“I agree,” I said and wrote our scores under our recording to model for the students how to record their scores when they played:
“Skylar has twenty-one and you only have thirteen,” Kerri said. To figure out who is the winner, add the remainders.” The students seemed to understand how to play and I wanted to give them fi rsthand experience with the game, so I said, “The game ends when the start number is zero, but Skylar and I are going to stop here so that you can play. “Sixty-six would be the next starting number,” Korina said, “because seventy-two minus six is sixty-six.” I agreed. So seventy-two divided by eleven is six with a remainder of six. Skylar decided to use eleven as his divisor. I asked how to create the next starting number, and Kylie explained, “You subtract the remainder from the last starting number. Johanna said, “Skylar has fifteen and you have thirteen.” “I’ll use your suggestion of eighteen,” I said. So forty and thirty-two make seventy-two.” “Since it’s my turn, Skylar gets to record.” He recorded 80 in the Start Number column. Joey said, “Remember to subtract the remainder from ninety-five. He reminded me to circle the remainder of 15, to put his initial beside the problem, and to cross off 20. Four times twenty is eighty, and ninety-five minus eighty is fifteen.” “If you use twenty as the divisor, then you can get a remainder of fifteen. Skylar looked overwhelmed, so I called on Kenzie for advice. I wrote 95 under the Start Number column. “Since it’s Skylar’s turn, I record,” I said.
Skylar told me his start number was ninety-five, and the class agreed. “Then we have to subtract my remainder of five from my start number of one hundred to create a new start number for Skylar to use.” We only get to use each number listed once in a game.” Skylar crossed off the 19. He has to cross off nineteen from the list of divisors. I continued, “Before Skylar can have his turn, we have to do two things. “Since it’s my turn to pick a divisor and divide, Skylar will record on our recording sheet, ‘One hundred divided by nineteen equals five remainder five.’ Circle the remainder and write my initial since it’s my turn.” Skylar recorded: “I like Zoe’s idea of using nineteen as the divisor,” I said. One hundred minus ninety-five is five and that five would be left over.” Nineteen is one less than twenty, so I think five times nineteen would be ninety-five. “With three there would be a remainder of one because if you count by threes, you land on ninety-nine, and that’s one away from one hundred.” “What number on the list would make a good choice?” I asked. “Ten time ten equals one hundred, so there wouldn’t be any remainder.” Lupe said, “One would be bad because one goes into all numbers with no remainder.”
Lucas explained, “If you want to win, then you have to choose a divisor that will give a big remainder.” Then I’ll divide one hundred by the divisor I chose, and Skylar will record on our sheet. Because I’m the first player, I start with one hundred and I have to choose a divisor from the numbers listed from one to twenty. The first player starts with a start number, or dividend, of one hundred. “Something important to remember is at the end of the game, both players add their remainders, and the player with the larger sum wins. “This time I’m going to go first to show what to do,” I continued. Be sure to write both your names on your recording sheet.” I explained as I pointed to what I’d written on the board, “When you play, you and your partner will make one recording sheet that looks like this. I chose Skylar and, as he walked to the front of the room, I wrote on the board: “To show you how to play, I need a volunteer.” “Today I’m going to teach you Leftovers with 100,” I began the lesson. Also, if you are familiar with The Game of Leftovers from the first division book, you’ll see here how to extend that game for older students.) (Note: Other lessons in the book address specifically how to teach long-division skills. The lesson presented below teaches students a game that reinforces all of these goals. Their new book helps students calculate with multidigit divisors and dividends (using a method that makes sense to them!) and also deepens students’ understanding of divisibility, relationships between dividends and divisors, and the meanings of remainders. Maryann Wickett and Marilyn Burns’s new book, Teaching Arithmetic: Lessons for Extending Division, Grades 4–5 (Math Solutions Publications, 2003), builds on the concepts and skills presented in Teaching Arithmetic: Lessons for Introducing Division, Grades 3–4 (Math Solutions Publications, 2002).
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