This is Common Core State Standard support video for mathematics. The standard is 1.OA.6. This standard in the operations and algebraic thinking reads: add and subtract within 20, demonstrating fluency for addition and subtraction within 10; use strategies such as counting on, making 10, decomposing a number leading to a 10; using the relationship between addition and subtraction, and creating equivalent but easier or known sums. So, here, the focus is on adding and subtracting within 20 using several different strategies. So, let’s just go through these strategies one by one with an example or two for each.
The first example is counting on. Now, this strategy, some of the main, key ideas would be that, first, you need to limit your sum addition context to adding no more than four to the larger addend. And, of course, you always want the kids to start counting from the larger of the two addends. And it’s always a good idea to have some type of visual aid, some manipulatives, and a number line, if available.
So, let’s take an example such as five plus three. Now, you’ll want kids to have some type of manipulative to work with, so something like this, the kids would start with five, and then, count on. So, it would be five plus, one more would be six, and then seven, and then eight. So, just counting on, they’d start with five and count up to eight. Taking the same idea, but using a number line, in this case, the students would start, well, first locate five, and start there and count one, two, three. So, they would be at eight.
Let’s take one more example. Let’s say the kids have 2 plus 12. Now, the manipulative that you might use would also help the students to realize that, hey, you don’t start with the two. You need to start with the 12. Again, you don’t want to ever count more than four in the counting on strategy. So, again, here, the kids would start with 12, and then count one more is 13, and one more is 14. Using the number line to assist, then again, we would locate the 12, and start here. We would count two. So here’s one more, and one more, so we’d be at 14. So, 2 plus 12 is 14.
Let’s look at the second strategy, making 10. Now, for some of these strategies, you want the kids to really understand some things walking in the door. So, in this case, it is really important that the kids have automatic recall of all the single-digit combinations for 10, such as 1 plus 9 is 10, 2 plus 8 is 10, 3 plus 7 is 10, and so forth. So, again, you want the kids to really have this knowledge down.
So, let’s try an example for making 10. Well, let’s see, most of the kids will probably focus on the seven, and if they know automatically that 7 plus 3 is 10, then, of course, the action would be that I need to take the eight and break it down to where I have a three in it. So, then, now I automatically have this idea of making 10 here, where I’ve got the 7 plus 3 is 10, plus 5 would be 15. Notice that this connects back to the idea of compose and decompose, because basically, I’ve done that here. I’ve kind of decomposed the eight and did some rearranging to again come up with the 7 plus 3 to get the easy sum of 10.
Now, not all kids think the same. Some might focus on the number eight and realize that you have to add 2 to the 8 to get the 10. So, then, they’ll break down the seven to five plus two, to again get the sum of 10 that you want for this strategy; slightly different, but not that different, to again, to arrive at your final destination of 15, in this instance.
Let’s look at the third strategy, decomposing a number leading to a 10. Now, a prerequisite here is that the kids really need to understand that it’s not just numbers that can be composed or decomposed. Operations can be composed and decomposed also. So, what we mean here is, for example, subtracting seven would be the same thing as subtracting five and then subtracting a two. You don’t have to subtract seven all together. Again, you can break it down into two or more operations.
The second example (and this would be a good strategy for kids, because for some reason adding nine proves difficult), they can think of adding nine as the same thing as adding a 10 and then subtracting a one, because that would be equivalent. So, let’s take an example of this strategy. Let’s say we have 17 minus 9. Looking at the 17, well, we know the 17, if you take away 7, that’s a 10. So, then, we can take the subtracting nine and decompose it, break it down to subtracting seven and subtracting two, again, with the intent of getting a 10 here. So, now, it makes it a lot simpler for kids: 10 minus 2 is 8.
Taking a second example of this strategy, 17 subtract 5; well, we know that 15 minus 5 is a 10. So, that involves breaking the 17 down to 2 plus 15, so that we get a 10. So, in this case, we have 2 plus 10 is 12, which is a correct solution for 17 minus 5.
Another strategy is using the relationship between addition and subtraction. Now, the focus of this standard is to add and subtract within 20, but in order to do that, the kids really have to have fluency for adding and subtracting within 10. So, a primary goal here would be that the kids really need an automatic recall of all the single-digit combinations for adding. So, all the single-digit combinations would be things like 7 plus 5 is 12, 8 plus 6 is 14, 9 plus 3 is 12, things like that where, again, you’ve got two single-digit numbers, and you’re adding them together. Now, that ingrained knowledge will lead to kids automatically relating to the subtraction facts. So, for example, if they know that 7 plus 5 is 12, they’ll automatically know that 12 minus 5 is 7 or that 12 minus 7 is 5. Again, very important for kids to know these facts to really be fluent in adding and subtracting within 20.
So, let’s take an example of the relation between addition and subtraction. If we have kids that have 7 plus 6 equals 13 as a foundation, if they have that down, and they have automatic recall, then that’ll really help them to, when they see something like 13 minus 7, well, they’ll know right off the top; well, let’s see 6 plus 7 is 13, so they know that the solution has to be a six.
Now, there’s research out there, and we have to be careful because this can become a habit. One of things that happens is that there’s a tendency to always have equations set up where we have the problem on the left side of the equal sign, and we always have kids, have the equal sign, then we put our answer on the right. But, what happens there is that kids start to lose the meaning of what the equal sign means. It starts becoming just a signal to do something, well, add, subtract, do something, and then put an answer over here on the right-hand side. So, to help offset that and prevent that habit, make sure that you take a problem like 13 minus 7 and put it in different forms where they would need to put the solution on this side, such as 13 minus 6, or in this case over here. Well, let’s see, what minus six would be seven? Well, let’s see, I know that 7 plus 6 is 13, oh, so this has to be a 13. So, again, set up the format for your problems to where you don’t always put the answer on the right-hand side. Get them used to different contexts, such as these here.
And the last of the suggested strategies, creating equivalent but easier or known sums: one of the things that helps here, now, the kids don’t have to know the name “commutative property,” but it really helps if they already have some kind of intuitive knowledge that when you add two things you could switch the order, and you’re still going to get the same sum. So, they’ll know that four plus three and three plus four are equivalent. Now, this last strategy would typically be used if students don’t yet know, they don’t have automatic recall of all the single-digit combinations for adding. And, in fact, this is a good strategy to lead to that automatic recall. So, what this strategy basically says is take numbers and break them down or a combine them together to make combinations that kids already have down in memory.
So, here, for example, the kids might already have down adding the doubles. So, if they know that 7 plus 7 is 14 automatically, then, use that to the advantage. So, in this case, you break down the eight to one plus seven. That way you’ve got a combination that the kids have memorized. And, so, now we have 14, because they know that pretty quickly, to get our solution of 15, in this case. Now, we mentioned that it’s important that kids have an intuitive idea of the commutative property. So, for example, if we take that same problem, but the kids just jump in and just write seven plus one plus seven. Well, again, you’ve got what you need here, but the kids have to realize that, okay, wait a minute, I don’t have this the way that I want it. So, I know that I can do this. That way, now we’ve got the seven and the seven together. Now, I’ve got the same basic solution that I did previously.
Here’s another example of creating equivalent but easier known sums. Let’s say, again, that kids have trouble for some reason with adding nine. And if they can think of that as adding 10 and subtracting one, if they break down the nine to 10 minus 1, then that makes it easier for some kids because they’ll know 7 plus 10 very easily as 17. And then it’s just a matter of doing something like the counting on strategy, although it’s kind of like counting down. So, 17 minus 1, they can easily figure out is 16. Again, the key here is adding and subtracting within 20, but it takes a while for kids to really become fluent with this. So, there are quite a few different suggested strategies that they can use, and this is basically, again, just to review examples of these different strategies.