When we teach young children about operations it’s helpful to use concrete objects to model what’s happening when we add or subtract so that kids can see what’s really going on, that students know what action is associated with each of these mathematical operations. In this lesson we’re going to use Base Ten Blocks and I have units, and I have rods, and that I have a Place Value Chart in order to solve a lesson with addition in regrouping. For the problem, we’re thinking about Erica who plays basketball.

She scored 18 points in the first half of the game and then 5 points in the second half of the game. How many points did she score altogether? We use addition and will need to regroup in order to solve this problem. I’m assuming for the model lesson here that students already know how to take ten units and exchange them for one 10s rod. They have an understanding of that equivalents and we’re now going to extend that understanding into addition. To solve the problem I’m gonna start by modeling. Erica scored 18 points in the first half so I have one 10 and eight 1s to represent that score and then she scored an additional 5 points in the second half for the game, so I add to my mat or I joined five more units to represent the five points in that second half the game. In order to add I know I’ve got a combine these. It looks like I’ve got a lot more than 10 so I’m gonna line them up on my 1s side and I see that I can exchange those 10 units for a second rod and when I do that I know that the answer to my problem is that she scored 23 points altogether.

There are a number of things we need to talk to students about when they solve a problem like this and I’m gonna move to a virtual based Ten Block representation like you might use on an interactive whiteboard in order to talk about some of those ideas. I’ll start the problem the same way where I have 18 represented as her score in the first half and I have 5 represented as her score in the second half. If I don’t want children to line up their pieces I can have them group or circle ten (1s) that they can exchange for a 10. There are going to be times though as students develop that we want them to work without Base Ten blocks at all and in this case I’ll keep my Place Value Mat but I’m gonna draw a representation. I’ll use a line segment and eight dots to represent the 18 points she scored in the first half and then I’ll add five more dots to represent the 5 points that she scored in the second half. I can create my group of 10 by circling it draw second line segment and my 10 side to represent that that is one 10 and by seeing what’s outside the circle three 1s and another 20 for my two 10s now I have 23. As students get comfortable with these representations I wanna move even one step further and write the problem in a traditional way where I would record 18 plus 5 and I know 5 plus 8 is 13 and represent regrouping in a more traditional format.

This makes sense to students at this stage when it’s the end of the activity the end of their learning progression because they know that what they’re writing down is what they built when they made their trade. They’ve seen 5 plus 8 equals 13 and how that becomes one 10 and three 1s and now I’m just teaching them a more formal mathematical way of representing it..