The In-Between Game, Grade 5

On Friday, we streamed our first live videoconferenced math lessons of the year into our district's professional development site, the Schultz Center for Teaching and Leadership. Approximately 100 Academy of Math participants from around the district gathered at the site for a day of PD. And, one component of the day was watching and debriefing a math lesson from the grade level you teach. Our live streams, from CCE, came from Kindergarten and Grade 5.

As a coach, I attend as many of the live lesson streams as possible, because classroom observation and classroom supporter is part of my role. And, on Friday, I must say that I was right at home, having taught on the Grade 5 Math/Science Team for four years myself.

The Grade 5 lesson was live from Bridget O'Connor's classroom. Bridget's students are currently in a unit of study focusing on fractions, decimals, and percents. Her mini-lesson focused on introducing students to a new game, In-Between. In the game players take turns placing a card next to another card. The card can be placed to the right of 10%, to the left or right of 50%, and to the left of 90% (think it like a number line), or under a percentage card if it is an equivalent fraction. As students place the cards, they explain their reasoning by stating the fraction and the equivalent percentage. The cards, as you look from left to right, must be in correct numerical order. They cannot place a card between two cards that are already touching. For example, if 1/6 was played touching 10% card, then 1/8 could not be played. The goal of the game is to try and place more cards than your competition. The student voluneer and Ms. O played a practice round, from the board in the front of the room, so students would be ready to tackle the game in pairs.

As the class transitioned from their mini-lesson to Work Period, Bridget pulled a small guided math group. She reexplain the directions and got the students started. She observed during their first round to make sure they understood and then began circulating the room conferring with pairs of students. She listened in on student's conversations, asked them probing questions, took their strategy in the game to the next level, and took notes if she wished to share their strategy, question, or conversation in Closing Session.
As I watched Bridget in action, I stayed as far out of site from the video camera as possible, but sat with pairs of students to listen in on their conversation and strategy. I was enamored with the depth of their thinking. I overhead one student say to another, "Why are you placing 3/8 next to 1/4?" And, the other replied, "I know 3/8 is 37 1/2% because 1/8= 12 1/2% and 2/8 is equivalent to 1/4, which equals 25%, so 3/8 is 12 1/2% + 25%." She went on to say, "I placed 3/8 there because I am blocking you from begin able to play your 2/6 card." She giggles, "You will get stuck with that card!" In another conversation, I heard one young man say to another, "I'm saving all my equivalent fraction cards for last (1/10, 1/2, 9/10), because I can always play them under the percentage cards." He continued, "I am wasting a turn if I place them any sooner."

After about 25 minutes of Work Period, Ms. O'Connor had students return to their seats for Closing Session. Once again she used the giant sized magnetic game board she had created at the front of her classroom to demonstrate. She focused on a few relevant conversations and strategies to move student thinking forward.
1) "One student moved the percentage cards further apart even after fraction cards were placed. Why did he do this?", she asked.
2) She presented a comment that was asked of her as she circulated, "Ms. O, we need to think fast, don't cut ourselves off, and look at my partner's cards before I make a play." She asked the students, "What does this mean?"
3) Ms. O asked a student to come to the front and present a strategy she saw him use, because he had formed a misconception. After working it out in front of the class, he discovered his error, corrected it, and decided he was leaving his equivalent fractions for last.
4) She asked, "Why did it take you longer to place the cards like 1/6, 5/6, 1/8, and 3/8?"

The Closing was interactive dialogue between the students and teacher. I think you'll agree it is a powerful part of the workshop model, one that should never be missed. And, one in which the student learning is deepened and where they build powerful connections.

This game, the In-Between Game, is one of student thinking, understanding, and connecting. It is also a game of strategy with the added element of a little luck--the students quickly figured out that they loved the equivalent fraction cards. And, there are many variations. I'm sure you'll agree that this is a game students should revisit frequently during Choice Time, and one in which they will become very strategic. Now, that is the way to develop young mathematicians!