Mathematics

K.MD.3 Transcript

This is Common Core State Standards support video in mathematics. The standard is K.MD.3. This standard reads: classify objects into given categories; count the numbers of objects in each category, and sort the categories by count.

So, looking at the terminology, the main things that the students are supposed to do are classify, count, and sort. Let’s look at the idea of classifying objects, and there’s different ways that you can have students do this. Students can classify objects by shape. They can do it by color. They can do it by size. And there’s other ways that they can also classify items. The rest of the standard states that students are supposed to count the numbers of objects. They have to sort them by count also.

Now, typically, when we address one standard, we can simultaneously address an additional standard or even more, for example, standard K.CC.3. This standard reads: write numbers from zero to 20; represent a number of objects with a written numeral zero to 20, with zero representing a count of no objects. So, it makes sense, and it’s a good idea to also address a standard like this one simultaneously and incorporate it with the activities of classifying objects and counting the numbers of objects.

Let’s look at one example using shape as our criteria. So, we’ve got all these different figures— circles and squares and stars, and so forth. So, students classify them based on shape, and we’re just using some straws or whatever to separate the different areas where we put them. Now, students are expected to count the number of objects in each category, and we can address that other standard by having students write the numerals that are associated with each of those quantities. And now students need to sort the categories by count.

An interesting question here is, “What do we really mean by sort?” If you look at what students have already done, well, they’ve already sorted them, and they’ve counted, and they’ve put the number associated with each one of these quantities already. So, are they done? Well, there’s another standard here, standard K.CC.6 that states: identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, for example, by using matching and counting strategies.

So, we’re going to take this a step further. We’re going to assume that, by sorting the categories by count, that means we have to put them in order, let’s say from fewest to most. Students will be getting practice in that other standard by making several comparisons, and again, having to put these in order from the fewest occurrences to the most occurrences. So, now we’re done, as students have gotten additional practice and addressed an additional standard.

An important point here when students are classifying by shape: okay, again that’s a criteria, that’s what they have to focus on. What’s important is that students need to realize that, again, shape is the one and only criteria. So, in an example like this, the orientation doesn’t matter. It doesn’t matter exactly how those figures are facing and so forth. Again, the critical piece here is that they’re classifying by shape. Here’s another example. Again, these are different colors, but it is shape that we’re going by. Likewise, here...we’ve classified them by shape. Even though these things, these different objects, are different sizes, that is not the criteria we’re going by. We’re going by shape.

Let’s try one where we’re classifying objects by color. Okay, so we give these students these different objects that are different colors. And so, they’ve classified them...red, green, and so forth. They’ve counted them, and so they’ve written the associated numerals, digits that go with each quantity. And they sorted them by count, and again, we’re making the assumption that we need to put them in order from the fewest to the most occurrences. And, in fact, when they write the digits, that helps, because they can double-check and make sure, like here, 2, 3, 4, 5. Yes, that’s in the right sequential order, because they know how to count their numbers.

Let’s look at classifying objects by size. One option is to use different sizes using the exact same types of figures, like in this case, circles. But you don’t have to be limited to that. We can use different objects. Just make sure that they’re different sizes. But a bit of caution here: don’t give them a situation like this where you have different objects, but it’s very, very hard to determine the size...what’s largest and what’s smallest and so forth. So, again if you’re going to use different types of objects, making it really obvious, as far as the size, what’s larger and what’s smaller.

So, in this example, we’re using a bunch of hexagons of different sizes. Yes, they’re different colors, but again, that’s not what we’re going by. Our criteria is size. So, students have done that...they’ve classified these based on size, and now we need to count the number of objects, and we have. There’s six here, two there, three there, and one there. And now we’re going to sort them by count.

Now, there’s a danger here. When we’re talking about size, you can be talking about the actual physical size. But, size can also be associated with quantity, okay? So, here’s a danger, a very real danger at this level. If this is the student’s final answer, and they’re expected to put it in order from fewest to most, this is not correct, because again, they sorted these by size, not by count, okay? Big difference, so to avoid that danger, it really helps if students write the digits, write the numerals that are associated with the quantities for each category. And now there’s no confusion. If they really focus on that, then they really will sort these from fewest to most, because the focus is on the count. So, if they really concentrate on the written numerals, they’ll go by count, not by the actual physical size.

So now, we’re going to do this by count, and we’re going to do it from the fewest to the most. Then their final solution will look like this. And again, very important, it’s very easy for students to confuse this if they are expected to sort them by count. Again, very real danger; don’t confuse that with sorting by size.

One more example using size as our criteria...notice here that we’re using some different lengths of sticks. I guess these could be like pieces of spaghetti. Notice here that the size is actually the length of these objects. So we’re going to classify these based more on the length, which I guess you could look at this as the size. So, the students have done that. We’ve classified them based on the size of these sticks, actually the lengths. And now we’ve done the rest. We counted the number of objects, we wrote the numerals associated with each of the quantities, and we’ve sorted them by count from the fewest occurrences to the most.

Now, there’s other ways that students can classify objects. So, like in this example, we have a bunch of hexagons. They’re all blue. They’re the same size. So, the differentiation here is what’s inside of them, and we do have some different patterns here. So, in completing this task, we’ve classified them using these patterns. We’ve counted the numbers and put the associated numerals associated with the different quantities. And we’ve taken the extra step of sorting these by count from the fewest to the most.

This standard, K.MD.3, is a standard that really lends itself to also addressing other standards simultaneously. So, for example, standard K.G.1 states: describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms, such as above, below, beside, in front of, behind, and next to. So, when students have all these different objects that they’re going to classify, they’re expected to use some of this terminology. Like, for example, that the circle that’s next to the square, that type of thing.

Standard K.G.2: correctly name shapes regardless of their orientations or overall size. So, that’s definitely another standard that can be addressed here. Again, these are different types of shapes, so students are expected to name, for example, that this is a circle, and this is a triangle and so forth. So, again, when addressing this standard, there’s a lot of other standards that can be addressed simultaneously when you do activities with your students.