Level C Lesson 17
Fractions on a Number Line
In lesson 17 the objective is, the student will plot fractions on a number line.
The skills students should have in order to help them in this lesson include, plotting whole numbers on a number line and basic understanding of fractions.
We will have three essential questions that will be guiding our lesson. Number 1, what is a fraction? Number 2, what are the parts of a fraction called, and what do they represent? And number 3, how can you create and plot a fraction on a number line?
The SOLVE problem for this lesson is, Jeff is plotting the progress of the participants in a 1-mile fun run on a number line. Alexis is one-third of a mile from the starting line. Her friend, Julie, is one-half of a mile from the starting line. How will Jeff represent Alexis’ location on a number line?
We will begin by Studying the Problem. First we need to identify where the question is located within the problem and we will underline the question. How will Jeff represent Alexis’ location on a number line? Now that we’ve 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 location of Alexis’ position on a number line.
During this lesson we will learn how to draw number lines and plot fractions on number lines. 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.
Today we are going to learn how place fractions such as one-half, one-fourth, one-sixth, and one-eighth on a number line. Let’s start by using our one whole fraction strip. How many one-half strips are equivalent to one whole unit? Two one-half strips make up
one whole unit. Let’s use this information with our graphic organizer to plot the fraction one-half on a number line. With our fraction strips we found that one unit can be legally traded for two one-half units. We will draw this underneath the fraction strips column in our graphic organizer. One unit has already been drawn for us, so we will shade this in, in blue. Underneath our one whole unit we want to represent two one-half units. And we will shade in our one-half units in brown. Be sure to label each one-half unit. We can see that there are two one-half units in one whole unit. We will use this information to help us to draw our number line. Let’s draw the number line underneath the drawings of our fraction strips. The beginning mark on our number line is going to be at zero. We will place this at the beginning of our drawing of one unit. Our end mark on our number line is going to be at the point one. We will place this mark at the end of our drawing of one unit. The space between zero and one on our number line is the same as the length of the one unit fraction strip that we have drawn. We know that there are two halves in the whole unit. So we need to divide our number line into halves. Where this division takes place is going to be labeled as one-half unit. Notice that where we have placed this mark is at the same place where we have drawn a line between our one-half units in our fraction strip drawing. We can plot one-half on the number line by placing a dot at the one-half.
Let’s talk about the fraction one-half and how it can be used to create the number line. Which value tells us how the line is divided? The two, which is the denominator. Which value tells us which interval we are identifying? The one, which is our numerator. We identified the first interval of our number line by placing a point at one-half. How could the one whole unit be written as a fraction? It can be written as two-halves, because it is the second interval of the group which also equals one whole. As it is the second interval of the group, our numerator is two.
Let’s take a look at another example together. Again we want to find a legal trade for one whole unit, this time using our one-fourth unit fraction strip. Four one-fourth strips make up one whole unit. Let’s use this information with our graphic organizer to plot the number one-fourth on a number line. Again, our fraction strip has already been drawn for us to represent one unit. We will shade this fraction strip in blue. Underneath our one whole unit we want to represent the legal trade that we completed using our fraction strips. We found that four fourths was equivalent to one whole. We want to draw these four fourths below our one whole unit and shade them in yellow. Be sure to label each fraction piece as one-fourth. There are four one-fourth units that equal one whole unit. Let’s create our number line underneath our fraction strips. Our beginning mark will again be at zero, and we will place this mark at the beginning of our one whole unit fraction strip drawing. And our end mark will again be at one. We will place this mark at the end of our one whole unit fraction strip. We said that there are four fourths in the whole unit. Let’s see how we can use the fraction to help us with the rest of our number line. Which value tells us how the line is divided? The denominator, which is four. Which value tells us which interval we are identifying? The numerator, which is one. Let’s take this information and continue to plot the point one-fourth on our number line. We said that the denominator helps us to see how many sections the line is divided into. The denominator is four. We want to have four equal sections. We will place a mark at the end of where each one-fourth piece has been drawn. This will help us make sure that these sections are equal. Our numerator helps us to see which of these sections represents the fraction. Our numerator is one, so we will place a point after the first interval on our number line. This represents the point one-fourth. We have now plotted the point which represents the fraction one-fourth on the number line. How could the one whole unit be written as a fraction? It could be written as four fourths, because it is the fourth interval of the group which also equals one whole.
In this next example we are going to plot the fraction one-half on a number line. We are not going to start by modeling with our fraction strips but if you need to refer back to your fraction strip please do so. Let’s begin by plotting the beginning and ending marks on our number line. One-half is between zero and one. How many parts will the section between zero and one be divided into? The denominator helps us to see how many parts to divide the number line into. So we will have two parts, because the denominator is two. We need to place a mark half way between zero and one on our number line to represent one-half. We will place a point at this mark to represent one-half.
For the fraction one-fourth we again want to place this fraction on our number line. One-fourth is between zero and one. So these will be our beginning and ending marks on this number line. How many parts will the section between zero and one be divided into? The denominator helps us to answer this question. We will have four parts, because the denominator is four. We want to place marks between zero and one, so that we have four parts. One-fourth is going to be represented by the first interval between zero and one. So we will plot the point one-fourth, and we will label this point. We can label all of the fourths between zero and one. After one-fourth, the next mark represents two-fourths, the third mark after zero represents three-fourths, and the fourth mark after zero represents one whole, which we could also write as four-fourths.
Let’s take a look at one more fraction together five-sixths. Five-sixths is between zero and one so we will put our beginning mark and end mark on our number line as zero and one. How many parts will the section between zero and one be divided into? We need to look at our denominator. We will have six parts, because the denominator is six. We want to create these parts by adding marks between zero and one, so that we have six parts. We need to add five marks in order to create these six parts. Let’s label each interval of our number line. The first mark after zero represents one-sixth. The second mark after zero represents two-sixths, and so on to three-sixths, four-sixths, and five-sixths. We can plot the point five-sixths by placing a dot where five-sixths is located on the number line.
Let’s take a look at the fraction two-fourths, and plot two-fourths on the number line. Again, this is going to be between zero and one, so we will put our beginning mark at zero and our end mark at one. How many parts will the section between zero and one be divided into? Remember to look at the denominator to help you answer this question. We will have four parts, because the denominator is four. We need to add three marks to our number line between zero and one to create these four parts. We will label each of these marks with the appropriate fraction, one-fourth, two-fourths, and three-fourths. Because we are asked to plot the point two-fourths on the number line, we will place a dot above two-fourths.
Now that we have learned how to plot fractions on a number line we are going to go back to the SOLVE problem from the beginning of the lesson. Jeff is plotting the progress of the participants in a 1-mile fun run on a number line. Alexis is one-third of a mile from the starting line. Her friend, Julie, is one-half of a mile from the starting line. How will Jeff represent Alexis’ location on a number line?
At the beginning of the lesson we Studied the Problem. We underlined the question, how will Jeff represent Alexis’ location on a number line? And we put this question in our own words in the form of a statement. This problem is asking me to find the location of Alexis’ position on a number line.
In Step O, we will Organize the Facts. First we will identify the facts. Jeff is plotting the progress of the participants in a 1-mile fun run on a number line, fact. Alexis is one-third of a mile from the starting line, fact. Her friend, Julie, is one-half of a mile from the starting line, fact. How will Jeff represent Alexis’ location on a number line? Now that we have identified the facts, we want to eliminate the unnecessary facts or those that will not help us represent Alexis’ location on a number line. Jeff is plotting the progress of the participants in a 1-mile fun run on a number line. Knowing that he’s plotting their progress is not going to help us to know where this point is going to be located on the number line, so we will eliminate this fact. Alexis is one-third of a mile from the starting line. This is going to be necessary to plotting her point on the number line, so we will keep this fact. Her friend, Julie, is one-half of a mile from the starting line. We’re only interested in plotting Alexis’ location at this point, so we do not need to know information about Julie, we will eliminate this fact. Now that we have eliminated the unnecessary facts, we will list the necessary facts. Alexis is one-third of a mile from the starting point.
In Step L, we Line Up a Plan. First we choose an operation or operations. Since we are plotting points on a number line we will not have an operation or operations, which we can include at this time. Now let’s write in words what your plan of action will be. We will draw a number line. Divide it into the number of parts indicated by the denominator of the fraction. And then plot the point.
In Step V, we Verify Your Plan with Action. First we estimate your answer. Our answer is going to be a drawing, so we are not able at this time, to estimate the answer. Now let’s carry out your plan. We said to draw a number line and we are going to divide it into the number of parts indicated by the denominator of the fraction. Alexis is one-third of a mile from the starting point, so we need to divide our number line into three sections. We will label these sections, one-third, and two-thirds. We can plot the point by placing a dot at one-third.
In Step E, we’ll Examine Your Results. Does your answer make sense? Here compare your answer to the question. Yes, because I am looking for the location of Alexis’ position on a number line. Is your answer reasonable? Here we compare your answer to the estimate. In this example we did not have a estimate. So this is not going to be applicable when we examine your results for this problem. Is your answer accurate? Here you can check your work. It may be helpful to use your fraction strips when you check your work for this problem. Yes, the answer is accurate. Finally we write your answer in a complete sentence. Alexis’ location on the number line is one-third or the first of three parts from zero to one.
Now let’s go back and discuss the essential questions from this lesson.
Our first question was, what is a fraction? A fraction is a way to represent part of a whole unit.
Our second question was, what are the parts of a fraction called, and what do they represent? The parts are the numerator and denominator; the denominator represents how many equal parts, and the numerator tells how many parts away from zero the fraction is located on the number line.
And our third question was, how can you create and plot a fraction on a number line? Use the denominator to tell you how many equal parts to have and use the numerator to tell you how many parts from zero to plot the fraction.