 Division by Subtraction is a strategy for dividing where students think of Division as repeated subtraction. Students subtract multiples of the divisor from the dividend until they reach zero. Today we're going to be looking at Division by Subtraction. And so I want you to try this problem in your book. Three hockey teams did a bottle drive as a fundraiser. They collected $261 worth of bottles. If the proceeds were divided evenly, how much did each team receive? This strategy allows students of varying levels of understanding to complete the division question and arrive at a correct solution. Students often begin by subtracting groups of 10 times the divisor, as these are easy groups to subtract, and move to subtracting larger multiples as they become more proficient. I used three times 10 because I knew it was 30, and 30 is less than 261. I subtracted that, and then I continued doing that step until I got to a number that was lower than 30. And of course I couldn't use 30 because it would be zero. So I used seven because I knew that three times seven was 21, and that's all that was left. And I added all the numbers up on the side to get 87. Okay, that's fantastic, Macy. Thank you. Did anyone do it a different way? Anyone use different numbers? Griffin, do you want to bring your chart paper up and show us how you did it? This student solved the problem using fewer steps. Our goal is to have students use fewer steps as they become more proficient at dividing. This looks awesome, Griffin. You want to explain to the class how you solved your problem? Sure. I used 80 and seven. I know that three eighties is close to 261, so I used three eighties to get 240, which bring me to 21. I know that three sevens is 21, which gave me zero remainder, so 80 plus seven is 87. So I know that each team got $87. Excellent. Great job. One of the things I've learned about division by subtraction is that it helps kids I find organize it better in their minds, go at their own pace, see the numbers. Macy and Griffin did a beautiful job of solving the problem. Who can tell me some similarities between these two solutions? Caitlin. They both add up on the side. They both put their numbers to the side and then added them up in the end. Excellent, excellent. Allen. Macy used eight tens and Griffin used 180 and they're both equal. Excellent. Okay, good job, students. Did anyone use a different number other than 10 or 80? While some numbers may be more efficient to use, there are a number of ways students can arrive at the same answer. This strategy allows the student to work at his or her own level of understanding. Today we're going to be continuing division by subtraction. Only this time we're going to be looking at solving problems that have remainders. The problem is during a scavenger hunt, six kids collected 428 pieces of candy altogether. If they divided the candy equally, how many pieces would each kid get? So I'd like everybody to give this a try. Division problems that involve remainders can be solved using the same method of subtracting multiples of the divisor until the result is less than the divisor. The number becomes the remainder. Adrian, can you explain your solution to the class? Sure. I started with 20 times 6 which is 120 and I minused it which gave me 308. I kept on doing it until I got to 68 and I can't do 20 anymore so I had to do 10. So 10 times 6 is 60 and minus that gives me 8 and then I do 1 times 6 which is 6 because I can't go higher than 8 and then I can't minus it. And that gave me 2 remainder and I added these up and it got 71. Using subtraction to divide allows students of all levels to solve a division problem. I believe this is a more effective way to teach. It's better in breaking down the question, letting the kids see the steps better. Even if they get the wrong answer they're able to go back, look at the numbers to their right and decide that this is where I went wrong, quickly fix it and keep going with the question. As you can see there is more than one way that students can come to a solution when solving a division problem. Our goal is to have students use more efficient strategies as they become more proficient at dividing.