Mathematics

1.MD.2 Transcript

This is Common Core State Standards Support Video in Mathematics. The standard is 1.MD.2. The standard reads: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that that length measurement of an object is a number of same-size length units that span it with no gaps or overlaps. Now, notice another part of this standard states: limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. The key here is whole number. Again, students at this age level still do not know fractions or estimation and some of those other concepts; so, again, very important to prepare your lessons ahead of time to make sure that what they’re measuring, those lengths, are going to come out to be nice whole numbers.

So, using some kind of physical object, be it a dowel or a one-by-two, or whatever object you want to measure the length, and let’s say students are going to use some paper clips. So, concentrating on the first part of the standard, again, express the length of an object as a whole number of length units by laying multiple copies end-to-end. So, students do that...comes out nice and whole number. The number of paper clips matches exactly, a nice whole number. And let’s say we have another object to measure, and this time some students are using crayons.

And so then we switch over to the second part of the standard which deals with understanding that the length measurement of an object is a number of same-size length units that span it with no gaps or overlaps. So what we have here is 6 paper clips for this measure and 3 crayons for this measure. Spaghetti is a pretty inexpensive item to use. So a good idea would be to take spaghetti and break it off into same-size pieces and give those to students and have that be the length unit. And it’s also a good idea to do something like this where you have a vertical orientation instead of always horizontal. Again, students measure with their spaghetti sticks, switching over to the second part of the standard, and we get the length of this as 7 spaghetti sticks.

Now part of the process should involve students taking an object and measuring it with different types of length units. So for example, some students might have these paper clips and measure this object. Some might measure the length with larger paper clips. Some might measure it with some kind of coin or checkers, something round that can also be used. And then some students can use our spaghetti sticks. And so some students got 4 as a length because they used the small paper clips. Others got 2 for the length using the large paper clips. Others got 8 because they used the coins or checkers, and others got 6 because they used the spaghetti sticks.

What’s important here is that a foundation is being laid for students to understand that even though this object physically doesn’t change length, that stays constant, the numbers that are involved as far as the measurement are different because of the size of the units. Some of the length units are smaller and some are larger. Now you can be creative. Let’s say you use spaghetti sticks or some other objects, and you put together a triangle for students to measure. So you would have them measure say the bottom segment, and let’s say with paper clips, then the left segment and the right segment. Then switching over to the second part of the standard, our units, our measurements would be 3 paper clips, 4 paper clips, and 5 paper clips for the respective lengths.

Now one of the things that can happen here is that we can be laying the foundation for other concepts. So what we can do here, something like this; we take the 3 segments for the triangle and lay them out flat. So in a very sneaky, covert way, you’re making a connection between the straight-line distance and perimeter. You’re not calling it perimeter or any thing yet, but again, students start seeing the connection that you have a total distance in each case, but the layout is different.

You can also use other types of scenarios where instead of a physical object, you’re measuring the length of the distance from one point to the other. So let’s say you wanted to know the distance straight across this circular object, be it a plate or whatever it is, that you’re using. So students would pick, let’s say paper clips, for your length units, and then they measure it out. And then we switch over to the second emphasis of the standard, and so we have 7 paper clips for the length. And just to emphasize one more time; again it’s very important that teachers prepare ahead of time and make absolutely sure that whatever their measurements end up being that it’s always going to be a nice whole number amount as far as the length.