This is Common Core State Standards support video for mathematics; the standard is 1.MD.C.4. This standard reads: organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Let’s break this standard down into the different components.
Let’s look at the first part dealing with organizing, representing, and interpreting data with up to three categories. There was a standard back in kindergarten, K.MD.B3, that states: classify objects into given categories; count the number of objects in each category and sort the categories by count. So, again, this is one is very related, so the students should have experience with this already. Now, this first grade standard lays a foundation for a second grade standard, 2.MD.D.10, where students are expected to draw a picture graph and a bar graph with single unit scale to represent a data set with up to four categories.
If we look at the second expectation about asking and answering questions about the total number of data points and how many in each category, there was a predecessor to this back in kindergarten, standard K.CC.B.5, that states: count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 to 20, count out that many objects.
And then, this last piece dealing with how many more or less are in one category than in another, there was a predecessor to this back in kindergarten, standard K.CC.C.6, where students are expected to identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group by using matching and counting strategies.
There was another kindergarten standard, K.OA.A.2, that states: solve addition and subtraction word problems, and add and subtract within 10, example, by using objects or drawings to represent the problem. There’s another first grade standard, 1.OA.C.6 that is connected to this. Students are expected to add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
Let’s take this example where we’re using some circles, and let’s say we decide to organize them by color. So, typically, we would do something like this. There’s our blues, our magentas, and our greens. Then, we could address the other parts of the standard where we ask and answer questions about the total number of data points and so forth. So, we would ask questions, such as how many green ones are there, how many more blue ones do we have than magenta, and so forth.
If we go back and look at that second grade standard that we looked at that connected to 1.MD.C.4, it deals with drawing a picture graph or a bar graph. Well, there’s a lot that we can do with standard 1.MD.C.4 to really lay the foundation for that. Let’s look at how we can do this. Rather than just arbitrarily arrange the circles like we did before, let’s start over, and why don’t we do it this way? Let’s stack our blue ones vertically, same thing here, same thing with the green. It doesn’t take a whole lot of imagination to see that, hey, this does look like a bar graph. In fact, if we fill in some of the missing parts, like our horizontal line segment, and then, if we do something like this to kind of put them in columns, then finish it out by doing something like this. So, notice what we have. We really have a really good foundation for bar graphs. In fact, we can take our vertical stacks of circles, and add a little bit more to it where we are, in fact, representing bar graphs. So, we put in a vertical line segment, and why not go ahead and include our numbers, in this case 1, 2, 3, and 4? By having them arranged in this way, students can probably answer the questions a lot easier. They can see that we have four total blues or they can easily answer the question, how many more blues do we have than greens?
Let’s take another example. Let’s say we are going to organize these by shape. So, there’s our circles, our triangles, and our squares. Now, we can leave them like this, but as we just discussed, it might be better to go ahead and rearrange these and put them vertically, but do them in such a way where they also align horizontally. Now, fill in the rest where we actually have a really good representation of a bar graph. And now, we can ask and answer questions about the total number of data points and so forth; for example, how many triangles do we have, or how many more squares do we have than circles?
Okay, let’s say we have our manipulatives here, and we want to organize these by size. Well, that might not be a very good idea, because it really is a little bit hard to tell here what’s bigger, what’s smaller. So, if you’re going to use size as the way to organize some objects, just be sure that it’s very, very easy to tell the size differences. In this case here, not such a good idea; it is hard to tell.
Let’s say we're going to organize these by color. So, we have our reds. We have our greens, and we have our blues. Again, we totally disregard the shape, because that is not how we are categorizing these. We’re doing this by color. Let’s go ahead and fill in our vertical segment and our numbers. And now, we can go ahead and ask and answer questions like the standard says, again, about the total numbers, for example, how many green ones do we have or questions like how many more reds do we have than blues?
If we look at our standards for mathematical practice, by doing the activities for this standard, students would reason abstractly and quantitatively. They would construct viable arguments and critique the reasoning of others. They would be modeling the mathematics. If we look at the last four, students would be looking for and making use of structure, as well as looking for and expressing regularity in repeated reasoning.