The object of this little exercise is to get students to be thinking about how different operations are tied into division.
I was hoping that students would score at least above 50 percent on the subtraction fluency test , but it turned out that out of 80 problems, the majority scored lower. Since subtraction has been a part of their mathematics since first grade, I was expecting better rates of fluency.
First, I had them do two or three timed tests in multiplication on their iPad ap, Timed Tests. They needed to do whatever their differentiated settings were during this test. I differentiate levels and many have mastered all the way to 16's.
When they were done, I asked them to set their settings on subtraction. This time, the test was set at 80 problems for 4 minutes, facts 1-20. I asked them to do one round. Only a few couldn't master the 4 minutes. But as I said above, scores in accuracy were on the low side.
As they tested, I encouraged counting up, using fingers, thinking about tens, etc. When all was done, we discussed our results. We discussed the feelings we had when we switched gears.
Materials: A box of "24" cards
We needed to review dividing two, three and four digit division by one digit division and do it in a way that was fun. Using 24 cards is a great way to mix up some numbers and create the greatest quotient or the least quotient, depending on how you use the numbers.
I passed out one card to groups of two students. I let them pick their partners today.
Rules of the Game
1.We would find the greatest quotient today, but it can be switched to least quotient too to make it interesting.
2. Students manipulate the numbers on the 24 card using 3 digit by 1 digit to do 5 problems, and then 4 digit by 1 digit to do 5 problems. The 4 by 1 digit, one digit will be used in both the dividend and the divisor and they have to figure out which will create the greatest quotient.
3. They do 10 rounds. Then, they check their work, using the inverse and then again using a calculator. The person with the most accurate answer wins the game.
This game is a lot of fun!
We began our game and I roved the classroom checking on how student's were doing. I am looking for differences in their thinking. The discussion continued with them explaining on why they thought their number would produce the greatest quotient. I was able to lead them into discovering that they needed the largest dividend divided by the smallest digit. There was lots of excited talk, discussion about how they divide and student's helping those partners who were still struggling.
Soon it was time to pick up the cards and join me in a circle on the floor to discuss what we had discovered about number sense, thinking through strategies and division. As we talked, students brought up how they had some things they had not completely understood before playing this game. I asked what strategy they used to find the greatest quotient? In the discussion, several students talked about using listing to produce the largest dividend and then find the smallest number for the divisor. I asked them if they needed to think about place value? Students responded with saying that you needed to think about the value of the number too. That place value was understanding that three digits meant the hundreds place value, but that you needed to choose the largest value for the hundreds place.
It was a good discussion!