Level C Lesson 20
Measure and Estimate Mass of Objects and Liquid Volume
In lesson 20 the objective is, the student will explore, calculate, measure and estimate mass of objects and liquid volume using standard units of grams, kilograms, liters, and milliliters.
The skills students should have in order to help them in this lesson include multiplication by ten.
We will have three essential questions that will be guiding our lesson. Number 1, how can I compare grams and kilograms? Number 2, how can I compare milliliters and liters? And number 3, what would be an appropriate unit of measure to estimate the mass of a large dog? Why?
The SOLVE problem for this lesson is, Dontae’s mom volunteered to help with the class party at the end of the year. There are twenty eight students in his class. Dontae’s mom is buying one liter bottles of fruit punch for the drink. If she plans on four servings per liter, how many liters of fruit punch does she need?
We will start by Studying to Problem. First we want to identify where the question is located within the problem and we will underline the question. How many liters of fruit punch does she need? 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 liters of fruit punch she needs.
During this lesson we will learn how to measure and estimate the mass of objects and liquid volume. We will use this knowledge to complete this SOLVE problem at the end of the lesson.
Throughout this lesson students will be working together in cooperative pairs. All students should know their role as either Partner A or Partner B before beginning this lesson.
As we start this lesson students will need to be seated in groups of four. Each group of four will need to have one large unit cube and one hundred small unit cubes. We are going to start by examining the large unit cube and the small unit cubes. If the large unit cube were filled with the small unit cubes, which cube would have the greater mass? The large unit cube would have the greater mass. How many of the small unit cubes do you think will fit inside the large unit cube? Groups can predict together how many small unit cubes they think it will take to fill the large unit cube, once predictions have been made let’s do a few activities to find out.
Let’s start by looking at, how many small unit cubes you think it will take to cover the bottom of the large cube? We can find out if we take our small unit cubes and we line them up in the bottom of the large unit cube. It works best if we start in one corner and create rows of small unit cubes. Our first row of small unit cubes tells us that there are ten unit cubes in this row. We continue to add rows of unit cubes until we have filled the entire bottom of our large unit cube. There are a total of ten rows of small unit cubes. Each row has ten unit cubes. So to cover the entire bottom of the large unit cube, it will take one hundred small unit cubes. Now let’s talk about how many small unit cubes tall the large unit cubes is? We can find this out by placing one small unit cube in the bottom corner of our large unit cube and stacking small unit cubes until we reach the top. The large unit cube is ten small unit cubes tall. So if there are one hundred small unit cubes in one layer of the large unit cube, how many layers of one hundred small unit cubes would it take to fill the large unit cube? Since we found that the large unit cube is ten small unit cubes tall, it will take ten layers of small unit cubes to fill the large unit cube. So how many small unit cubes are needed to fill the large unit cube if the small unit cubes filled it to the top? Since each layer has one hundred small unit cubes and we would need ten layers to fill the large unit cube to the top, it will take one thousand small unit cubes to fill the large unit cube to the top.
What we have been working with in this example is Mass. Mass is the amount of space in an object. In order to measure mass, we will call the small unit cube a gram. One small unit cube equals one gram. So how many grams will fit in the large unit cube? Since we found that it would take one thousand small unit cubes to fill the large unit cube our answer is one thousand grams. The large unit cube with one thousand grams represents a kilogram! Which has the larger mass: one gram or one kilogram? The kilogram has the larger mass as this object has more space. So how many grams does it take to cover the bottom of the kilogram container? Remember that we found that it takes one hundred of our small unit cubes to cover the bottom of our large unit cube. Since each of our small unit cubes represents one gram we know that it takes a total of one hundred grams to cover the bottom of the kilogram container. How many grams can be stacked in the corner to determine the height? In the last activity we found that it takes ten small unit cubes to create the height of the large unit cube. Since each of the small unit cubes represents one gram it takes a total of ten grams to determine the height of our kilogram. How many grams does it take to completely fill the kilogram container? One thousand grams. So how many grams equal one kilogram? One thousand grams equal one kilogram.
As we said earlier Mass is the amount of space in an object. It is measured in grams and kilograms. What are some objects you see every day that would be measured using grams? We would use grams to measure a slice of bread, or a piece of paper. What are some objects you see every day that would be measured using kilograms? We would use kilograms to measure a dog, or a backpack.
Take a look at this pencil. What would be the most appropriate unit for measuring the mass of a pencil? The gram would be most appropriate because it is used to measure smaller amounts of mass.
How about this math textbook? What would be the most appropriate unit for measuring the mass of a textbook? The kilogram would be most appropriate because it is used to measure larger amounts of mass.
Now let’s look at this loaf of bread. Do you know the exact mass of the loaf of bread? No, because there are no marks to show the measurement. Let’s decide what would be the most accurate measurement unit for the loaf of bread. Would it be about one kilogram; about one gram; exactly one gram; or exactly one kilogram? One gram weighs about the same as a paper clip. Since we know that a loaf of bread weighs more than a paper clip, about one gram, and exactly one gram would not fit for the measurement for the loaf of bread. So it’s either about one kilogram or exactly one kilogram. Since we don’t know the exact mass of the loaf of bread the most accurate measurement unit would be about one kilogram.
Now let’s take a look at the box of sand. Do you know the exact mass of the sand in the container? Yes, because there is a container with marks showing the amount and a key to tell us how much each mark represents. The key says each mark equals one gram. Since there are ten marks going up the side of the container and the sand fills the container all the way to the top. Let’s decide what would be the most accurate measurement for the container of sand. Because we are given the measurement marks and the key we know that we can find the measurement exactly. Since each mark equals one gram our most accurate measurement for the container of sand is exactly ten grams. Sometimes an exact measurement is possible as it was with this example. And sometimes it is only possible to estimate the mass of an item.
Let’s take a look at this box of sand. The box below is full of sand. It has a mass of ten kilograms. John has five boxes full of sand. If each of the boxes has a mass of ten kilograms, what is the total mass of the five boxes? Five boxes each having a mass of ten kilograms gives us a total mass of fifty kilograms.
Taking a look at this next box, this box is full of sand as well. It has a mass of fifteen kilograms. If Kate has two boxes, what is the total amount of sand she has? Two boxes each having a mass of fifteen kilograms is a total of thirty kilograms.
What is the difference between the amounts of sand John and Kate have? We found that John had fifty kilograms of sand and Kate has thirty kilograms of sand. Fifty take away thirty equals twenty kilograms. The difference between the amounts of sand John and Kate have is twenty kilograms.
In the last activity, the small unit was one gram and the larger unit was one kilogram.
In the next activity, the small unit will represent one milliliter, and the large unit will represent one liter. If the liter cube was filled with the milliliter units, which has the greatest volume: one milliliter or one liter? The liter would have the greater volume. How many milliliters does it take to cover the bottom of the liter container? We can find out by placing our milliliter cubes inside the bottom of the liter container. It’s best to start in one corner and work our way across in rows making sure that there is no space left between each one of our milliliter cubes. We will continue to add milliliter cubes until we have covered the entire bottom of the liter container. We can see that each row of milliliter cubes has a total of ten milliliters. There are a total of ten rows each row having ten milliliter cubes. So it takes one hundred milliliters to cover the bottom of the liter container. How many milliliters can be stacked in the corner to determine the height? We will start with one milliliter cube in a corner of our liter container and stack the milliliter cubes until we reach the top of the liter container. We will start with one milliliter cube in the bottom corner of our liter container and stack the cubes until they reach the top of the container. The height of the liter container is ten milliliters. Now that we know how many milliliters it takes to cover the bottom of the liter container and how many milliliters it takes to determine the height of the liter container, how many milliliters does it take to completely fill the liter container? It will take one thousand milliliters to completely fill the liter container. So how many milliliters equal one liter? One thousand milliliters equals one liter.
When we talk about volume we are talking about the amount of space a liquid occupies. It is measured in milliliters and liters. Let’s discuss some liquid volumes you see every day that would be measured in milliliters. Water in a teaspoon would be measured in milliliters and a bottle of hand lotion would be measured in milliliters. Let’s discuss some liquid volumes you see every day that would be measured in liters. A carton of milk would be measured in liters and gasoline for a car would be measured in liters. So let’s look at this glass of liquid. What would be the most appropriate unit for measuring the volume of the liquid in the glass? The milliliter would be most appropriate because it is used to measure smaller volumes. How about this water can? What would be the most appropriate unit for measuring the volume of the liquid in the water can? The liter would be most appropriate because it is used to measure larger volumes.
Next let’s look at this carton of juice. Do you know the exact volume of juice in the carton? No, because there are no marks to show the measurement. So let’s decide what would be the most accurate measurement for the juice in the carton. Is it about one liter; about one milliliter, exactly one milliliter, or exactly one liter? Since we do not know the exact volume, it is either about one liter or about one milliliter. For the carton of juice, about one liter would be the most accurate measurement.
Now let’s take a look at the water in this container. Do you know the exact volume of the water in the container? Yes, because there is a container with marks showing the amount and a key to tell us how much each mark represents. The key tells us that each mark equals one milliliter. So let’s decide what would be the most accurate measurement for the volume of the water in the container. Since we know the exact measurement it will be either exactly ten milliliters or exactly ten liters. Since each mark equals one milliliter our best answer is exactly ten milliliters.
This next container below is filled with water. It has a volume of one liter. Sara has to fill four containers with water for a science lab. If each container has a volume of one liter, what is the volume of the four containers? Four containers each having a volume of one liter gives us a total volume of four liters.
Karissa is working on a different science lab. The amount of water she needs is shown below. Let’s identify the volume of the container. The container is labeled three L. The L stands for liter. So the volume of this container is three liters.
What is the difference between the volume of water Sarah is using and the volume of water Karissa is using? Sarah is using four liters and Karissa is using three liters. So the difference is one liter.
We are now going to go back to the SOLVE problem from the beginning of the lesson. Dontae’s mom volunteered to help with the class party at the end of the year. There are twenty eight students in his class. Dontae’s mom is buying one liter bottles of fruit punch for the drink. If she plans on four servings per liter, how many liters of fruit punch does she need?
At the beginning of the lesson we Studied the Problem. We underlined the question, how many liters of fruit punch does she need? And put this question in our own words in the form of a statement. This problem is asking me to find the number of liters of fruit punch she needs.
In Step O, we will Organize the Facts. We will start by identifying the facts. Dontae’s mom volunteered to help with the class party at then end of the year, fact. There are twenty eight students in his class, fact. Dontae’s mom is buying one liter bottles of fruit punch for the drink, fact. If she plans on four servings per liter, fact, how many liters of fruit punch does she need? Now that we have identified the facts, we want to eliminate the unnecessary facts. These are the facts that will not help us find the number of liters of fruit punch she needs. Dontae’s mom volunteered to help with the class party at the end of the year. Knowing that Dontae’s mom is helping with the class party will not help us to find the number of liters of fruit punch, so we will eliminate this fact. There are twenty eight students in his class. We need to know the number of students so that we can figure out how many liters of fruit punch she needs. So we will keep this fact. Dontae’s mom is buying one liter bottles of fruit punch for the drink. Knowing that the bottles are in liters will help us to solve this problem. So we will keep this fact. If she plans on four servings per liter, knowing how many servings she can get out of each liter will also help us to find the number of liters she needs to buy. So we will keep this fact as well. Now that we have eliminated the unnecessary facts, we are going to list the necessary facts: Twenty eight students; four servings per liter.
In Step L, we Line Up a Plan. First we choose an operation or operations to help us to solve the problem. We know that we are looking for the number liters of fruit punch she needs and our facts are that there are twenty eight students and four servings per liter. We can use division to find the number of liters needed so that each student gets a serving. Now let’s write in words what your plan of action will be. We are going to divide the number of students by the servings per liter.
In Step V, we Verify Your Plan with Action. First we will estimate your answer, twenty eight students and four servings per liter. We know that this will be less than ten liters. We can now carry out your plan. We said in our plan that we wanted to divide the number of students which is twenty eight, by the servings per liter, which is four. Twenty eight divided by four equals seven. Dontae’s mom will need seven liters of fruit punch.