Whose Piece Is Larger?

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Objective

SWBAT use models to compare unit fractions.

Big Idea

Students are always concerned about whether they get their equal piece when things are divided. In this lesson, students will use fraction bars to visually see how to compare fractions

Gather the ingredients

20 minutes

Materials: blank fraction bars

Fraction Pad

Vocabulary: 

less than- a symbol used to comapre numbers with the lesser numbers shown first. E.g.,(1/2<3/4)

greater than- a symbol used to compare numbers with the larger number shown first.E.g.,(3/4>1/2)

 

Connection:

To get started, I begin this lesson by explaining the importance of being able to compare fractions. I ask students if any of their parents have ever divided something between them and their sibling, and they felt that their sibling's piece was larger than theirs? 1 student's response: "My mom had a snickers and she cut it into three pieces. She gave me and my cousin a piece and put the other piece up." I write the fraction 2/3 on the board and draw a fraction bar under it. Another student shares, "My mom had a Kit Kat bar and she gave me and my two cousins one." I write the fraction 3/4 on the board and draw a fraction bar under it. I explain that I wrote 3/4 to show that three pieces out of the four pieces of the Kit Kat bar was eaten. I probe students to see if they can figure out by looking at the fractions if they are equal. No, because there were three pices of the snickers bar and two people ate it. There were four pieces of Kit Kat and three pieces were eaten. Which fraction do you think is larger? 3/4. Why? Because there were more pieces of the Kit Kat bar.  I check to see if all students agree with that response before continuing the lesson.

I draw the fractions bars again on the board, except this time, I make sure that they are directly above each other. Beside each fraction bar, I write the fraction that I want each bar to represent. I ask if anyone explain why I put the fraction bars above each other? To show that the candy bars are the same size. I say, "You're on the right track, but the candy bars don't necessarily have to be the same size, but in order for me to determine which fraction is larger, I must place the bars above each other to make sure that when I compare the fractions, they are of equal length.

The purpose of the bars is to divide them into the total number of pieces that the snickers and Kit Kat was cut into. Would anyone like to come up and pretend that this bar is the snickers and show how it was divided. The student comes up and draws to lines to show that the candy was divided into three equal pieces.  I ask them if the snickers divided evenly? Yes. Can I get a volunteer to show how the Kit Kat was divided. A students comes up and adds three lines to show that Kit Kats are in fourths. Was this bar divided equally? Yes.

To further explain, I show students that the numerator tells me how many parts I need to shade. So if I have 2/3 for the snickers, how many parts of this bar should I shade? 2. I color the two bars to show and explain that 2 out of the 3 pieces of candy was eaten. How many should I shade on the bar for the Kit Kat? 3. Why? Because 3 out of the 4 pieces were eaten.  I color 3 of the 4 bars.  Now, let's look at the bars, can you all see which fraction bar has the largest amount colored. Yes, 3/4.

To ensure that students are grasping the concept, I write the fractions 5/8 and 1/3 on the board and have students tell me step-by-step what I should do compare the fractions. The responses were outstanding. They walked me step-by-step from drawing the bars, making sure they were the correct length, dividing them into equal parts by looking at the denominator, coloring the parts by using the numerator, and showing me that 5/8 was larger than 1/3. MP8- Look for and express regularity in repeated reasoning.

 

Mathematical Practices:

MP.7. Look for and make use of structure

MP. 8. Look for and express regularity in repeated reasoning.

Knead The Dough

10 minutes

Materials: blank fraction strips (1).doc  Comparing Circles.docx

 During this session of the lesson, students need more time creating their own fraction bars using several fractions to compare them. I want students to be able to apply this strategy when fractions are given, but no bars. Therefore, students must remember that the fractions bars must be the same length and that they are shaded correctly. Some students were confused when they were determining how many bars to color or how many parts to divide their bars into. To assist them in their learning, I have created some comparison circles for them to note the similarities and differences.  I want them to use the information the record to discuss it with other groups later on in this lesson.

To ensure that students are familiar with the terms, We discuss them again. I ask students if they can name the two parts of a fraction. Numerator and Denominator. What does the denominator show? The whole amount of equal parts.  What does the numerator show? Parts of the whole. I also ask the students to explain how a fraction is set up. Numerator over the denominator.  I think that you are ready to do some exploring of your own. Everyone is going to be divided into 6 equal groups, which means that four students will work together. In my bag, I have 24 fractions. Each student will pull one fraction from the bag. You will use your fractions along with your group members to compare the fractions. I would like for you to make 6 comparisons. I demonstrate how they can be done. If 4 students select 1/2, 2/3, 3/4, 5/6, they can compare (1/2_2/3), (1/2_3/4), (1/2_5/6), 2/3_3/4), (2/3_5/6), and 3/4_5/6). I make sure there are no questions and remind them that I will be moving around the classroom to check for understanding and clear up misconceptions.

 Monitoring Groups:

Can you tell me what this fraction bar represents. It represents 4/8. What other fraction are you comparing it to? 2/4. How did you know to color two bars on this fraction bar? I colored two because the four tells that there are four equal parts in the whole but only 2 out of the whole should be shaded. Based on what you shaded, how does 4/8 and 2/4 compare. They are the same size. Correct, but the correct terminology to use when comparing fractions is equal, so what sign are you going to place in between the two fractions? Equal.  

For struggling students, I give them pre-printed fraction bars and discuss with them what fraction those bars represent. After writing the fraction on each bar, I proceed to assist them in comparing them by looking at them and determining which has more or less shaded. I continue to circle the room to assist students. Student responses are being used to determine if they understand the skill. Students are asked to share with the class what fractions they compared and the class used thumbs up for agree or thumbs down for disagree. Amazingly, they do exceptionally well.

Setting the Temperature

25 minutes

Materials:  comparing fractions.docx

I notice that the students are mastering the skill really well as a group. Therefore, I decide to see if this skill can be mastered independently.  I give students a worksheet so that they can create their own fraction bars to compare fractions. Can someone explain how not drawing the bars the same length can make your comparisons incorrect. They have to be the same size because we have to draw the number of parts in the bars. If we don't draw them the same size, they can't be used to compare each other.  I have an example at the top of your page for you to use as a reminder on how to compare fractions. Is everyone clear on the instructions. Yes. I continue to monitor students as they complete this worksheet. I will continue to support those who are getting numerators and denominators mixed up. All students perform the task extremely well.

I make sure to take note of students responses. I use their responses to check for understanding, and to determine if additional time should be spent reviewing this skill.