By popular demand, our math game tutorials series will continue through February and we will continue adding to our tutorial library! Teachers (especially those in our M³ Project Schools!) are raving about our math game tutorial videos!
Most of the time, in our math workshop, the games we bring the kids for their Math with Someone station are connected with the content we’re teaching – if we’re teaching multiplying decimals to 5th grade, we want students to be playing a corresponding, standards-based game that will help solidify that concept.
But this week, we’re going to approach math games a bit differently and bring you three games that don’t actually have to do with a specific area in math (like multiplication or addition). Instead, these games are designed to help kids become more strategic in their thinking and this string of strategy games should be threaded throughout our math workshop.
As we know and have discussed before, students of the 21st century are really suffering from that disease of entitlement and instant gratification. As a result of having answers and information at their fingertips through Siri or YouTube, they don’t typically want to put effort into anything that is a mental challenge. Unfortunately, a lot of our students just want the answers, the short cuts. They want us to just tell them what to do so they can do it.
However, we need students to think! We need them to be critical thinkers and innovators, so we have to help them learn to flex their mental muscles. Strategy games in math centers are the perfect starting place! These games give students a chance to question their metacognition as they think through different scenarios in order to be successful and win the game.
This ties in the 8 Mathematical Practices perfectly (get a free download of an 8 Math Practices placemat for early childhood or the posters for elementary in our store!). These standards have raised the rigor of our curriculum and demand that students go beyond regurgitating information. Not only must students know the answer, but they must also be able to explain why they know what they know.
A Note on Strategies
There are strategies involved in these games! As these videos were designed for students to use to learn to play the games, they will NOT give away those strategies during the tutorials! We recommend you do the same as you interact with students about the games. Explaining the strategy to students shuts off the metacognition that we’re looking for kids to practice. We really want students to self-discover these strategies and tips on their own as they play.
Rotten Apples helps kids question their metacognition as they play through possible scenarios. They must do a little bit of predicting to decide their partner might do if they make a certain move and then what might happen in the end.
This game is incredibly simple – that’s one of the reasons I love it! It doesn’t involve a game board or any materials other than 13 counters. If I’m playing in the classroom, I like to use the 2-sided counters because they easily show us which apples are good (12 red ones) and which one is rotten (the last one flipped to the yellow side). If you’re playing at home, you could play with pennies and have a nickel as the rotten apple. You could use M&Ms and an Oreo – anything where you can have 12 of one thing and one of something different will work! I remember playing with my son at restaurants and using sugar packets as good apples and a Sweet ‘n Low as the rotten apple.
You can play with students as young as 4-years-old all the way up through adults!
- Lay the “apples” down in front of both players.
- Decide who goes first.
- The more they play, students might decide that there’s strategy in choosing to go first or to go second! Let them play and experiment!
- On their turn, a player can choose to take 1, 2, or 3 “apples” or counters.
- The next player takes 1, 2, or 3 apples.
- Continue to take turns drawing apples until one player loses the game by being “stuck” with the rotten apple.
That’s it! Those are the basics! But as you and I both know, it’s not that simple. It’s completely up to each player how many apples they want to take. Students will need to learn to watch and see how many counters remain as the pile starts to dwindle and they’ll need to play through different scenarios to see what might happen if they make a certain move.
After a period of continuous play, we like to have kids come up with a strategy they think would make it to where they would always be able to win by avoiding the rotten apple. Most kids will discover, in a few rounds of play, that when the Rotten Apple and four other counters are left, and if it’s their turn, they’ve lost and they give up. I’ll prompt their thinking, however and ask why they would say that. We want them to process and come to a conclusion like this: There’s one rotten apple and four regular counters left, so if I pull one, my partner will pull three, and I’ll be left with the rotten apple. If I pull two, my partner will pull two and I’ll be left with the rotten apple. If I pull three, my partner pulls one, and I’ll still be left with the rotten apple.
That kind of thinking starts the discussion as to why that happens. Some students will have different theories, which you want them to share with the whole class. “I think, if you go first, you always win!” Ok – let’s try it! The whole class pairs up and plays to see if the person who goes first always wins. No? “Well, I think if you go second, you’ll always win!” Let’s test that out! By testing their theories, you’re not autocorrecting or giving them the answers, but you’re letting students come up with that hypothesis and allowing them to test and see if it’s true.
Some students might notice that it has something to do with odd or even numbers of apples pulled during a turn. Ok, you say, so tell me more about that, and they may have a theory as to why they should always do an odd or even pull during their turn.
In the end, we never want to reveal the secret of the strategy to the students. To you, reader of this blog, we will tell you that there is a mathematical reasoning way to how you could always win at Rotten Apple, but does it matter if you go first or second? That’s for you to discover as you play!
This game is very similar to Tic Tac Toe in many ways except one very important one – there are no ties and always a winner in 9 Holes! Bonus: it really causes students to question their metacognition!
Simplicity is another perk for this game. You could print a game board from our Math Strategy Games download (on sale now for 50% off in our store!) or you could make your own pretty simply at a restaurant or doctor’s office waiting room, or even in a classroom with a dry erase board.
Draw a large square, and put a large plus sign in the middle to create four boxes. Why is it called “9 Holes” when you only see 4 boxes or areas? You actually play on the intersection of lines for this game. The nine holes where you play your counters are at the intersection of lines – in each of the four corners, the middle, and where each line meets the border.
I also like to play this with the 2-sided counters, but you could certainly play with clear counters, pennies and nickels, Cheerios and Cheez-its – its up to you!
- Each player starts with three of their color counter along the edge of the board.
- Taking turns, players put their counters, one at a time, at the intersections on the game board trying to get three in a row – vertically, diagonally, or horizontally.
- Typically, in a game like Tic Tac, when you play your counter, it’s stuck and you can’t move it. In 9 Holes, you can continuously move your counter around if you realize you need it to block your partner from getting three in a row.
- Continue placing counters until one player gets three in a row
If a student is blocking somebody with a counter, but then they take/move that counter to help them get three in a row, they have to be careful that they don’t unblock their partner who could then come in and win the game.
One of the things I like about 9 Holes is that we can help kids to really question themselves and start to think through different scenarios – if I do this, this will happen? What if I put my counter here, would that work better? They can kind of play out the scenarios in their head to see if they could get three in a row.
Sometimes your strategy might be defense and, the whole time, you’re just trying to prevent your partner from getting their three-in-a-row. Other times, you might be more on the offense. Sometimes, you play and someone wins quickly without really realizing it, even though you are both looking at the same board.
9 Holes: Level 2
This is an optional level if students are becoming bored with this game and you need to add some differentiation. The only change from the basic play is the way you move counters. In level 2, instead of being able to pick up and move your counters anywhere on the board, you can only slide them on a line to another empty hole. You can’t go diagonally, you can only move on the straight line segments.
This introduces a whole new level of complexity that requires additional layers of strategy. Between you and me, it has to do with where you first play your counters. Students have to strategically think about where they’re going to play their first counter and then think through subsequent possible moves.
Across the Pond
This game is aptly named because the game board looks like a pond – think lily pads and logs. The “frogs” sit on the lily pads (green square on either side of the pond. Each player has five “frogs,” represented by five counters or five of the same object, that sit in a line on their side of the pond and the goal is to get your frogs to the other side of the pond first. Get the game board in our Math Strategy Games download!
- Line up five “frogs” on either side of the pond.
- Players take turns moving two of their frogs in the same direction. It can be any direction, diagonal, forward, backward, left, or right – but it must be the same direction for both frogs.
- You can’t jump frogs like you can jump checkers and only one frog may occupy a space at any time. If the space is occupied, find somewhere else to move!
- Logs (brown spaces on the game board) are dead spots that frogs can’t hop onto.
- The first player to have all five frogs make it across the pond wins!
The complexity of this game comes in the 8 Mathematical Practices because students are taking turns to play and have to be aware of all the frogs on the game board. They have to be forward thinking, to look at where their frogs are on the pond in relation to where their opponent’s frogs are. Do they play offense and decide how they are going to move to get closer to the other side of the pond, or defense to protect their lily pads so their opponents frogs can’t make it to the other side??
To differentiate this game and make it a bit easier while students are learning, start with moving just one frog at a time to get across the pond.
Level 1: Moving the one frog across the pond and seeing what different strategies might be there.
Level 2: Playing the full rules of the game, which is moving two frogs in the same direction at the same time.
This will be a great game to add to your repertoire!
Remember that strategy games are an important part of math workshop! You don’t want to just have number games or games that are just place holders or “busy work” while you’re doing Math Workshop. It is a question of quality vs quantity. Make sure you compare any math games to the criteria outlined in Shannon’s Top Five Tips! One of the tips is the reason we love these strategy games so much – games should use as many of the 8 Mathematical Practices! Our students need more practice in becoming strategic and playing through these scenarios to figure out the next move that will be most successful!
Join us next week – I can’t wait to tell you about our newest products – the Math Mights pencil toppers and Addition/Subtraction dice! We’ll be showcasing different kinds of games that you could play with them (either in a Math with Someone station or as a whole class activity) that allow kids to show off the different strategies they know!