Exactly 109

Math Recess students love to play games - Warm up games, pattern games, concept teaching games, practice skill games, thinking and strategy games, board games, card games, stick games, chip games, coding games - The type or style does not matter. They love playing games. Their love of games is born through the idea that they can learn through play, just like playing outside at recess. Play is a big part of what we do, Math Recess is no different. By the end of second grade, my students are game aficionados or, as I fondly call them, Game Snobs. They become experts at sniffing out the really good-to-play games, game that keep them thinking- especially when they lose- from the plethora of experiences across all curriculum and years, and it all starts in Math Recess Kinder Style.

In Math Recess Kinder Style, every day is a game day, even when it is not. I call an investigation or a task a game; it’s all about the spin. If my Kinders are having fun and making connections, it is a Game Day because games are all about the fun. It is essential that Math Recess is fun, and I believe the goals go well beyond growing their understanding and skills, and to developing a passion for digging in, getting messy, discovering what lies just beyond the numbers, the shapes, and codes, and especially learning how to grow from failure.
Failure is a good thing, like veggies, and the sooner they learn how to fail the better able they will be to grow from it. Failure teaches us so much. We learn about persistence and resilience. We learn it doesn’t hurt that bad if you can find the learning within the experience. When a Kinder experiences failure, they ask, “What did I learn from that fail?” Then they state/record it. It is common to hear things like, “Well, that didn’t work...This time I will try….” or “Hmmm, clearly this isn’t about odd and even numbers…or is it?” Being able to see what is now known is a great skill and a fabulous way to spin from failure to forward.

For an introduction to a new concept, I started with a story. Stories are a gateway to Math Recess. Stories draw students in. Stories are anchors for common knowledge. Stories bring abstract to life. For developing understanding of doubles, I read Two of Everything by Lily Toy Hong and pulled out the old Halloween cauldron that sits on the shelf waiting for this experience each year, As I read, the items from the story fell into our black pot and they were pulled out again just like in the story - five pieces of gold in one pouch becomes 10 pieces of gold in two pouches. The hair pin from Mrs. Haktak’s hair becomes two hair pins, The Haktak’s one winter jacket becomes two winter jackets. Mrs. Haktak becomes two wives, and Mr. Haktak becomes two husbands. Kinders were excited and engaged in the magic of doubling." How does that happen in your pot too?" At least one student pops up to see what I have hidden in my pot. They see nothing beneath the black felt covering the items below. It’s …Math-magical.

I was the only one approved to use the magic pot, so Kinders used mini pots and the magic mirrors. They dropped their cubes in the pots and spilled them out in front of the mirrors, counted their cubes in pairs- 2,4,6, 8- one on the table and one in the mirror. They worked with partners, one putting cubes to the pot and writing the equations for the team, 2+2=4. The other spilled and counted cubes. Each figuring the total and sharing. If they had different answers, they worked together to count the cubes accurately until they agreed and confirmed, ”Look, we know we are right because we did that already. The equation is on our paper. See?" Changing rolls each turn as they played Magic Doubling Pots. Not a game at all? They worked together to count, share, and compare, all the while having fun. We had a room filled with giggles and laughter. All joyful noise for sure, so Magic Doubling Pots is a game.

Exactly 109 game was their next excursion in to the land of doubles. With their token on zero, they rolled a single die. Some had 6-, 8- or even 20-sided die…their choice. In Math Recess, choice is important- Choice gets quicker buy in and is a fabulous differentiation tool. Buy-in leads to engagement and learning. After the roll, they doubled the value, moved their token double the number on the die. They could not count the die number of spaces twice. No, they needed to double the roll and then move. They are always welcome and encouraged to use a tool that will be productive, like fingers, counters, Cuisenaire Rods, or even Base10 Blocks. All available to them. They were encouraged to use a strategy, like "What I already Know" and “Count-on,” - "I already know 5 + 5= 10, so 6+6 is really 5+5+ +1+1 or 12." As they neared Exactly 109 without going over many found themselves moving backward and forward and back again, over and over and over. As we neared the end of the class, Kinders began sharing frustration, as they kept missing 109. All it took was one to broach the idea of always missing 109 to get others chiming in and agreeing if felt impossible.

Since they have learned to use smaller numbers when in a mathematical pickle, and they were in an Exactly 109 pickle, I asked what other numbers might act like 109 on their 0-109 chart. After some discussion, they settled on 19. It was a good number that would work the same as 109 because it is in the same column as 109- it shared the same one’s place. Together we rolled the die and played to 19. Again we could not reach 19, no matter how many times we hopped forward and backward. After several minutes of back and forth, Abby asked, “Stephanie, is this ANOTHER one of those games we cannot win?!?” It was the Cheshire Cat smile growing across my face that had the entire class groaning “OHHHHH, STEPHANIE!!!”

In my typical fashion, I said, “Let's see if it really is impossible.” The token was moved back to 0, I picked up the die and asked, “If we rolled a 1, where would be land?”

“2!” I highlighted the space on the chart.

“If a 2 is rolled?”

“4!” I highlighted the space on the chart.

“If 3 is rolled?”

“6!” I highlighted the space on the chart.

“if 4 is rolled?”

“8!” I highlighted the space on the chart.

“If 5 is rolled?”

“10!” I highlighted the space on the chart.

“If I rolled a 6?”

“12!” I highlighted the space on the chart.

“If I rolled a 7?”

“14!” I highlighted the space on the chart.

“If I rolled an 8?”

“16!” I highlighted the space on the chart.

“If I rolled a 9?”

“18!” I highlighted the space on the chart.

“If I rolled a 10?”

“20!” I highlighted the space on the chart.

“How can we land on 19?” I asked.

Silence.

I wait because waiting gives them time to think, to mul, to revisit what they know, and to question.

Murmurs of thinking.

One hand shot up in the air. Followed by many more hands, signaling they had some big thoughts on this problem.

“Those are all “EVEN NUMBERS!”

“Why is that significant or important?”

Waving hands abound.

“Because 19 is odd number.”

“Our sums were all even.”

I say, “AND……”

I see a the hand of a child, who has had to work so hard to grow her understanding of all things mathematical. I asked for her ideas, and she said, “You always get an even number.”

“When do I always get an even number?
She continued on, “When you add two of the same number, you get an even number….(wait time). .. odd and odd make even, even and even make even. You always get even.”

I smiled and offered her a nod, a nod that shouts her thinking was spot on, well said, and oh so appreciated. She smiles and sits taller in her chair.

To the class I ask, “So that means….?”

This same little Kinder says, “So…..(thinking time)...there is no way to get 19 or 29 or 59, or even 109. You gave us one of those IMPOSSIBLES ….AAAGGGAAAAIIINNN!”
An Air-Five was sent across the room. (During covid, with me remote teaching via zoom, we do not high five, just send air-fives.)

After moment of joyful noise, I asked, “Do you want to know how to win?”

“YES!” from one and all, even the teachers.

“Tomorrow, we play again with a new rule.”

Fist pumping and chants about loving new rules closed the class for the day.

I never want to leave them on a downer. In playing Exactly 109, where failure was the only thing possible, they learned a lot- moving by tens on the 100 chart was up and down a row, what happens with the summing of even and odd numbers (We will revisit this later to really see/do explore how adding, subtracting, multiplying, and dividing impact odd/even numbers.), they listened to each other’s ideas and built on. They practiced persistence and experienced resilience. Best of all, they walked away understanding that one cannot reach exactly 109 with even numbers, and tomorrow brings about more goodness in Math Recess.

Exactly 109 Day 2

After a quick review of how to play, “What’s the new rule?” comes from an excited Kinder.

“Okay, sit up. Here it comes… (drum rolls).. When you write the equation down, you earn ONE space on the board. You can use it immediately or you can save it to use any other time you choose.”

“YES!”

“Why are you excited by this new rule? How do you think it will help you?”

“We need to get to an odd number.”

“109 is odd.”

“We can add one when we want.”

“If we get to 108, I just have to add one.”

“Hey, if I have seven points, I just need to get to . . . 102.”

After I modeled how to record, save/use the points earned, they were off. Another game where they played on their own. They rolled, wrote, and moved for the rest of the session. About halfway through game play, I asked if they thought it best to use their extra space when they earned it or saved it and why, letting them know this would be a discussion point at the end of class. As it turned out most used their points as they went, moving from an odd number back to an even. I played along side them, my help and direction was not needed. (Oh, I love those moments - the independence and confidence is so high I am in the way.) At the end of class, I shared my game board and equations list. I had 13 written equations, so I had 13 free spaces to move. I was on 86. I asked if I could win in the next roll. Some said no because I looked so far away. Some said yes because I must have asked for a reason.

“If I want to use all my 13 points, what number do I have to be on to win- land exactly on 109?”

Hands shot up and we waited for others to get there using their own board. Some used their new understanding of moving up by tens and others counted back along the board and “Slide back" to the end of the previous row.

“You need to get to 96 on your next turn to win.”

“You need to roll a five. Five and five is ten.”

“How will that help me win?” I asked.

“If you get a 5, you add ten, 86 plus ten is 96.”

I started to count the individual spaces, and then I heard, “Jump down a row. That is ten.”

I finished counting the spaces and then paused. “Yes, hopping down one row is moving by ten. Thanks.”

I pointed to being on 96, so how do I get to 109?”

Hands waving in the air.

“Use your spaces earned. You have 13."

I started to count the spaces until I heard, “No! Don’t count them ALL.”

“What?” I questioned.

“Jump ten and count on.”

As I jumped to 106, they all said, “Ten,” and with each movement, “11, 12, 13.”

Joyful noises, as I landed 109. This was our success.

Once the excitement settled, I asked if they had ideas for a new rule for the next time we play?

“How about you can’t use all your point in one turn?”

“Yea, you can only use 2….(Before I could ask why)…oh no that is not helpful at all. You get back on even numbers… You can use NO MORE than 5.”

Ideas spilled out.

“Okay, you have some good ideas. I want you to play this game at home over the break and come up with at least one new rule. Test it for playability…How well it plays, does it make the game more or less fun?” If you have a rule you like, really play with it at home. Get others to play with you. Each player puts a different token on the board. Post a video on Seesaw, telling me about the rule you tested- even if it is a rule that you don’t like after playing it, tell me. I want to know what doesn’t work too. Remember, failure leads to forward.”

I left them playing Exactly 109 and finding a new rule. They love coming up with new rules because they know I teach one rule at a time and each new rule means another day of game play.

And that was Exactly 109 Day 2.