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# 4.7: Metric Units of Mass and Capacity

Difficulty Level: At Grade Created by: CK-12

## Introduction

The Metric Park

Mrs. Andersen’s class is having a great time at the science museum. Sam and Olivia are very excited when the group comes upon the metric playground. This playground has been built inside the museum and combines playground toys with metrics.

The first one that they try is the metric seesaw. Sam sits on one side of the seesaw and Olivia sits on the other side. Since they weigh about the same, it is easy to keep the seesaw balanced. Under Sam, there is a digital scale. Under Olivia there is the same scale with a key pad. Sam’s weight shows up under the scale.

Sam weighs 37 kg.

“Next, we have to convert kilograms to grams and punch it in so both of our scales will have the same reading,” Sam tells Olivia.

Olivia pauses, she can’t remember how to do this.

“Let’s move on to something else, I can’t remember,” She tells Sam.

The two move on to a birdbath. Together, they need to fill one 4.5 liter birdbath with water using a scoop. Once they have it filled, the sign above the birdbath will light up and tell them how many milliliters are in 4.5 liters.

“I think I can figure this out without filling the birdbath,” Olivia says.

Can you figure it out? How many milliliters can be found in that 4.5 liter birdbath?

This lesson is all about metrics, but by the end, you will be able to master the tasks at the metric park.

What You Will Learn

In this lesson you will learn the following skills:

• Identify equivalence of metric units of mass.
• Identify equivalence of metric units of capacity.
• Choose appropriate metric units of mass or capacity for given measurement situations.
• Solve real-world problems involving metric measures of mass or capacity.

Teaching Time

I. Identify Equivalence of Metric Units of Mass

In the United States, the most common system of measurement is the Customary system of measurement. The Customary system of measurement for mass or weight is measured in pounds and tons. Outside of the United States and when people work with topics in science, people use a system called the Metric system. The metric system measures mass or weight differently from the customary system.

How do we measure mass in the Metric system?

In the metric system we use different standard units to measure mass or weight.

This text box lists the units of measuring mass from the largest unit, the kilogram, to the smallest unit, the milligram. If you think back to when you learned about measuring length, the prefix “milli” indicated a very small unit. That is the same here as we measure mass.

How can we find equivalent metric units of mass?

The word equivalent means equal. We can compare different units of measuring mass with kilograms, grams and milligrams. To do this, we need to know how many grams equal one kilogram, how many milligrams equal one gram, etc. Here is a chart to help us understand equivalent units.

Here you can see that when we convert kilograms to grams you multiply by 1000.

When you convert grams to milligrams, you multiply by 1000.

To convert from a large unit to a small unit, we multiply.

To convert from a small unit to a large unit, we divide.

Example

5 kg = _____ g

When we go from kilograms to grams, we multiply by 1000.

5 kg = 5000 g

These two values are equivalent.

Example

2000 mg = _____ g

When we go from milligrams to grams, we divide.

2000 mg = 2 g

These two values are equivalent.

Now it is your turn to practice. Convert each metric unit of mass to its equivalent.

1. 6 kg = _____ g
2. 3000 g = _____ kg
3. 4 g = _____ mg

Take a few minutes to check your work with a peer.

II. Identify Equivalence of Metric Units of Capacity

When we think about capacity, often referred to as volume, we think about measuring liquids. In the Customary system of measurement, we measure liquids using cups, pints, ounces, gallons etc. In the Metric System of measurement, we measure capacity using two different measures, liters and milliliters.

Since there are only two common metric units for measuring capacity, this text box shows them and their equivalent measures.

Liters are larger than milliliters. Notice that prefix “milli” again.

When converting from large units to small units, you multiply.

When converting from small units to large units, you divide.

Let’s apply this in an example.

Example

4 liters = _____ milliliters

Liters are larger than milliliters, so we multiply by 1000.

4 liters = 4000 milliliters

Use what you have learned to write each equivalent unit of capacity.

1. 5 liters = _____ milliliters
2. 2000 milliliters = _____ liters
3. 4500 milliliters = _____ liters

Take a minute to check your work with a neighbor. Did you divide or multiply when needed?

III. Choose Appropriate Metric Units of Mass or Capacity for Given Measurement Situations

When you think about the metric units for measuring mass, how do you know when to measure things in grams, milligrams or kilograms? To really understand when to use each unit of measurement we have to understand a little more about the size of each unit. If you know measurements in the customary or standard system of measurement, such as ounces and pounds, you can compare them to measurements in the metric system of measurement, such as milligrams, grams, and kilograms. Grams compare with ounces, which measure really small things like a raisin. Kilograms compare with pounds, which we use pounds to measure lots of things, like a textbook. What about milligrams?

Milligrams are very, very tiny. Think about how small a raisin is and recognize we would use grams to measure that. Scientists are one group of people who would measure the mass of very tiny items. These things would be measured in milligrams.

If you think about things that would be seen under a microscope, you would measure the mass of those items in milligrams.

A milligram is \begin{align*}\frac{1}{1000}\end{align*} of a gram.

Use what you have learned to select the correct metric unit for measuring the mass of each item.

1. The weight of five pennies
2. The weight of a person
3. The weight of a car

What about capacity? How do we choose the correct unit to measure capacity?

There are two metric units for measuring capacity, milliliters and liters.

This comparison may seem a little more obvious that the units for mass. A milliliter would be used to measure very small amounts of liquid. Milliliters are much smaller even than ounces. A liter would be used to measure much larger volumes of liquid.

A milliliter is \begin{align*}\frac{1}{1000}\end{align*} of a liter.

Would you measure a bottle of soda in liters or milliliters?

You would measure it in liters. A 2 liter bottle of soda is a standard size for soda bottles. Think about milliliters as the amount of liquid in an eyedropper.

## Real Life Example Completed

The Metric Park

Remember back to the metric park? Well, now you are ready to help Sam and Olivia with those conversions.

Let’s take another look at the problem.

Mrs. Andersen’s class is having a great time at the science museum. Sam and Olivia are very excited when the group comes upon the metric playground. This playground has been built inside the museum and combines playground toys with metrics.

The first one that they try is the metric seesaw. Sam sits on one side of the seesaw and Olivia sits on the other side. Since they weigh about the same, it is easy to keep the seesaw balanced. Under Sam, there is a digital scale. Under Olivia there is the same scale with a key pad. Sam’s weight shows up under the scale.

Sam weighs 37 kg.

“Next, we have to convert kilograms to grams and punch it in so both of our scales will have the same reading,” Sam tells Olivia.

Olivia pauses, she can’t remember how to do this.

“Let’s move on to something else, I can’t remember,” She tells Sam.

The two move on to a birdbath. Together, they need to fill one 4.5 liter birdbath with water using a scoop. Once they have it filled, the sign above the birdbath will light up and tell them how many milliliters are in 6 liters.

“I think I can figure this out without filling the birdbath,” Olivia says.

Can you figure it out? How many milliliters can be found in that 4.5 liter birdbath?

First, let’s underline all of the important information.

Next, Sam and Olivia need to convert 37 kg into grams. There are 1000 grams in 1 kilogram, so there are 3700 grams in 37 kilograms.

You can see why it makes so much more sense to measure someone’s weight in kilograms versus grams.

The birdbath holds 4.5 liters of water. Now that you know that there are 1000 milliliters in one liter, you can figure out how many milliliters will fill the birdbath by multiplying 4.5 \begin{align*}\times\end{align*} 1000. We move the decimal point three places to the right when we multiply by 1000.

Wow! You can see why it makes much more sense to measure the amount of water in the birdbath in liters versus milliliters.

## Vocabulary

Here are the vocabulary words that are found in this lesson.

Customary System
The system of measurement common in the United States, uses feet, inches, pounds, cups, gallons, etc.
Mass
the weight of an object
Capacity
the amount of liquid an object or item can hold

## Technology Integration

Other Videos:

http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/6_Weight_and_Capacity/index.html – Great animated video on weight and capacity using metric units and customary units

## Time to Practice

Directions: Convert to an equivalent unit for each given unit of mass.

1. 5 kg = ______ g

2. 2000 g = ______ kg

3. 2500 g = ______ kg

4. 10 kg = ______ g

5. 2000 mg = ______ g

6. 30 g = ______ mg

7. 4500 mg = ______ g

8. 6.7 g = ______ mg

9. 9 kg = ______ g

10. 1500 g = ______ kg

Directions: Convert to an equivalent unit for each given unit of capacity.

11. 4500 mL = ______ L

12. 6900 mL = ______ L

13. 4400 mL = ______ L

14. 5200 mL = ______ L

15. 1200 mL = ______ L

16. 3 L = ______ mL

17. 5.5 L = ______ mL

18. 8 L = ______ mL

19. 9.3 L = ______ mL

20. 34.5 L = ______ mL

Directions: Choose the best unit of either mass or capacity to measure each item.

21. A dictionary

22. A flea under a microscope

23. A jug of apple cider

24. An almond

25. Drops of water from an eyedropper

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