten-sided die (I love those things - you should buy dozens of them at the start of each school year....) Some people use a 1-6 die to play the game - the numbers are a little easier to work with, but I don’t think it works as well. Having a “0” makes the game extra challenging, and rolling a zero can provoke a nice discussion about what its meaning and effect.
I didn’t put rules on each of the sheets, because I think it’s easier to demonstrate if the kids are not reading them (and if they take the game home to parents, they should be able to explain it to them.) The rules are quite simple: players work in teams of 2 - 3, each with a game board. They take turns selecting cards (or rolling a ten-sided die) and then placing the digit in one of the place value columns. At the end of 7 rounds, they add up all the tenths and hundredths (and thousandths, if that’s the version you’re playing) and then do the regrouping/exchanging to make a single decimal. They then compare how close their decimal is to 1 and record it. Whomever is closest to 1 is the winner.
Some important tips:
Make sure your students understand that there are 7 rounds, so if they use put large numbers in the tenths place in the early rounds, they’ll surely go over 1.
Once a number is placed during a round, it cannot be moved around in a later round.
Emphasize that this game is combination of strategy and luck: the luck is what number you’ll get. The strategy is in how you use that number. At the end of the game, have them look back and ask what they could have done differently to get closer to 1.
You can add an extra rule to make things more interesting: at the end of the game, each player can change the value of one of the numbers they placed by erasing it and moving it to a different column, and then re-calculating how close he/she is 1.
There are “Puzzlas” you can use for homework, as well as blank ones that you can make for yourself. There is no answer sheet for these, because there is no “right answer.” This is intended for your students to discuss their different strategies to optimize their outcome.
There are also “DIY” (Do It Yourself) sheets where kids can place the numbers, and then show how they will add up to exactly 1. Again, different strategies will be needed. You may need to put some restrictions on how many of each number they can use, or that they have to place numbers in all columns (this is to prevent a student from putting 5 in the tenths column twice, and then all 0s for the rest of the columns....) It is your call on this one; maybe you can even have the students come up with their own restrictions.