Level E Lesson 13 Write Expressions

In lesson thirteen the objective is, the student will write simple expressions with numbers and interpret numerical expressions.

The skills students should have in order to help them in this lesson include knowledge of word wall words from the “L” Step of SOLVE and knowledge of number sentences.

We will have three essential questions that will be guiding our lesson. Number 1, what is a verbal expression? Number 2, what are three phrases that could mean subtraction? And number 3, what are three phrases that could mean multiplication?

The SOLVE problem for this lesson is, Mario and Alicia are shopping for favors for a party. They are celebrating their birthdays together. Mario and Alicia plan to purchase packs of chewing gum and pencils. Each pack of pencils costs fifty cents, and each pack of gum costs twenty-nine cents. If there are a total of nine people at the party, write a verbal and a numerical expression for the total cost of the favors.

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. In this problem what we are looking for has not been worded as a question. Instead it is written as a statement. So we will underline this statement, write a verbal and a numerical expression for the total cost of the favors. Now we will put this statement in our own words. This problem is asking me to find the way to write verbal and a numerical expression for the total cost of the favors.

During this lesson we will learn how to identify and write verbal and numerical expressions. 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.

To begin this lesson we are going to use a set of six clues to fill in the six boxes each with one digit that will give us a six digit number. Each mathematical clue that we are going to be given is written in words. This is called a Verbal Expression. For box A the clue is four more than three. Notice that the clue is written in words only. Again we call this a verbal expression. What is four more than three? Four more than three is seven. So we will place a seven in box A. For box B our clue is, sixteen decreased by seven. Sixteen decreased by seven is nine. So we will place a nine in box B. Our third clue is, twelve divided by two. The answer to this verbal expression will be placed in box C. Twelve divided by two is six. For box D the clue is, double four. When we double four we get eight, we will place the number eight in box D. For box E the verbal expression that is our clue is nine less than twelve. Nine less than twelve is three. We will place a three in box E. And the verbal expression for box F is one added to three. One added to three is four. The six digit number that we were looking for is seven hundred ninety six thousand eight hundred thirty four.

Now let’s talk about the vocabulary that we use when writing verbal expressions. There are four symbols that are included for the various operation words. The first symbol represents addition. The second symbol represents subtraction. Our third symbol represents multiplication. And our fourth symbol represents division. There are several operation words that can be used to represent each of these four operations. What operation is indicated for the word “sum”? The word sum means addition. We will place this word inside of the addition symbol. What operation is indicated for the word “quotient”? The word quotient means division. We will place the word quotient inside of the division symbol. What operation is indicated for the word “difference”? The word difference means subtraction. We will place the word difference inside of the subtraction symbol. And what operation is indicated for the word “product”? The word product means multiplication. We will place the word product inside of the multiplication symbol.

Now that we have talked about some of the vocabulary that is used in verbal expressions, let’s work with a few verbal expressions together. Each pair of students will need a set of two colored counters to participate in this activity. Our first verbal expression is two more than four. How many counters should we start with on the desk to represent this verbal expression? We want to start with four counters. Place four counters in the space in front of you. Identify the second value in the expression. In the expression two more than four, the second value is two. We will place two counters in the space in front of us in a separate location from the four original counters. What operation is used with the words “more than”? More than means addition, so we will add our four counters together with our two counters. Let’s place this information into our graphic organizer. For the verbal expression two more than four the operation is addition. The model that we created with our counters is to start with four counters and add two more counters to the original four.

Let’s take a look at another verbal expression together, four groups of six. What operation is used with the words “groups of”? Groups of, indicates that we will use multiplication. How many items are in each group? There are six items in each group. Let’s start by representing one group of six using our two colored counters. How many groups? We need four groups. Let’s create the other groups so that we have a total of four groups with six items in each group. There are four groups of six. Let’s include this information on our graphic organizer. For the verbal expression four groups of six the operation is multiplication. The model that we created with our two colored counters is to make four groups with each group having six counters. We can circle our groups to show that there are four groups. We have represented several verbal expressions.

Now we want to take verbal expressions and turn them into Numerical Expressions. Let’s look at the verbal expression add twelve and ten then multiply by two. What operations will we use? We will use addition and multiplication. What two values will we add? We need to add twelve and ten. What value will we multiply by? We will multiply by two. Which operation do we perform first? Add twelve and ten then multiply by two. We will do addition first, because of the wording “add and then multiply”. We want to add first. We said that we would add (twelve plus ten). We put this inside of parenthesis to show that we are going to do this first. Then we want to multiply by two. We will show that we are multiplying the sum of twelve plus ten by two. So the numerical expression is two times the quantity twelve plus ten. We have many different ways to show multiplication. Take a look at the different ways below. We can represent multiplication using the dot. We can also represent multiplication using an x or we can represent multiplication without a symbol by placing the number that we are multiplying by directly next to the parenthesis.

Let’s take a look at one more verbal expression together. This time we want to subtract seven from sixteen and then divide by three. What operations will we use? We want to use subtraction and division. What two values will we subtract? Sixteen and seven. What value will we divide by? We will divide by three. Which operation do we perform first? Let’s read the verbal expression again. Subtract seven from sixteen and then divide by three. Subtraction will be performed first, because of the wording “Subtract and then divide by”. So we will subtract first. We want to subtract seven from sixteen. So we will represent this as (sixteen minus seven). We put this inside of parenthesis to show that we are going to do this step first. And then divide by three. We will take the difference of sixteen and seven and divide this by three. The numerical expression is, the quantity sixteen minus seven divided by three.

Now we will create a foldable to help us to organize the information we have learned in this lesson for future reference. Each student will need to start with a sheet of colored paper. You want to hold this sheet of paper horizontally in front of you. We are going to fold down the top of the paper to almost the bottom of the page, leaving about a half an inch at the bottom, and crease the fold at the top. Now we want to fold this paper into thirds. Start by folding the left side of the paper about a third of the way over, and crease the fold. Open this fold back up and do the same thing from the right side of the paper, folding about a third of the way over, and crease this fold. Now open up the paper to see that you have created three sections. You will lift the top flap and cut to the fold on the two creases to create three flaps. Fold the three flaps down and fold the half of an inch of paper which was left at the bottom up over the flaps. You’re going to label the first flap on the left with the words Write Expressions. On the inside of this flap you will complete this section with your teacher including information about “Write Expressions” underneath this flap.

Now we are going to go back to the SOLVE problem from the beginning of the lesson. Mario and Alicia are shopping for favors for a party. They are celebrating their birthdays together. Mario and Alicia plan to purchase packs of chewing gum and pencils. Each pack of pencils costs fifty cents, and each pack of gum costs twenty-nine cents. If there are a total of nine people at the party, write a verbal and a numerical expression for the total cost of favors. In Step S, we Studied the Problem. First we underline the question. In this particular problem the question is more of a statement, so we underlined the statement. Write a verbal and a numerical expression for the total cost of the favors. Then we put this statement in our own words. This problem is asking me to find the way to write a verbal and a numerical expression for the total cost of the favors.

Now we will organize the facts. We need to start by identifying the facts. Mario and Alicia are shopping for favors for a party, fact. They are celebrating their birthdays together, fact. Mario and Alicia plan to purchase packs of chewing gum and pencils, fact. Each pack of pencils costs fifty cents, fact, and each pack of gum costs twenty-nine cents, fact. If there are a total of nine people at the party, fact, write a verbal and a numerical expression for the total cost of the favors. Now that we have identified the facts we want to eliminate the unnecessary facts, or those facts that will not help us to write the verbal and numerical expression for the total cost of the favors. Mario and Alicia are shopping for favors for a party. Knowing why they are shopping is not going to help us to write the verbal and numerical expression for the cost of the favors, so we will eliminate this fact. They are celebrating their birthdays together. Knowing that they are celebrating their birthdays together also will not help us to write the verbal and numerical expressions, so we will eliminate this fact as well. Mario and Alicia plan to purchase packs of chewing gum and pencils. Knowing what they are purchasing does not help us to write the verbal and numerical expression for the cost, so we will eliminate this fact as well. Each pack of pencils costs fifty cents. Knowing the cost of the pencils will help us to find the total cost so we will keep this fact. And each pack of gum costs twenty-nine cents. This is also important to finding the total cost, so we will keep this fact. If there are a total of nine people at the party, knowing how many people are at the party will be important as well for knowing the total cost of the favors, so we will keep this fact as well. Now that we have eliminated the unnecessary facts we will list the necessary facts. Nine guests, pencils costs fifty cents, gum costs twenty-nine cents.

In Step L, we will Line Up a Plan. First we will choose an operation or operations to help us to solve the problem. We know the number of guests and the cost of the pencils and the gum. We will need to use addition and multiplication in our verbal and numerical expression. Now let’s write in words what your plan of action will be. We will write the expression in words and then substitute in the numbers and symbols to write it as a numerical expression.

In Step V, we Verify Your Plan with Action. First we estimate your answer. In this example we are not finding a total cost we are just writing the verbal and numerical expressions. So writing an estimate of our answer is not applicable to this problem. Now let’s carry out your plan. We said first that we wanted to write the expression in words. Our verbal expression is, to add the cost of the pencils and gum, then multiply by the number of guests. Once we have written the expression in words, then we said that we wanted to substitute in the numbers and symbols to write it as a numerical expression. Our numerical expression is the cost of the pencils plus the cost of the gum, so we have fifty cents plus twenty-nine cents. Since we are doing this step first we put this in parenthesis. And then multiply by the number of guests. Since we have nine guests, we multiply by nine. Our numerical expression is the quantity fifty cents plus twenty-nine cents times nine.

Now we can Examine Your Results. Does your answer make sense? Here you want to compare your answer to the question. Yes, because we are looking for the verbal and numerical expressions. Is your answer reasonable? Here you want to compare your answer to the estimate. This is not applicable as we did not come up with an estimate in the V Step. Is your answer accurate? Here you want to check your work. Yes. Our answer is accurate. Finally we write your answer in a complete sentence. The verbal expression for the information is “add the cost of the pencils and gum, then multiply by the number of guests”. The numerical expression is, the quantity fifty cents plus twenty- nine cents times nine.

Now let’s go back and discuss the essential questions from this lesson.

Our first question was what is a verbal expression? It is an expression that uses only words, with no symbols.

Our second question was what are three phrases that could mean subtraction? Decreased by; take away; and minus are examples of phrases that could mean subtraction. You may come up with others.

And our third question was, what are three phrases that could mean multiplication? The words times; multiplied by; and double; are examples of phrases that could mean multiplication. You may come up with others.