Level D Lesson 24
Measurement with Word Problems
In lesson 24 the objective is, the student will use addition, subtraction, multiplication and division to solve word problems involving measurement equivalence.
The skills student should have in order to help them in this lesson include basic multiplication and division facts zero through nine, SOLVE, multiplication and division equations, measurement equivalence found in lesson 23, conversions with: inches and feet, milliliters and liters, grams and kilograms, ounces and pounds as well as computation with time.
We will have three essential questions that will be guiding our lesson. Number 1, how can I solve for an unknown quotient or difference in a measurement problem? Number 2, how can I solve for an unknown product or sum in a measurement problem? And number 3, how can SOLVE help me solve a word problem?
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.
We will be completing two SOLVE problems together in this lesson. Each pair of students will need a set of 48 centimeter cubes in order to participate in this first SOLVE problem.
Addi’s dad is putting a border around their flower bed. He is using a board that is four feet long. What is the length of the board in inches?
We will begin by Studying the Problem. First we will identify where the question is located within the problem and underline the question. What is the length of the board in inches? Now that we have identified the questions we want to put it in our own words in the form of a statement. This problem is asking me to find the board’s length in inches.
In Step O, we will Organize the Facts. We will begin by identifying the facts. Addi’s dad is putting a border around their flower bed, fact. He is using a board that is four feet long, fact. What is the length of the board in inches? Now that we have identified the facts we want to eliminate the unnecessary facts. These are the facts that will not help us to find how long the board is in inches. Addi’s dad is putting a border around their flower bed. Knowing where the border is going to be placed will not help us to find the length of the board in inches, so we will eliminate this fact. He is using a board that is four feet long. Knowing the length of the board in feet is important to helping us find the length of the board in inches. So we will keep this fact. Now that we have eliminated the unnecessary facts we are ready to list the necessary facts. Four foot board, need the length in inches.
In Step L, we will Line Up a Plan. We will choose an operation or operations to help us to solve the problem and write in words what your plan of action will be. We want to start by solving this problem at the concrete level using our centimeter cubes to help us. Let’s talk about the problem so far. What are we trying to find, or what is the unknown value? The number of inches in the board. Do we know how many inches are in a foot? Yes, we know there are twelve inches in a foot. Explain how we can create a model using the cubes. We can build an array putting twelve cubes, representing the number of inches in a foot, in each of four rows.
Let’s do that in Step V, Verify Your Plan with Action. First we estimate our answer. We can estimate between forty five and forty eight inches. Now let’s carry out your plan. We said that we would use the centimeter cubes. We want to place twelve centimeter cubes in each of four groups. One group of twelve centimeter cubes, two groups of twelve centimeter cubes, three groups of twelve centimeter cubes, four groups of twelve centimeter cubes. There are a total of forty eight cubes. Do you know the number of groups in the concrete model? Remember when we create a concrete model the number of rows represents the number of groups. There are four rows, so yes, we know the number of groups. There are four groups. Do you know the number of items in each group? Remember that in a concrete model the number of items in each row represents the number of items in each group. Yes, we know the number of items in each group. There are twelve items in each group. So how can you set up a plan using the centimeter cubes to represent the total number of inches in four feet? Remember that when we set up our plan do we not want to use any numbers. Place centimeter cubes on the workspace. Create an array to show the number of inches or items in each foot or group.
Now let’s take what we did in our concrete model using the centimeter cubes and use that information to create a picture to solve the problem. Let’s write in words what your plan of action will be using a picture. We can draw an array of squares to show the number of inches or items in each foot or group.
Let’s go to Step V, and carry out our plan. Draw twelve squares in each of four rows. This represents twelve inches in each of four feet or twelve items in each of four groups. Our picture represents a total of forty eight inches.
Let’s return to Step L, and talk about how we can use a table to help us to solve this problem. We can create a table to show the relationship of feet to inches. Do we know the number of inches in one foot? Yes, there are twelve inches in one foot. We will record a one under feet and twelve under inches in our Table. Do we know the number of inches in two feet? Yes, there are twenty four inches in two feet. If there are twelve inches in one foot, we double the twelve, or multiply two by twelve, as twelve is the number of inches in one foot. We will record a two under feet and twenty four under inches in our Table. Now let’s complete the rest of the Table. Three feet is equivalent to thirty six inches. Three times twelve equals thirty six. Four feet is equivalent to forty eight inches. Four times twelve equals forty eight.
We are going to return to Step L one more time. This time we are going to create a plan using an equation. We can write an equation showing the number of feet multiplied by the number of inches in each foot equals t, the total number of inches in the length of the board.
Let’s carry out our plan. We said that we would create an equation showing the number of feet which is four multiplied by the number of inches in each foot which is twelve equals t. Four times twelve equals t. Remember that t stands for our unknown value, which is the total number of inches in the length of the board. Four times twelve equals forty eight. So t equals forty eight inches. The answer of forty eight matches the answer we found in the picture and the table.
We are now ready to Examine Your Results. Does your answer make sense? Here compare your answer to the question. Yes, because we were looking for the number of inches in four feet. Is your answer reasonable? Here you want to compare your answer to the estimate. Yes, because it is close to our estimate of between forty five and forty eight inches. And is your answer accurate? Here you want to check your work. Yes, our answer is accurate. We are now ready to write your answer in a complete sentence. The board is forty eight inches long.
We are going to complete one more SOLVE problem together. Dano is saving money for the summer. He has saved forty eight dollars from the money he earns doing odd jobs for his grandparents. If he plans to spend the same amount for three different activities, how much will he spend for each activity?
We will begin by Studying the Problem. First we want to identify where the question is located within the problem and we will underline the question. How much will he spend for each activity? 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 amount he will spend for each activity.
In Step O, we will Organize the Facts. We will begin by identifying the facts. Dano is saving money for the summer, fact. He has saved forty eight dollars, fact, from the money he earns doing odd jobs for his grandparents, fact. If he plans to spend the same amount for three different activities, fact, how much will he spend for each activity? 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 amount he will spend for each activity. Dano is saving money for the summer. Knowing that he is saving money for the summer does not help us to find how much he will spend for each activity. So we will eliminate this fact. He has saved forty eight dollars. Knowing the amount of money that Dano has saved will help us to find the amount that he spends on each activity. So we will keep this fact. From the money he earns doing odd jobs for his grandparents. Knowing how Dano earned the money is not going to help us to find how much he spent on each activity. So we will eliminate this fact. If he plans to spend the same amount for three different activities. There are a couple of facts here that we need to know. We need to know that he spends the same amount and also that there are three different activities. Both of these will help us to find how much he will spend for each activity. So we will keep this fact as well. Now that we have eliminated the unnecessary facts we can list the necessary facts. Has forty eight dollars, three activities, spends the same for each activity.
In Step L, we will Line Up a Plan. First we will choose an operation or operations to help us to solve the problem. What is the unknown value? The unknown value is the amount he can spend per activity. We known the amount of money that Dano has and we know that he wants to spend the money equally on three activities. So we can use division to help us to find the amount of money that he will spend on each activity. We can now write in words what your plan of action will be. Let’s use an equation to solve the problem. We can write an equation to show how to divide the total amount of money by the number of activities.
In Step V, we Verify Your Plan with Action. We will begin by estimating your answer. We can say that Dano’s going to spend about fifteen dollars on each activity. Now let’s carry out your plan. We said we wanted to write an equation to show how to divide the total amount of money which is forty eight dollars by the number of activities which is three. We can set up the equation as forty eight divided by three equals q. Q is our unknown value, which is the amount of money he can spend per activity. Forty eight divided by three equals sixteen. Q equals sixteen dollars.
In Step E, we’ll Examine Your Results. Does your answer make sense? Here compare your answer to the question. Yes, because we were looking for the amount he could spend on each activity. Is your answer reasonable? Here compare your answer to the estimate. Yes, because it is close to our estimate of about fifteen dollars. And is your answer accurate? Here you want to check your work. Yes. The answer is accurate. We are now ready to write your answer in a complete sentence. Dano can spend sixteen dollars on each activity.
Now let’s go back and discuss the essential questions from this lesson.
Our first question was, how can I solve for an unknown quotient or difference in a measurement problem? Draw a picture, make a table, or set up an equation to solve.
Our second question was, how can I solve for an unknown product or sum in a measurement problem? Draw a picture, make a table, or set up an equation to solve.
And our third question was, how can SOLVE help me solve a word problem? SOLVE gives me an organized way to set up a problem and solve it in steps.