It's division time--and I am always shocked at how students freak out about division...and how much "harder" it is than multiplication. I always promise them that I can make it easier for them! I posted a picture on Instagram the other day and I had a bunch of requests for more details on the "Herding Game"!
To begin, I wanted students to really understand the idea that multiplication and division are so linked that we can almost use them interchangeably in our minds—but that our math language needed to reflect what we are doing. What do I mean? We often teach students what many call “turn around” facts. We tell them that 4 x 3 is the same as 3 x 4. But is it? Is four boxes of 3 pies the same as 3 boxes of 4 pies? No it isn’t. They both represent 12 pies—but the situation is totally different. To help students see this, I made up a game a few years ago...and it has proven to be super effective--and FUN!
I told the students that they were going to be a “herd” of animals today and that I had researched a whole bunch of animals that traveled in herds. I also let them know that when animals who travel in herds are threatened, they sometimes break into smaller groups to protect each other. I told them that I was going to break them into smaller groups today and then we would write the mathematical equations that we discovered in the process. We counted our “herd” and found that we had 22 animals this day.
I taped off an area of one of our empty classrooms (this would have been fun to do outside as well with a chalked off area) to have as our “holding pen” for extra animals that couldn’t find a group. I also put some animal “tokens” in the pen so that each child who ended up there took a token—and the token was a “get out of the pen free” card so the same students didn’t always up there. For some reason, some students WANT to land in the holding pen so they don't actively participate in the herding...so once is enough!
Here's how we play.
First of all, I called out a type of animal (buffalo, giraffes, zebras, wild boars, cows, bison, elephants…) and the size of the group I wanted them to form. For example…
“Elephants—form groups of 5!”
The students scampered to make their groups, and I asked for help writing the equation on the board. I had to help a bit, but with coaching, we got it. I asked,“So I just formed four groups of 5?"
I wrote 4 x 5 = 20. "What about the leftovers?" I wrote (4 x 5) + 2 = 22
We tried again. “Giraffes—form groups of 2!” Students quickly paired up and we wrote the equations.
22 ÷ 2 = 11
11 x 2 = 22
No remainders this time!
The students were getting the hang of the game so I decided to move to the next steps. “Buffalo—form groups of 7.”
The students struggled a bit to make their groups—but eventually the leftover buffalo found its way to the holding pen. We worked
to write the equations this time. 22 ÷ 7 = 3 groups with 1 remaining
(3 x 7) + 1 = 22. We tried again..."Make 3 herds of antelope!" (Different than herds of 3, right?)
Everything was going beautifully--until one of our specialist teachers showed up...so we had to redo the game a few times with 23 animals!
We continued with several more rounds until I could see that the students were getting the hang of it! We wrote down some of our rounds on the board (when I remembered!) and then I asked them to try to do some mental math to determine what would happen if I asked them to make groups of 9…then groups of 6. They did a great job! I knew that I had given my entire class enough to go on—and I was ready to continue the work with my more struggling students back in the classroom.
While my other students were working on some multi-step problem solving, I pulled some of my struggling students to try our “herding” activities in a smaller group. I made some cute little animal tokens to use as counters and we started working to tell herding stories. I wanted to see if they could apply the skills of the game a little more independently and could make the shift to recording their math equations on their own.
Much like the game, I told herding stories but this time gave each student a baggies of animals—and I was able to change the number of animals in the herd at will. So the questions began…
“You have a herd of 12 animals. Divide them into 3 groups—what do you get?”
“You have a herd of 16 animals. Divide them into 8 groups—what do you get?”
“You have a herd of 20 elephants. Divide them into 5 groups—what do you get?”
We did several rounds where the groups worked out with no remainders, but after a few minutes, I moved to working with remainders. Students started really seeing the connection between their multiplication facts and the division problems! We kept track on the recording sheet to make sure that we were getting the practice with the math language and grouping concepts. I really started seeing light bulbs go off!
As a follow up, I introduced "The Pretzel Game"...perfect for practicing these division with remainders situations. See what you think and give it a try! I probably should make more copies of this...I only have two right now and my students are clamoring for it!
If you want to see more, here are the two resources I used to get this division unit going!