We know how important it is that students are able to show flexibility with numbers and manipulate them mentally, rather than relying on the standard algorithm. Just like a chef uses what she knows about flavors and pairings to create a meal without a scripted recipe, we want students to be able to naturally choose strategies that work for the situation.
But how do we get here? How do we get students to a place where they are able to use numbers and operations flexibly and naturally? Besides modelling for students, we can give them purposeful opportunities to use numbers in flexible ways. For example, instead of giving students a problem to work through. give them an answer and allow them to brainstorm the problem for that answer.
Another way we can help students build this flexibility is through strategic games.
Here is a division game that students love as they learn more complex division skills such as remainders. The game involves strategy and number sense, keeping students engaged and eager to play.
Division Golf: A Strategic Division Game
To play Division golf, your students will work in partners. Each pair of students will need a deck of cards with the J, Q, K, and Aces removed (keep only the numbers 2-9). To keep score, students will need a piece of paper and a pencil or a mini whiteboard.
Like real golf, the goal of Division Golf is to be the player with the lowest score (this score will be made up of the remainders you have when you divide).
First, shuffle the cards and place them face down. Player #1 draws three cards and uses them to create two numbers (one 1-digit number and one 2-digit number). The goal is the have the fewest remainders when you divide.
For example, suppose you draw a 9, 4, and 8. Here are a few of the different division expressions you could build: 94÷8, 98÷4, 48÷9, 49÷8, etc.
94÷8 would leave you with a remainder of 6. 98÷4 would leave you with a remainder of 2. 48÷9 would leave you with a remainder of 3. 49÷8 would leave you with a remainder of 1. Of the four expressions listed here, 49÷8 would be the best one to choose because it has the lowest remainder. This becomes Player #1’s score.
Remember, this is a golf game so the goal is to get the lowest score.
Players alternate turns. This game can be played for a specific amount of time, or it can be played like traditional golf where each player gets nine turns, and the player with the lowest score at the end is the winner.
Game Modifications and Adaptations
When playing any game in the classroom, it is essential that your students feel successful. If the game is too difficult, your students will “check out” and resist even trying. This is when classroom management issues arise, and learning is not optimal. To get the most out of this game, ensure that it is a “just right” challenge for your students – not too easy, but also not too difficult. I recommend always starting a bit too easy, and then moving up from there until you find the sweet spot. Here are some ways that you can adapt this game to ensure that it is perfect for your unique classroom.
To make this division game easier:
- Decrease the number of rounds to 5.
- Give your students counting pieces that they can use to model the division problem. You might use counters, beans, base ten blocks, or even simply a personal whiteboard to draw a model. Manipulatives will make the remainders easier to see.
- Allow the students to use only 2 of the cards if they wish. For example, if a 9, 4, and 8 are drawn, students could choose to use only the 4 and 8 to make the expression 8÷4. This would give them no remainders, so their score for that round is 0!
- If having to choose between the three cards is too challenging right now, have them draw only 2 cards.
- If you have not yet introduced the word, “remainder,” you might call it “leftovers” for now. For example, 7 divided by 3 is 2 with 1 leftover. This can be shown with counters so students can see it in real life.
- Add an extra card! Students can then make a 3-digit by 1-digit expression.
- Play “18 holes” (or rounds) rather than 9.
- Change it up! Make the goal to be the highest score (or most remainders) instead of the lowest!
As students play this division golf game, they will likely develop strategies that help them keep their scores low. Have them put their mathematical reasoning into words and share these with the class.
The more opportunities students are given to explore and work with numbers, the more flexible their thinking will become. This game is just another way to help make that happen.