Here is an excellent, excellent game that will get your students thinking carefully and deeply about subtraction, no matter what their age is. If they are in 1st or 2nd grade, they can pratice finding pairs of numbers with single digit answers, and if they’re older, they can practice creating problems that are done mentally or by hand, with or without regrouping (it’s not “borrowing,” folks; for the last time, it’s not “borrowing”) up to three by three digits. It also involves a vast amount of estimation, which is always good for your kids’ brains.
Here’s the idea: instead of having kids do lots and lots of mindless problems on a cruddy worksheet, why not turn the question around: how would you locate pairs of numbers that are a certain distance apart? I’ve made this like a “yahtzee” game, in that you can’t just make pairs that are 1 or 2 apart. Nay, you have to fill out as many spaces on the grid as you can using different combinations: you can find two single digit numbers that are 9 apart (not many there, my friend) or earn more points by finding a double digit minus a single digit that are 9 apart. Want to earn even more points? Find two double digit numbers that are 9 apart
Here are some tips on how to use this in your classroom:
Make sure students understand the difference in the columns; that is, if they’ve filled in a single - single that is 4 apart, they can’t do it again because the box has been filled. They can do two numbers that are 4 apart, but only if it is double minus single digit, or double minus double.
You can decide how many “turns” each player gets until the game is “over.” There are 27 spaces to fill, and some students may lose a turn because they can’t fill any of their spaces (especially as the spaces fill up and there are fewer empty ones to fill.) You can make it 10 “rounds” or set a time limit of 30 minutes for the two players to do as much as they can.
Emphasize that there are different ways to find numbers that are a certain distance apart. For example, if you see a 9, the two numbers that are 5 away are 4 and 14; if the student can make either of these numbers, it can be filled in. 9 - 4 can be recorded in the “5 apart, single - single” box, or 14 - 9 can be recorded in the 5 apart, “double - single” box. It is important for students to see that when we say “difference” in regards to subtraction, we mean the “distance” between two numbers.
Some students will write the subtraction backwards - that is, they’ll write “4 - 9” as being 5 apart. While it is true, one of the properties of subtraction is that it is not “closed” using whole numbers: 4 and 9 are indeed 5 apart, but if you write it as a subtraction problem, the smaller amount has to be removed from the larger. Otherwise, 4 - 9 = -5, which is something that can be pointed out as a topic they’ll learn about when older.
I’ve also included some “DIY” versions of the game; this is especially good for students who need additional challenges, because they have to set their own goals for what they would like to try. Perhaps they’ll use intervals like 50 -55 to find differences, which could be very challenging, as the narrower the interval, the harder it is to find that number.
• Finally, part of the rules are that you can’t use 0 as the subtrahend in more than one box. I’m sure you understand why!