Today I want to review using place value to add and subtract larger numbers. I put the numbers 120 + 245 on the board vertically. I ask students how they might add such large numbers?
I have several volunteers come up and show us their strategies for adding the larger numbers. I reinforce the adding of hundreds, tens and ones if a child shows that strategy, if that does not come up, I will ask "could I add the hundreds digits?" What would that give me?" "What about the tens?" "What about the ones?"
I repeat this process with the numbers 356 + 313.
I know that the numbers they generated in their data will give them some situations over 10 in the ones column, or over 100 in the tens column and I will address this in the Teaching the Lesson section, but for the warm up, I don't choose any digit combinations that add to over 9.
Now I present a subtraction problem the same way. I put 456 - 124 on the board and ask can we use what we know of hundreds, tens and ones to subtract this problem? I ask for a volunteer to show us this on the board. We talk about subtracting the ones ---- 6 - 4, then the tens ----- 50 - 20, and then the hundreds ----- 400 - 100. We also talk about starting with the ones (which will make it easier when they do need to regroup later on).
I ask them to solve the problem 596 - 375 in their math books. What do they find? I have several volunteers come and show us their solutions.
I want to help students to be able to add and subtract with the data they have gathered. I know this may call for regrouping, which they are not quite ready for and so I need to provide some strategies for dealing with these numbers.
I tell students that they have generated some very large numbers by rolling clay balls and logs (spheres and cylinders) down a ramp. Now, I want them to be able to solve some problems about the distances. Today, we are going to talk about some strategies that we might use to deal with larger numbers.
I show students the numbers 66 and 39. I create a scenario. A person rolled a white log 66 cm and a white ball 39 cm. I want to know the difference in the distance the items traveled, or how much further the log rolled. I ask, "What can I do to find the difference?" We discuss student ideas, such as counting up from 39 to 66, or down from 66 to 39. What tools might I use? (Number line, number grid, tally marks, pictures, blocks.) I ask students to pick a tool. and use their best strategic thinking to find the difference. I am asking students to make sense of a problem here and then use a strategy to persevere in solving the problem (MP1). I am also encouraging students to use concrete models here to solve the problem (2NBT.7)
Next, another story. I have a yellow ball that rolled 146cm, and a yellow log that rolled 58 cm. Can I still count up or down? Is there a way to make that easier? If no one has an idea I say, "What if I count up 2 from 58 to get to 60? Next, can I count by tens to 140?" We try...70, 80, 90, 100, 110, 120, 130, 140. How much was the difference, to get from 60 to 140? 80. Did we have any other changes? We already had 2 so altogether? 82 Are we done with the ones? We have 6 ones left, so what is 82 + 6? 88. So our difference is 88 cm.
We practice several other combinations of counting up and down.
Next we try a problem where we have 186 - 62. We discuss how we can pretend that the 100 is not there, count from 62 to 86, and then add the 100 back on.
When I feel that students are able to apply a variety of strategies to manipulate larger numbers, I present some of the problems that students created from their data the previous day. I ask students to work independently to solve the problems.
I want students to review their own work. Having me correct papers when students are not in the room provides little learning experience for the children. They may or may not look at my corrections, and for most of them, they will just take the papers home.
Today I take the time to review the problems with the group. I encourage students to share their solutions. We go over each problem and share solutions. Students see how others solved the problems. They gain confidence in themselves when they see that they figured the problem out. Part of being successful in math is in believing you can be successful in math. I want my 2nd graders to not only have a foundation of skills and knowledge, I also want them to believe in themselves as capable problem solvers.