Third Grade Math: Understanding Volume

In third grade, you'll learn how to measure and compare different amounts of liquids and solids. To do this, you'll need to understand volume and mass, which you'll also need to know about for science class.

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What Is Volume?

Volume is the amount of space that is inside a container, like a jar or a measuring cup. In math and science, this space is often measured in liters. This empty space can be used to measure amounts of liquid by filling it up. For example, when a 2-liter bottle is filled with soda pop, you know that you have two liters of soda. If the bottle is half full, you know that you only have one liter of soda.

Mass is usually measured in units like grams or kilograms, and it tells you how heavy something is. Two boxes that are the same size have the same volume, but they might have different masses if they have different things inside of them. For example, imagine that you and your sister both get Christmas presents in boxes that are exactly the same size. However, your box is filled with feathers, and your sister's box is filled with solid gold. The boxes both have the same volume, but your sister's box will have greater mass.

Measuring Liquid Volume

We already discussed how volume is the amount of space inside an object. If that space is empty, then volume tells you how much liquid could fit inside of it. Liquid volume is often measured by pouring the liquid into an empty measuring cup or a beaker that has units of volume marked on the side. For example, if you're baking a cake and the recipe calls for 1/2 cup of milk, you would fill one cup halfway full to measure it. Remember that in math and science, liquid is usually measured in liters. The abbreviation for 'liter' is L. For instance, 12 liters would be abbreviated '12 L.'

Solving Problems with Liquid Volume

Now that you know how to measure volume in liters, you can solve word problems with liquid volume. Doing math problems with units of volume is the same as doing them with regular numbers. For example, if you have one liter of water, and you add another liter of water to it, then you have two liters of water (1 + 1 = 2). If you have six liters of water and you divide it equally into three separate containers, each container will have two liters of water (6 ÷ 3 = 2).

Measuring Mass

You'll usually measure mass using a scale. If you're measuring smaller items, like pieces of candy or coins, you'll probably measure them in grams. A gram has about the same mass as a paper clip, and 100 grams equals one kilogram. The abbreviation for 'gram' is g, and the abbreviation for 'kilogram' is kg. For example, 18 grams would be written, '18 g,' and 24 kilograms would be written, '24 kg.'

Solving Problems with Mass

You can solve word problems with mass the same way you did with the volume problems. For example, if you have 15 kg of watermelons, and you give your friend five kilograms, you'll have ten kilograms left (15 - 5 = 10). Here's one more example, this time with multiplication. If Angela's older brother is three times her mass, and Angela's mass is 30 kg, her brother's mass would be 90 kg (30 x 3 = 90).

Practice Problems

1. If you have five liters of water, and your friend has three liters of water, how much water do the two of you have altogether?

You would have eight liters of water, because 5 + 3 = 8.

2. Sammy had ten kilograms of Halloween candy, and he wanted to give some to five of his friends. How much candy can he give to each friend?

Since 10 ÷ 5 = 2, Sammy can give each friend two kilograms of candy.

3. Jason is making cookies, and the recipe calls for four grams of sugar. Jason is doubling the recipe, so he needs to use twice as much sugar as the recipe calls for. How much sugar should he use?

Jason should use eight grams of sugar, since 4 x 2 = 8.
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