Mental Math Drill: How many ways can we make 10? How many ways can we make 100?
I had students partner up and practice naming the math facts to ten. Then I had them discuss how many ways they could make one hundred.
One boy said," Too many! I can't count all the ways!"
I said yes, that there are a lot of ways to make one hundred, but lets try together. I asked them how they figured out how to find the ways of making ten. I wrote 10 on the board and drew math mountains with ten being at the top for the total. I wrote the number 1 at the base of the mountain and asked what the other addend was. They told me 9 and we continued by putting a 2 on the next math mountain.We continued until we got to 5. I asked what they thought would happen when I listed 4 as an addend? One student said that it would be six on the other side of the math mountain and that it would repeat.
I asked if we could do this with 100? Could we start by subtracting 1, and then 2 and so forth? Would that give us all the ways to make 100? I asked them if there would be a point, like after 5 + 5 that the addends would repeat (or be commutative)? They predicted that yes.
I asked, where? One of my students said that if it happened at 5 then it probably would happen at 50. So we tried 100-51 = 49. Then we listed 100-50 =50. Then I drew the last math mountain as 100 - 49 = 51. Soon students saw what happened to the facts and that they would repeat.
To conclude: I asked: Does 100 have a certain amount of a set of addends? They agreed that it did. I asked if all numbers had a point where the addends repeated? They predicted it was true.
We started with reviewing with our favorite little rap about subtraction to remember the process. Students danced around and sang the rap. I played it twice because they loved it.
I had them sit down and get out their notebooks that contained samples of their classwork. I aksed them to look at their notes about subtraction.
I posed the question: What is the one thing you have learned about subtracting multi-digit numbers that really helped you be successful? One boy raised his hand and he said that he liked the way I explained subtraction across zeros and that he understands where the 9's and 10's come from that are over the top of the zeros. I wrote an example on the board to remind the others about what he was saying. After we discussed that we needed to continually think about the value of the number after we regroup and strategies like lining numbers up properly, students were ready to take the quiz. I passed it out and they took their time working on it using a separate piece of paper if they needed room to subtract.
Next, we quickly reviewed the steps to estimating a subtraction problem. We discussed rounding to the lead number and using our basic fact understanding to subtract. We practiced one problem on the white board. I asked for any questions and no one seemed to have any, so I moved on to word problem strategies.
I told them that their quiz would contain two word problems. One would be a mutliple step problem. I asked for suggestions on how to solve multiple step word problems involving addition and subtraction.
One student raised his hand and told us that we needed to take apart the problem using KWS ( What do I know?, What do I want to know? and How will I solve it? ). I asked how we would know that the problem was multiple step? Another student explained that the problem would be talking about more than one thing, like something having to be added to another thing for a total. "Then you might have to subtract that from something else."
Another student said "Subtract it from the total total." ( It was her way of saying that there would be a difference between the added total and the total that needed to be subtracted from.) This little dialogue showed me that they are thinking about numbers and developing number sense. (MP2)
I also told them they needed to explain their work and their thinking on this quiz. It would be a little challenging and that I wanted their very best written work, so that if they needed to plan they could use a separate sheet of paper to list or draw our their plan.
This Subtraction Quiz 1 is one of the first quizzes that extends and pushes them to really write well about subtraction and multiple step word problems. Included are estimation and exact algorithms and I expect them to show all of their work. I passed the quiz out and they began their work. I was hoping that they would show significant growth in solving and explanation of word problems and that those who struggled with regrouping would master it. If they do not, they may take this quiz over and over up to the point of the final exam to prove mastery. The goal is to master fluent subtraction of multi-digit numbers, solve multiple step word problems and be able to round and manipulate numbers to estimate.