This is Common Core State Standard support video for mathematics K.NBT.1. This is a kindergarten standard in the number and operations in base 10 domain, and it reads: compose and decompose numbers from 11 to 19 into 10 ones and some further ones; example, by using objects or drawings and record each composition or decomposition by a drawing or equation; example you take 18 and you break it down to 10 plus 8: understand that these numbers are composed of 10 ones and 1, 2, 3, 4, 5, 6, 7, 8, or 9 additional ones.
Let’s start with this idea of compose and decompose that the standard stresses. Now, this is a really important idea in mathematics. A lot of fundamental math, basic arithmetic, deals with putting things together and taking things apart, which typically results in some type of rearrangement. What we’ll do is we’ll organize these rearrangements into processes called the four basic operations: adding, subtracting, multiplying, and dividing, which brings us back to this big idea of compose and decompose that this standard stresses.
Now, let’s say we have these objects: we’re having the students work with them. According to the standard, we need to take this bundle and rearrange it in such a way where we have 10 ones. So, we want to take these and have the students rearrange them in such a way where we’re going to end up with 10 ones. So, we have them go through a process, something like this, and they keep doing this until we get to the desired result. So, what we now have is the desired result of 10 ones, separated off as its own little group, plus an additional 4 ones over here for a grand total of 14 ones.
Now, at this point, kindergarten students aren’t required to know the equal sign, but it’s good to go ahead and set things up this way so they start getting used to it. And in fact, what we can also do is, maybe go back and tie this back to the original drawing, and have it to where students see that regardless of how those 14 objects are arranged, they’re still equivalent. But, if we rearranged them like the standard wants where we have a set of 10 here, that’ll make the counting so much easier for the students.
So, according to the standard, we need to do that with any possible number from 11 to 19. And again, if this would have been 11 and they would have been all jumbled up, we rearranged them in such a way where now, we have this scenario. We have 10 ones plus one more for a grand total of 11. Now, notice that this is starting to foreshadow place value, but we’re not there yet because we’re still having the students think of this is as 10 ones rather than 1 ten. And again, just going through the process, this would be 12. So again, we want them to rearrange them so that we have, again, 10 ones plus some additional number of ones, which in this case would be two more; so, for a grand total of 12 ones.
The standard emphasizes this idea of compose and decompose. Now, let’s say we had this type of scenario where, instead of having the items all together in one group at the beginning, say we had something like this, which would be 8 ones and 7 ones, which is 15 ones. But, this is a pretty tough addition fact for some students.
So, look what really happens if the students take this standard and apply it to this slightly different scenario. If the students were to take one of the objects from here, and move it over to the other group, then we will have this new picture, which then, of course, becomes 9 ones plus 6 ones. And if students were to take this a step further and take one more of these and move it to the other side, then we would have this situation, which is 10 ones plus 5 ones to be our 15, which again, aligns with what this standard is saying, but it’s a slightly different context.
But, what this standard focuses on is starting with something like this, like 15, and this is the final destination that we want to get to. Now, if we’re on a trip like this, it would be a shame to just have tunnel vision and only watch the highway and not pay any attention to the scenery. So, when kids go on this trip, and we get to this destination, well, let’s pay a little bit more attention to the scenery. Well, first of all, one of the nice things about this standard is that it’s instilling the idea in the kids that when I have something like 15, it’s not like it’s a concrete block that’s 15 pounds that I can’t take apart. I can.
So, our first step in getting to that final destination will be to do this. But, notice where we are, that I’ve broken this up to 14 plus one to be 15. And then, if we move one more we’re here, at 13 plus two. We move one more, we’re here at 12 plus three. One more and we are at 11 plus four equals 15. One more step in the journey, and we’re here at the final destination. But again, look what happened along the way. We have these additional combinations of 15: 14 plus one, 13 plus two, 12 plus three and 11 plus four, in addition to the 10 plus five. So, what we have here, in a way, it’s a sneaky method of teaching the students some of the other addition facts when again, when we’re going through this process of what this standard calls for, of rearranging the items to where we have one set of 10 ones with some additional ones when you have a number of between 10 and 20.