# Customary Units

Does your child have a hard time grasping customary units? It can be a very frustrating concept to understand. Here’s a little different way to learn customary units. It may just be the thing your child needs.

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Hey, there. It’s Adrianne from Math for Middles. I’m so excited to be with you today. We’re going to be talking about customary units, which can be a really tough topic for a lot of kids. Lots of teachers like to start with the adorable Gallon Man. While he’s super cute, sometimes he just isn’t that effective at teaching customary units to students because they get confused about which one goes where, which part was his arm. It causes a little bit of overwhelm. But for others, it works just fine. But I’m going to show you an alternative way to introduce these concepts to your students.

When kids hear the word gallon, they may immediately think of gallon of milk. It may make it hard to visualize how in the world quarts, pints, and cups fit inside of it, let alone remember how it works. The shape is weird. How does it go in evenly? One hurdle that must be made is that the idea that it doesn’t matter what the shape of a gallon is, it’s about the volume.

Think of the ice cream buckets at Walmart. They are a gallon of ice cream. The shapes couldn’t be more different. But their volume is the same. The idea behind this is called conservation. Students need to understand that when I pour the milk into that ice cream gallon, it’s going to fill it all the way up because they’re the same volume. We need to establish that the size of the container needs to hold the same volume and have kids explore with this and discover that 16 cups of liquid can fit inside of a gallon. One fantastic hands on resource that you could do with your kids is have them actually test this out, pouring in 16 cups of a liquid into that gallon bucket, or pints, or quarts, or even fluid ounces. Imagine how long that would take. But all of that’s really good sensory input for them to help them understand that it doesn’t matter what the shape is, but these are the units that go inside of that gallon.

For our purposes today, we’re going to be using proportional reasoning. We’re going to start out with our main unit, which is the gallon. I’m using a square because it helps it make it super easy to give a representation of the smaller units that are inside of the gallon.

We have one gallon. Our gallon can be broken up into four equal parts. There are four quarts in a gallon. The word quart comes from quarter, meaning one-fourth pieces. We have four equal pieces inside of our gallon, and they are called quarts. Now, the word quart comes from quarter. That’s the tie. That’s the relationship. That word is really important to talk about, how it ties, how it goes together. We can see here we have four quarts inside of one gallon.

From quarts to cups, we’ll continually keep breaking up our gallon into two more additional pieces inside of each quart. The next measurement is called pint, P-I-N-T. The word pint comes from old French, I believe, and it means the mark inside of a larger quantity. It just has to do with the word mark. Pint came from paint. It’s kind of a similar word. We can see here that we can break up each quart, again, by two inside of each one. Four times two equals eight. There are eight pints inside of a gallon.

Again, we’re going to cut up each pint into two. Again, here we go. Now we’re going to cut it this way. These are our cups. We have 16 cups inside of a gallon. Eight times two is 16.

Now, here’s where the pattern of multiplying by two is broken, with our fluid ounces. Inside of each cup, there will be eight equal pieces inside each cup. All together, we can see there’s the eight. We’re going to have groups of eight all throughout this gallon. It’s a tiny measurement. It’s really small. As we can see, it gets overwhelming super quick. Look at all that. It almost looks like a prison. That’s kind of funny. All together, there are 128 fluid ounces inside of the gallon. Again, we can see that eight times 16 is 128. That’s how many fluid ounces are inside of a gallon.

Using this method helps us see the relationship between each unit and how they are part of the main unit, the gallon. How do we use this? Let’s do some problems with this.

I need three gallons. One, two, three. The question wants to know how many quarts are inside of those three gallons. Quart comes from quarter. We need to break it into four equal parts. I start with three gallons, and I know there are four quarts inside each gallon. I’m going to multiply to get how many quarts are inside those three gallons. Three times four equals 12.

Let’s do another one. We need eight quarts. We got our four quarts that are both inside of this. I can see that there’s two gallons here as well, but I’m not making gallons. I’m making pints. Pints are cut into two equal pieces inside of each of those eight quarts. Then we can count them up there are 16 inside of those eight quarts. We used multiplication again. We started with eight quarts. We know that there are two pints inside of each quart. We multiplied and got 16.

Let’s do another one. We are going to need 16 cups. There we go again, cutting them into twos. It’s asking us how many quarts does 16 cups make. All 16 cups fit inside of that gallon square. How many quarts do you see? That’s the pink lines. Remember that quart comes from the word quarter. We’re going to regroup these cups into quarts. Here’s one quart, two quarts, three quarts, four quarts. There are four quarts that can be made from 16. In this problem, we used division because we went from a smaller unit to making a bigger unit. We were making new groups. 16 divided by four equals four.

Let’s do another one. This is our last problem with visuals. We have 128 fluid ounces. It wants to know how many pints can be made from these small units, these fluid ounces. Here’s one group, two, three, four, five, six, seven, eight. We made a bunch of groups. There are going to be eight groups. We divided by 16 because all of the green inside here, those are fluid ounces. Okay? Isn’t that fun? It’s so fun. I just love it.

Okay, the visual is really powerful and very helpful. But it becomes laborious. If we’re relying on the visual all the time, it’s going to slow us down in our computation. I’m going to show you some relationships here. Here’s our conversions. We have our unit of a gallon over here on the left and all the way to our fluid ounces on the right. When I go from bigger quantities and I need to make smaller quantities, I’m moving from the left to the right in my conversion chart. I’m going to be multiplying. When I go from smaller quantities on the right side and I need to make bigger ones on the left side, I’m going to be dividing.

Now, I’m going to show you one more problem and how we can do this without having to draw any models. Here’s the problem for us. We have 64 cups. We need to figure out how many quarts are in there. First I’m going to identify what unit am I starting with. I’m starting with cups. Where am I going? Well, I’m going to be moving to the left. Okay? Now I realize, okay, I’m going to have to divide. Now I’m going to write down 64 divided by how many? How many am I going to need? There are four quarts, right? So we’re going to use that number four, and then we’re going to calculate our answer and we’ll see that we have 16 quarts. Okay?

That’s how we’re going to be doing these unit conversions. They’re super helpful. I hope you really enjoyed this video. If you’ve got more questions about how we can tie some of these visual representations to just doing it with the numbers, let me know. Send them to me in an email over at hello@mathformiddles.com. If you liked this video, please like and share it with your friends.

#### Adrianne Meldrum

Owner of Math for Middles

I’m the owner and creator of the math videos here at Math for Middles. I’ve tutored students for over ten years. When I am not creating here, you’ll find me down by the river with my family. Interested in working with me? Connect with me here.