3.2: Measuring Metric Length
Introduction
The Kid’s Area
There are a lot of children who visit the ice cream stand each week. Most times they sit with their parents at a large picnic table.
Jose has collected a few small picnic tables to put near each other for a small “kid’s area.” Mr. Harris loves the idea. Jose gets to work arranging the tables.
Jose has four small picnic tables for his kid’s area. He wants to put the tables about 1.5 meters apart. He thinks that this will give the kids plenty of room to not be on top of each other.
He puts out the tables and then gets a ruler and a meter stick. Which tool should Jose use to measure the distance between the two tables?
If he wants the tables to be 1.5 meters apart, how many meter sticks will the distance actually be?
Once Jose gets the tables set up, he wants to design a new placemat for the kids to eat off of. For his placemat, should Jose use a ruler or a meter stick when he measures out the design?
Which makes more sense?
This lesson is all about metric measurement. In the end of the lesson, you will be able to help Jose with his kid’s area.
Pay close attention! In the United States we don’t have a lot of experience with Metrics. You will need all of the information in this lesson to be successful.
What You Will Learn
In this lesson, you will learn the following skills:
- Identify the equivalence of metric units of length
- Measure lengths using metric units to the nearest decimal place.
- Choose appropriate tools for given decimal metric measurement situations
- Choose appropriate decimal units for given metric measurement situations
Teaching Time
I. Identify Equivalence of Metric Units of Length
This lesson focuses on metric units of measurements. In the United States, we use the customary system of measurement more than we use the metric system of measurement. However, if you travel to another country or complete work in science class, you will need to know metrics.
What are the metric units for measuring length?
When measuring length, we are measuring how long something is, or you could say we are measuring from one end to the other end. That is the length of the item.
Here are the common metric units of length from the smallest unit to the largest unit.
Millimeter
Centimeter
Meter
Kilometer
A millimeter is the smallest unit. Millimeters are most useful when measuring really tiny things. You can find millimeters on some rulers.
A centimeter is the next smallest unit. Centimeters can also be found on a ruler.
A meter is a little more than 3 feet. A meter is a unit that would be very helpful to a carpenter or to someone working in construction.
A kilometer is used to measure longer distances. You often hear the word kilometer mentioned when talking about a road race that is 5k (or 5 kilometers) long.
How can we convert metric units of length?
When working with the customary units of length: inches, feet, etc., we know that we can convert them from one to another to change the units we are working with. For example, if you have 24 inches, it might make more sense to say that we have 2 feet.
We can do the same thing when working with metric units.
Here is a chart to help us with the conversions.
\begin{align*}& 1 \ km \qquad 1000 \ m\\ & 1 \ m \qquad \ \; 100 \ cm\\ & 1 \ cm \qquad \; 10 \ mm\end{align*}
Now that you know the conversions, we can change one unit to another unit. Let’s look at an example.
Example
5 km = ____ m
Here we are converting kilometers to meters.
How can we convert larger units to smaller units?
We can convert larger units to smaller units by multiplying.
There are 1000 meters in one kilometer.
Example
\begin{align*}5 \ km &= \underline{\;\;\;\;\;\;\;\;\;\;} \ m\\ 5 \times 1000 &= 5000 \ m\end{align*}
Our answer is 5000 m.
Example
600 cm = ______ m
Here we are converting smaller units to larger units.
How can we convert smaller units to larger units?
We can convert smaller units to larger units by dividing.
There are 100 cm in one meter.
Example
600 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} 6
Our answer is 6.
Now it’s time for you to try some. Complete the following conversions.
- 2000 mm = ______ cm
- 3 km = ______ m
- 4000 cm = ______ m
Check your answers with a neighbor. Be sure that you both have completed the conversions correctly.
II. Measure Lengths Using Metric Units to the Nearest Decimal Place
Sometimes when we convert metric units we don’t have a whole number answer. In the last section, all of the examples ended with whole numbers.
Example
2000 mm = 200 cm
These are both whole numbers.
What happens when we convert smaller units to larger units and they don’t end up as a whole number?
When this happens, we end up with an answer that is a decimal. If we remember our rules for working with decimals and place value, we can be very successful at converting these small units of measurement to larger units.
Example
1 mm = ______ cm
Here we are converting a smaller unit to a larger unit, because of this we know that we are going to divide.
There are 10 mm in one centimeter, so we are going to divide 1 by 10.
Think about this, we are dividing 1 whole into 10 parts-our answer is definitely going to be a decimal.
1 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} .1 (one tenth)
Our answer is that 1 mm = .1 cm.
We can also round our answer to the nearest tenth.
What if we had a problem where we wanted to convert 1.5 mm to cm?
Example
1.5 mm = ______ cm
Once again, we are going to be dividing by 10.
When we divide by 10 in this example we end up with an answer of .15
1.5 mm = .15 cm
We can round this answer to the nearest tenth.
.15 rounds to .2
We can say that .2 is the closest tenth of a cm to 1.5 mm.
Just as we were able to round whole numbers, we can round decimal measurements too.
Let’s look at another example where we will get a decimal answer.
Example
1 m = ______ km
Here we are converting a smaller unit to a larger unit.
There are 1000 meters in one kilometer. We divide by 1000.
1 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} .001
Here our answer is one-thousandth of a kilometer.
Now it is time for you to try a few.
- 2 m = ______ km
- 8 mm = ______ cm
- 4 cm = ______ m
III. Choose Appropriate Tools Given Decimal Metric Measurement Situations
Now that you have learned all about converting different measurements, it is time to think about which tools to use to measure different things.
We know some metric units for measuring length are millimeters, centimeters, meters and kilometers.
Millimeters and centimeters are found on a ruler.
There is a meter stick that measures 1 meter.
A metric tape measure can be used to measure multiple meters.
If you wanted to measure long distances, you could use a kilometer odometer, like in a car, to measure distance.
What tool should we use when?
A tool is designed to make measuring simpler. If we have a difficult time choosing an appropriate tool, or choose a tool that isn’t the best choice, it can make measuring very challenging.
Let’s think about tools and when we should use them depending on what and/or where we are measuring.
Here are some general suggestions:
If the object is very tiny, use a ruler for millimeters. If the object is less than 30 cm use a ruler for centimeters. If the object is between 30 cm and 5 or so meters use a meter stick. If the object is greater than a few meters, use a metric tape measure. If the object is a long distance, for instance across town, use a kilometer odometer.
Example
What would we use to measure the following object?
This object is a paperclip. It is definitely smaller than the length of a ruler, so we can use a ruler to measure it.
Example
What about measuring a road race?
A road race is usually a significant distance, so we are going to use a kilometer odometer to measure it.
Now it is time for you to choose an appropriate tool.
- The width of a table
- An ant
Take a minute to check your work with a peer. Discuss any differences in your answers.
IV. Choose Appropriate Decimal Units for Given Metric Measurement Situations
Now that we know about using the appropriate tool, we also need to choose the best unit to measure different things.
The common metric units of length are millimeter, centimeter, meter and kilometer.
When is the best time to use each measurement?
You can think about this logically. Let’s start with millimeters.
A millimeter is the smallest unit. There are 10 mm in one centimeter, if an object is smaller than one centimeter, then you would use millimeters.
Who would use millimeters? A scientist measuring something under a magnifying glass might use millimeters to represent a tiny specimen.
A centimeter is the next smallest unit. We can use a ruler to measure things in centimeters. If an object is the length of a ruler or smaller, then it makes sense to use centimeters to measure.
Meters are used to measure everything between the length of a ruler and the distance between two cities or places.
Most household objects such as tables, rooms, window frames, television screens, etc would be measured in meters.
Kilometers are used to measure distances. If we are looking to figure out the length of a road, the distance between two locations, etc, we would use kilometers.
Think about each example, which is the best unit to measure the objects listed below?
- The height of a picture on the wall
- A caterpillar
- The width of a penny
Explain your answers to a neighbor. Be sure to justify why you chose each unit of measurement.
Real Life Example Completed
The Kid’s Area
Now that you have worked with the Metric System, let’s go back and look at Jose’s work with the kid’s area.
Here is the problem once again.
There are a lot of children who visit the ice cream stand each week. Most times they sit with their parents at a large picnic table.
Jose has collected a few small picnic tables to put near each other for a small “kid’s area.” Mr. Harris loves the idea. Jose gets to work arranging the tables.
Jose has four small picnic tables for his kid’s area. He wants to put the tables about 1.5 meters apart. He thinks that this will give the kids plenty of room to not be on top of each other.
He puts out the tables and then gets a ruler and a meter stick. Which tool should Jose use to measure the distance between the two tables?
If he wants the tables to be 1.5 meters apart, how many meter sticks will the distance actually be?
Once Jose gets the tables set up, he wants to design a new placemat for the kids to eat off of. For his placemat, should Jose use a ruler or a meter stick when he measures out the design?
Which makes more sense?
First, let’s underline the important questions and information in this problem.
Now let’s look at the first question. Jose wants to measure a distance that is much longer than a ruler. He could use a ruler, but think about how many centimeters are in one meter. If Jose is wishing to make his work the simplest that it can be, then he should use the meter stick.
For 1.5 meters, Jose would have to measure out 150 centimeters.
If Jose uses the meter stick, then he would need to measure one and one-half lengths of the meter stick to have the accurate measurement between the tables.
For the placemat design, Jose is going to be working with a much smaller area. He can use a ruler for this design since most placemats are about the size of a piece of paper. Jose will be able to work well with his ruler while a meter stick would be very difficult to work with.
Vocabulary
Here are the vocabulary words that can be found in this unit.
- Metric System
- a system of measurement more commonly used outside of the United States
- Length
- the measurement of a object or distance from one end to the other
- Millimeter
- the smallest common metric unit of measuring length, found on a ruler
- Centimeter
- a small unit of measuring length, found on a ruler
- Meter
- approximately 3 feet, measured using a meter stick
- Kilometer
- a measurement used to measure longer distances, the largest common metric unit of measuring length
Technology Integration
James Sousa, Converting Between Metric Units
Other Videos:
- http://www.mathplayground.com/howto_Metric.html – This video expands on the basic information of the metric system. It also begins working with metric conversions.
- http://www.teachertube.com/viewVideo.php?video_id=8896 – The Metric System song to “Arms Wide Open” by Creed this is sung by two science teachers.
Time to Practice
Directions: Complete the following metric conversions.
1. 6 km = ______ m
2. 5 m = ______ cm
3. 100 cm = ______ m
4. 400 cm = ______ m
5. 9 km = ______ m
6. 2000 m = ______ km
7. 20 mm = ______ cm
8. 8 cm = ______ mm
9. 900 cm = ______ m
10. 12 m = ______ cm
Directions: Write each decimal conversion. Round to the nearest hundredth when necessary
11. 1 mm = ______ cm
12. 5 mm = ______ cm
13. 8 cm = ______ m
14. 9 cm = ______ m
15. 12 m = ______ km
16. 8 m = ______ km
17. 22 mm = ______ cm
18. 225 mm = ______ cm
19. 543 mm = ______ cm
20. 987 mm = ______ cm
Directions: Choose the best tool to measure each item. Use ruler, meter stick, metric tape or kilometric odometer.
21. A paperclip
22. The width of a dime
23. A tall floor lamp
24. The width of a room
25. A road race from start to finish
Directions: Choose the best metric unit for each measurement situation.
26. The length of a small table
27. A book
28. A cell phone
29. The length of a room
30. The distance from Boston to Cincinnati