Level E Lesson 24
Measurement Conversions
In lesson 24 the objective is, the student will convert among different-sized measurement units within the metric measurement system and use these conversions in solving real-world problems.
The skills students should have in order to help them in this lesson include Measurement Equivalence, Decimal Comparison, Fractions, and Multiplication and Division of Decimals.
We will have three essential questions that will be guiding our lesson. Number 1, how can I convert measurement units to larger measurement units? Number 2, how can I convert larger measurement units to smaller measurement units? And number 3, how can I use measurement conversions in real life?
The SOLVE problem for this lesson is, Arnold’s uncle is helping him build two model airplanes for a science project. Arnold and his uncle will compare the distances the airplanes fly. The first airplane flies eight hundred centimeters, and the second airplane flies five hundred centimeters. What is the difference, in meters, in the flights of the two planes?
We will start by Studying the Problem. First we want to identify where the question is located within the problem and we will underline the question. What is the difference, in meters, in the flights of the two planes? Now that we have identified the question, we want to put this question in our own words in the form of a statement. This problem is asking me to find the number of meters difference between the two planes flights.
During this lesson we will learn how to work with measurement conversions. We will use this knowledge to complete this SOLVE problem at the end of the lesson.
Throughout this lesson students will be working in cooperative pairs. All students should know their role as either Partner A or Partner B before beginning this lesson.
To begin this lesson each pair of students will need one hundred centimeter cubes, a ruler, and a piece of string.
We have three basic units of metric measurement for distance. They are Centimeters, Meters, and Kilometers.
With your partner, line up one hundred centimeter cubes in a row and compare the one meter string to it. Go ahead a do this now. If the line of one hundred centimeter cubes equals one meter, how many centimeters are in a meter? There are one hundred centimeters in a meter. Can you identify some items in the classroom that can be measured using centimeters and meters? We can use meters to measure the distance from one end of the room to the other. And we can use centimeters to measure a pencil’s length. So which unit of measurement would be the most appropriate to measure the length of an index card? Centimeters, because the length of the index card is short and can be measured using the centimeter marks on a ruler. Which unit of measurement would be most appropriate to measure the length of the classroom? We would use meters, because it is easier to measure a longer distance with the meter string. Go ahead and measure the length of the classroom with your partner using your meter string. *If a meter stick is available, measure the length of the classroom using the meter stick! Sometimes, you may need to find a distance that is too large to measure with a meter stick. Can you name some examples of these distances? The distance from home to school and the distance between towns, are examples of distances that are too large to measure with a meter stick. A kilometer is larger than a meter. If we placed one thousand meters end to end they would be equivalent to a kilometer. Therefore, one kilometer equals one thousand meters.
Now let’s place in order the following measurement units from smallest to largest. The smallest measurement unit is centimeters. The next smallest measurement unit is meters. And our largest measurement unit is kilometers.
Looking at the line of centimeter cubes you and your partner created, how many groups of ten can the meter be divided into? We can divide the meter into ten groups of ten. We have a total of one hundred centimeters cubes, so we can create ten groups of ten centimeter cubes. How many centimeters are in one tenth of a meter? There are ten centimeters in one tenth of a meter. How would this be written in decimal form? Zero point one, which is read as one tenth.
How many centimeters are in one hundredth of a meter? There is one centimeter in one hundredth of a meter. How would this be written in decimal form? We write zero point zero one, which is read as one hundredth. Which is the greater value, one tenth, or one hundredth? One tenth is the greater value. You can check this by lining up the decimals.
Now let’s compare the relationships between the units listed above. What do each of the words have in common Kilometer, Meter and Centimeter? They have in common the word “meter.” Let’s underline it in each unit and then write the abbreviation for each unit. We abbreviate kilometer with the letters km. We abbreviate meter with the letter m. And we abbreviate centimeter with the letters cm. A meter is the “benchmark” unit. How many meters should be recorded under the word meter? We will record one meter. Now identify how many meters are in one centimeter as a decimal. Remember that there are one hundred centimeters in one meter. So there is one hundredth of a meter in one centimeter (zero point zero one). Next identify how many meters are in one kilometer. There are one thousand meters in one kilometer.
Now let’s examine the values of the digits for the units. What digits are used? We used zeros and ones. What part of a meter is one centimeter? One centimeter is one hundredth of a meter. What happens to the decimal point for a centimeter when compared to a meter? The decimal point moves two places to the left to show hundredths. Why does the decimal point move? There are one hundred centimeters in a meter, and when one meter is divided by one hundred centimeters, the answer is one hundredth meters. When changing meters to centimeters, did you move from larger to a smaller unit, or from a smaller to a larger unit? You moved from a larger to a smaller unit. This is called a conversion. What operation would you use to convert meters to centimeters? You would use multiplication. Now explain what happens to the number value when converting to find how many meters are in one kilometer. We are going from a larger unit to a smaller unit, so the number value will be larger. What operation would you use to convert kilometers to meters? You would use multiplication, because we want to know how many meters are in one kilometer. Let’s summarize what we know. We need to multiply when moving from a larger unit to a smaller unit. And we need to divide when moving from a smaller unit to a larger unit.
Let’s apply this information to our graphic organizer. Let’s look at the first problem together. What is the problem asking us to find? This problem is asking us to find how many centimeters are in three meters? Under the column means we will place the question, how many centimeters are in three meters? Identify what measurement unit we already know. We already know the number of meters. Next identify the unit we are converting to. We are converting to centimeters. Are we moving from larger to smaller units or smaller to larger units? We are going from meters to centimeters, so we are moving from larger to smaller units. Record this in the box for unit direction. When moving from larger to smaller units, what operation do we use? We use multiplication. We record multiplication as our operation. How many centimeters are in one meter? There are one hundred centimeters in one meter. We will record this under the conversion of one unit. One meter equals one hundred centimeters. Now explain how we can find the number of centimeters in three meters. We can multiply three by one hundred to find the number of centimeters in three meters. Three times one hundred equals three hundred centimeters. We will record for our solution. Three times one hundred equals three hundred centimeters. So three meters is equal to three hundred centimeters. Determine what happened to the number of zeros in the product when three was multiplied by one hundred. Two zeros were added.
Now let’s look at the second problem together. Explain what this problem is asking us to find. This problem is asking us to find how many meters are in two hundred centimeters? Let’s place this question in the box means. What measurement unit do we know? We know the number of centimeters. Identify the measurement unit we are converting to. We are converting to meters. Are we moving from larger to smaller units or smaller to larger units? We are moving from centimeters to meters. So we are moving from smaller to larger units. Record this information in the box for unit direction. So when moving from smaller to larger units, what operation do we use? We use division. Record the operation in the box provided. How many centimeters are in one meter? One hundred centimeters are in one meter. In the box for conversion of one unit we will record one hundred centimeters is equal to one meter. Explain how we can find the number of meters in two hundred centimeters. We can divide two hundred by one hundred to find the number of meters in two hundred centimeters. Two hundred divided by one hundred equals two meters. We will record this in our solution box. Two hundred centimeters is equal to two meters. What happened to the number of zeros in the quotient when two hundred was divided by one hundred? Two zeros were removed.
When working with the metric system, all the prefixes centi, kilo, milli can be used with any of the basic measurement units. Next, we will apply what we learned about equivalence with meters to the units of grams and liters. The same prefixes and relationships can be used with liters and grams that were used with meters. So if one kilometer is equivalent to one thousand meters, then one kilogram is equivalent to one thousand grams. What fractional part of a kilogram is one gram when written in decimal form? One gram is one thousandth of a kilogram. If one liter is equivalent to one thousand milliliters, what fractional part of one liter is one milliliter when written in decimal form? One milliliter is one thousandth of a liter.
Let’s record the information that we just discussed in the tables. A kilogram is abbreviated using the letters kg. And a gram is abbreviated using the letter g. A kilogram is equal to one thousand grams. And gram is equal to one thousandth of a kilogram.
In the next table we will summarize liters and milliliters. The abbreviation for liter is the capital letter L. And the abbreviation for milliliter is ml. One liter is equivalent to one thousand milliliters. And one milliliter is equivalent to one thousandth of a liter.
Let’s use this information to complete the graphic organizer. We will take a look at problem one together. Explain what this problem is asking us to find. The problem is asking us to find, how many grams are in three kilograms? We will record this question in the box labeled means. How many grams in three kilograms? Identify the measurement unit we already know. We already know the number of kilograms. Now identify the measurement unit we are converting to? We are converting kilograms into grams. Are we moving from larger to smaller units or smaller to larger units? We are moving from kilograms to grams, so we are moving from larger to smaller units. Record the unit direction in the graphic organizer. When moving from larger to smaller units, what operation do we use? We use multiplication. Record the operation in the graphic organizer. How many grams are in one kilogram? There are one thousand grams in one kilogram. We will record this information in the box conversion of one unit. One kilogram equals one thousand grams. Explain how we can find the number of grams in three kilograms. We can multiply three by one thousand to find the number of grams in three kilograms. Three times one thousand equals three thousand grams. Record the solution in the graphic organizer. We have found that three kilograms is equals to three thousand grams. Now determine what happened to the number of zeros in the product when three was multiplied by one thousand. Three zeros were added.
We are now going to go back to the SOLVE problem from the beginning of the lesson. Arnold’s uncle is helping him build two model airplanes for a science project. Arnold and his uncle will compare the distances the airplanes fly. The first plane flies eight hundred centimeters, and the second plane flies five hundred centimeters. What is the difference, in meters, in the flights of the two planes?
At the beginning of the lesson we Studied the Problem. We underlined the question, what is the difference, in meters, in the flights of the two planes? And put this question in our own words in the form of a statement. This problem is asking me to find the number of meters difference between the two planes flights.
In Step O, we will Organize the Facts. First we will identify the facts. Arnold’s uncle is helping him build two model airplanes, fact, for a science project, fact. Arnold and his uncle will compare the distances the airplanes fly, fact. The first plane flies eight hundred centimeters, fact, and the second plane flies five hundred centimeters, fact. What is the difference, in meters, in the flights of the two planes? Now that we have identified the facts, we are ready to eliminate the unnecessary facts. These are the facts that will not help us to find the number of meters difference between the two planes flights. Arnold’s uncle is helping him build two model airplanes. Knowing that they are building two model airplanes will not help us to find the number of meters difference between the two planes flights. So we will eliminate this fact. For a science project. Knowing that the airplanes are for a science project also does not help us to find the number of meters difference between the two planes flights so we will eliminate this fact as well. Arnold and his uncle will compare the distances the airplanes fly. Knowing that they are going to compare the distances does not give us the details necessary to finding the number of meters difference between the two planes flights. So we will eliminate this fact as well. The first plane flies eight hundred centimeters. This is the detail is necessary to finding the number of meters difference between the two planes flights. So we will keep this fact. And the second plane flies five hundred centimeters. We also need this information in order to find the difference between the two planes flights. So we will keep this fact as well. Now that we have eliminated the unnecessary facts, we are ready to list the necessary facts. The first plane flew eight hundred centimeters. The second plane flew five hundred centimeters. We are looking for the difference in meters.