3.7: Measuring with Customary Units
Introduction
Table Lengths
The next day while the seventh graders were setting up the tables for the bake sale, Mr. Potter the custodian came to them with an idea.
“Hey kids, I think I have a bigger table for you,” he said.
“That would be great!” exclaimed Tyrone.
“I think it is larger than this one, but I’m not sure. Go to my supply closet and grab a tool to measure with, then come back and measure this table. After you're finished, meet me in the auditorium and I’ll show you the other one. Then you can decide which one is best,” suggested Mr. Potter.
“Okay,” Tyrone said.
Tyrone went to the supply closet and grabbed a ruler. He came back to the bake sale area to measure the table.
“What are you going to do with that?” Felix asked.
“Measure this table,” Tyrone said, as Felix laughed. “What are you laughing at?”
“Your choice of tools, you should choose a tape measure," Felix replied.
“Really? Why?” Tyrone asked looking up from the table.
Do you know why it makes more sense to use a tape measure verses a ruler? Tyrone isn’t sure, but Felix seems to know why. This section is all about measurement and measuring with tools and units. Pay attention to this lesson and at the end, you will be ready to help Tyrone understand why one tool is better than another.
What You Will Learn
By the end of this lesson, you will be able to demonstrate the following:
- Identify equivalence among customary units of measure.
- Choose appropriate tools for given customary measurement situations.
- Choose appropriate customary units for given measurement situations.
- Solve real-world problems involving operations with customary units of measure.
Teaching Time
I. Identify Equivalence among Customary Units of Measure
Throughout our study of fractions, we continuously worked with units of measurement. Whether it was \begin{align*}\frac{1}{4}\end{align*} of a pound, \begin{align*}3 \frac{1}{2}\end{align*} feet or \begin{align*}2 \frac{2}{3}\end{align*} cups, we use fractions all the time when we are measuring things.
In this lesson, we will learn more about the units themselves, what they measure and how they relate to each other. By the time you are finished, you’ll be able to measure everything you see. Using fractions helps make your measurements even more accurate.
The Customary System of measurement is the system of measurement most widely used in the United States. This system includes measurements of length, mass, volume, and units of volume that are most often used in cooking. Take a look at the chart below.
Customary Units of Length
\begin{align*}& \text{inch} \ (in)\\ & \text{foot} \ (ft) && 12 \ in.\\ & \text{yard} \ (yd) && 3 \ ft.\\ & \text{mile} \ (mi) && 5,280 \ ft.\end{align*}
Customary Units of Mass
\begin{align*}& \text{ounce} \ (oz)\\ & \text{pound} \ (lb) && 16 \ oz.\end{align*}
Customary Units of Volume
\begin{align*}& \text{ounce} \ (oz)\\ & \text{cup} \ (c) && 8 \ oz.\\ & \text{pint} \ (pt) && 16 \ oz.\\ & \text{quart} \ (qt) && 32 \ oz.\\ & \text{gallon} \ (gal) && 4 \ qt.\end{align*}
Customary Units of Volume Used in Cooking
\begin{align*}& \text{teaspoon} \ (tsp)\\ & \text{tablespoon} \ (tbsp) && 3 \ tsp.\\ & \text{cup} \ (c) && 16 \ tbsp.\end{align*}
Unlike the metric system, there is not a specific way of relating the customary units of measurement to each other. If a foot is 12 inches, you might expect that the next largest measurement unit of length, a yard, to be 12 feet. However, this is not the case. A yard instead, is 3 feet.
Nevertheless, there are some identifiable relationships among the units of measurement. For now, refer to the above chart when working with customary units of measurement. As you get more and more familiar with the units and the various measurement tools, you will acquire an automatic sense of measurement and how the various units relate to each other. Let’s look at some examples that deal with equivalence or equal measures.
Example
6 feet = ___ yards
We are going to convert feet into yards. There are three feet in one yard. If we divide 6 feet by 3 feet, we will have the correct number of yards.
\begin{align*}6 \div 3 = 2\end{align*}
6 feet = 2 yards
Example
2 tablespoons = ___ teaspoons
We are going to convert tablespoons to teaspoons. To do this, we multiply. There are three teaspoons in one tablespoon.
\begin{align*}2 \times 3 = 6\end{align*}
2 tablespoons = 6 teaspoons
There is a hint.
If we go from a larger unit to a smaller unit, we multiply. If we go from a larger unit to a smaller unit, we divide.
Make a note of this rule and then continue with the lesson.
3R. Lesson Exercises
- 12 pounds = ______ ounces
- 6 yards = ______ feet
- 48 inches = _____ feet
Take a few minutes to check your answers. Are they accurate?
II. Choose Appropriate Tools for Given Customary Measurement Situations
Measurement is the system of comparing an object to a standard. As we have seen, the customary system includes units of length (feet or inches), weight or mass (ounces and pounds), and volume (cups or gallons). When we make a measurement of length, weight, or volume, we are comparing the object against a standard (1 foot, 1 ounce, 1 teaspoon).
Tools for customary measurements provide these standards. The ruler is a tool for measuring length, and width. You can find short rulers that are 1 foot, or 12 inches in length, or you can find what are known as yardsticks, which measure 1 yard, 3 feet, or 36 inches. Another way to measure length is with a measuring tape, which can be uncurled to measure longer lengths. Measuring tapes usually show inches and feet.
The balance or scale is the appropriate tool for measuring weight or mass in ounces and pounds.
When we are cooking, we often use a measuring cup to measure out portions of liquids or dry ingredients. Measuring cups come in different sizes. The most commonly used measuring cup measures exactly 1 cup, but you can also find \begin{align*}\frac{1}{2}\end{align*} cup, \begin{align*}\frac{1}{3}\end{align*} cup, and \begin{align*}\frac{1}{4}\end{align*} cup sizes.
Example
Choose the appropriate tool for making the following measurements:
a) the weight of an apple
b) the length of a swimming pool
c) the length of a caterpillar
If you think about each item, it is easy to determine the best tool for each measurement.
The answers are:
a) Balance or scale
b) Yardstick or measuring tape
c) Ruler
3S. Lesson Exercises
Choose the best tool for each measurement.
- Milk for a recipe
- A garden plot
- A bunch of bananas
Take a few minutes to compare your answers with a friend. Discuss any differences and then continue with the next section.
III. Choose Appropriate Customary Units for Given Measurement Situations
We use measurement to help us complete essential tasks in everyday life. If you are building a house, you will have to decide how long and how wide your house will be. If you are baking a key lime pie, you will need to know how many cups of lime juice to use.
Using the correct units of measurement makes our lives easier. You can measure the distance from your house to Paris, France in inches, but that’s a lot of inches! That’s why we measure that distance in miles.
When you need to measure something, always consider the most reasonable unit to use before measuring. If you choose a unit that is too small, you will get a large number that is hard to keep track of. If you choose a unit that is too large, it will be more difficult to be precise in your measurement.
Let’s look at an example.
Example
What unit of measurement would you use to find the volume of a jar of jam?
Since a jar is small, we use ounces to measure it.
Ounce is the answer.
Part of figuring out the best unit of measurement to use is using common sense. We have to think about what we are measuring and how we are measuring, then you will be able to figure out the correct tool and unit of measurement that we need to use in order to get the job done.
3T. Lesson Exercises
Choose the correct unit of measurement for each item.
- A sack of grain
- The distance from one city to another
- The length of a pencil
Check your work with a peer.
IV. Solve Real-World Problems Involving Operations with Customary Units of Measure
When we shop for food, we use units of measurement and money together. This combines some of our early work with decimals and with this lesson’s work on measurement. Let’s look at an example.
Example
Juan is making a quiche. He has to go to the grocery store to get cheese, milk and ham. He buys 12 oz. of cheese at 39 cents per ounce, \begin{align*}\frac{1}{2}\end{align*} gallon of milk, which is on sale for $2.79 per gallon and \begin{align*}\frac{3}{4}\end{align*} pound of ham at $6.99 per pound. How much does Juan spend at the grocery store?
First, we need to figure out how much Juan spent for each item. The cheese cost .39 per ounce and he bought 12 ounces, so the cost of the cheese is \begin{align*}0.39 \cdot 12\end{align*}, which equals 4.68. Juan spent $4.68 for the cheese. He bought a \begin{align*}\frac{1}{2}\end{align*} gallon of milk at $2.79 per gallon, so the cost of the milk is \begin{align*}2.79 \cdot \frac{1}{2} = 1.40\end{align*}. Juan spent $1.40 on milk. Last, he bought \begin{align*}\frac{3}{4}\end{align*} pound of ham at $6.99 per pound, so the cost of ham is \begin{align*}6.99 \cdot \frac{3}{4} = 5.24\end{align*}. Juan spent $5.24 on ham. Now, we add up the three prices.
\begin{align*}\$4.68 + \$1.40 + \$5.24 = \$11.32.\end{align*}
The answer: Juan spent $11.32.
Now let’s go back to the original problem presented at the beginning of this lesson and use what we have learned to solve it.
Real-Life Example Completed
Table Lengths
Here is the original problem once again. Reread it and underline any important information.
The next day while the seventh graders were setting up the tables for the bake sale, Mr. Potter the custodian came to them with an idea. “Hey kids, I think I have a bigger table for you,” he said.
“That would be great!” exclaimed Tyrone.
“I think it is larger than this one, but I’m not sure. Go to my supply closet and grab a tool to measure with, then come back and measure this table. After you're finished, meet me in the auditorium and I’ll show you the other one. Then you can decide which one is best," suggested Mr. Potter.
“Okay,” Tyrone said.
Tyrone went to the supply closet and grabbed a ruler. He came back to the bake sale area to measure the table.
“What are you going to do with that?” Felix asked.
“Measure this table,” Tyrone said, as Felix laughed. “What are you laughing at?”
“Your choice of tools, you should choose a tape measure,” Felix replied.
“Really? Why?” Tyrone asked looking up from the table.
Think about what you have learned in this lesson. Now do you understand why Felix recommends that Tyrone use a tape measure?
Think about the size of a table. A table is an item that is larger than the length of a notebook or a textbook. When an item is larger than a notebook or a textbook, you should use a tape measure. While Tyrone could use a ruler, it is harder to measure it and keep track of each length of the ruler. With a tape measure, the measurement is clear and exact.
Tyrone decides to take Felix’s advice. In no time at all, he has measured the table and is off to meet with Mr. Potter.
Vocabulary
Here are the vocabulary words that are found in this lesson.
- Customary System
- the system of measurement used in the United States.
- Equivalence
- equal measures
- Measurement
- Comparing an object to a standard
Technology Integration
Khan Academy U.S. Customary and Metric Units
James Sousa, American Unit Conversions
Other Videos:
http://www.youtube.com/watch?v=EaJc4UnjVzw&feature=related
Time to Practice
Directions: Fill in the blanks with the equivalent measurement.
1. 6 pints = ___ quarts
2. 2 cups = ___ tablespoons
3. \begin{align*}3 \frac{1}{2}\end{align*} pounds = ___ ounces
4. \begin{align*}\frac{1}{2}\end{align*} mile = ___ feet
5. 56 ounces = ___ pounds
6. 24 inches = ___ feet
7. \begin{align*}5 \frac{1}{2}\end{align*} feet = ___ inches
8. \begin{align*}\frac{1}{2}\end{align*} pound = ___ ounces
Directions: Fill in the blanks with the equivalent measurements for 3 yards.
9. ___ inches
10. ___ feet
Directions: Fill in the blanks with the equivalent measurements for 4 cups.
11. ___ tablespoons
12. ___ teaspoons
Directions: Choose the appropriate tool for making the following measurements:
13. the weight of a violin
14. the volume of a small amount of oregano
15. the volume of a glass of milk
16. the length of one side of your desk
Directions: Choose the appropriate unit of measurement for making the following measurements:
17. the length of a football field
18. the volume of a car’s gas tank
19. the length of an insect
20. the weight of a tennis shoe
21. Mrs. Withers bought a 3 gallon bag of garden soil. She is using the soil to fill flower pots, which hold 10 oz each. How many 10 oz. flower pots can she fill from the bag of garden soil?
22. At the shotput tournament, Roger throws the shot three times. The first time, he throws it 51.5 feet, the second throw is 54.25 feet and the third throw is 52 feet. Rounding to the nearest hundredth, what is the average distance that Roger throws the shot? [Average = (throw 1 + throw 2 + throw 3) \begin{align*}\div\end{align*} (number of throws)]
23. Felix’s mother makes Felix drink 4 tablespoons of orange juice everyday to keep Felix healthy. How many cups of orange juice does Felix drink per week?
24. Nelson built a motor scooter which runs on olive oil. If he uses 1 gallon of olive oil he can travel for exactly \begin{align*}\frac{1}{2}\end{align*} mile. The distance from his house to school is 2,700 feet. Can Nelson make it from his house to school using only 1 gallon of olive oil? Explain your answer.