July 2022
Welcome to EFM's July Newsletter!
News
Math Activities for Educators We created a page on our website dedicated to math resources for educators. Two months ago we announced Math Games for Tutoring, which is a special subset of EFM games particularly useful for giving students targeted practice on a specific topic. Recently we added Math Games for Classroom Breaks to that page. These games are quick and easy fillers for when you have some time between classroom lessons, or for when you need an uplifting change of energy. Look for more material for educators to be added in the coming months!
EFM Study in Kenya Working with our partner IDEMS, we used their software platform to create a mobile app for Android phones, which is being field tested in a six-week pilot study in Kenya. I can't resist throwing in one quick quote from that study: Before knowing about the early family math app, I did not know what activities I could do with my child. The app has given me stories and activities to enable me to have a good time with my child.
Electronic Donations Our Donate page on the EFM website now has the option of receiving electronic donations. Because this option is available by going to our Facebook page, I'll save you a click and direct you to the EFM Facebook page, where you will find a shiny new blue "Donate" button that is badly in need of a workout. We are all unpaid volunteers and we make all our materials available for free. Donations are the key to paying for not only our website, but also future programs we hope to create, such as free decks of playing cards with EFM activities on them.
New Activities to Enjoy!
The activities this month come from Math for Love. Their website has a large array of great resources for families and educators. As big believers in play-based learning, it is not surprising that they have a lovely collection of free games to choose from, and I have chosen two to use this month.
Dots and Boxes with Numbers
I remember going out to restaurants with my two children and the fun they had when the restaurant offered paper placemats and crayons. Often, one of the games on the placemat was dots and boxes, and this led to fun times of creating squares and seeing who could make surprising runs of squares.
The basic game of dots and boxes is simple and well known. It is covered in Chapter 3 in EFM. Start by creating an array of dots in a grid pattern. For a young child, that might be as small as 3 by 4 (as pictured below). Next, the players take turns drawing one horizontal or vertical line connecting two neighboring dots. If the new line completes a 1 by 1 box, the player earns one point and gets to draw another line. A player is not obligated to finish a box if there is another preferred move. When no more lines can be drawn, the player with the most points wins. An easy way to keep track of points is to put an initial inside each box as it is earned.
Although this is traditionally played with little squares, it can also be played with dots in patterns that produce triangles or hexagons. The main problem with doing this is that it's harder to draw the dot patterns.
Here is an example of a partially completed game.
Dots and Boxes is played by most people with relatively little thought until near the end, and that's fine. It can be a very pleasurable way to spend time together, and the end portion of the game still provides plenty of opportunities to hone strategic thinking. However, for the enthusiasts out there, this can be a very deep game which is described in great detail in an excellent book by Elwyn Berlekamp called The Dots and Boxes Game.
Using Numbers The single big change for Dots and Boxes with Numbers is that the boxes are no longer all worth one point. The value assigned to each square is drawn in before the game starts.
Here is the same game as before, but filled in with two possible sets of values. In the first game, the person "C" who finished off the two boxes has earned a total of three points. In the second game, some negative values have been used, and the total value of the two boxes is just one point. If you choose to use negative values, you can finesse this by saying that those are values that are going to be subtracted, which is a great way to introduce subtraction into this game – it can also be a way to subtly introduce negative numbers!
Using numbers completely changes the strategy of the game in some fun ways. It also provides an opportunity to practice addition and subtraction in a setting where making and reasoning about the calculations feels strategic and not just doing pointless routine practice.
Fill in the Blanks
This is a game that can be enjoyed by any number of players. There are many possible ways to configure this game. They all involve establishing a configuration of blank spaces that each player will fill in with random digits as they are generated, and a goal to achieve when those blank spaces are all filled in. Generate the random digits using a die, a set of playing cards, or an electronic device.
A simple version of this activity is for each player to have two blanks that are used to create a 2-digit number _ _ and a third blank _ to use as a trash bin. The goal is to create the largest number possible. When the first random digit is announced, each player must decide whether to put it in the ones or tens digit of their number, or the trash. Once any digit is placed, that number can never be moved. Similarly, the second and third numbers are placed, after which the player with the largest two-digit number wins.
Here is an example of two players playing this version where the random numbers generated were 6, 2, and 5. Player 1 decided to "go for it" with the first number 6, and Player 2 hoped for better (which didn't work out very well on this occasion).
There are lots of options for this game.
Use 3-digit or 4-digit numbers
Change the number of digits in the trash bin
The winner is the one who minimizes (instead of maximizes) the result
Add two or three two-digit or three-digit numbers
Subtract two numbers and minimize the result, but negative answers lose
Maximize adding two or three numbers with a limit that you can't go over
For example, the game Don't Break the Bank on Math for Love involves maximizing the sum of three 3-digit numbers, but you lose if you go over the limit of 1000 and "break the bank."
There is no reason to restrict this to addition and subtraction. For example, you could maximize a 1-digit number being multiplied by a 2-digit number, where the result should not be larger than 200. There is lots of room to play around with this and to let your child suggest possible versions of their own.
If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, I would love to talk with you about ways we can work together.
Chris Wright
July 18, 2022
Chris@EarlyFamilyMath.org
Facebook | Instagram
Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.