Math Lesson – 4th grade- Comparing and Ordering Fractions

Standard

MATH LESSON PLAN

JMU Dept of Early, Elementary, & Reading Education

 

Katelyn Bell

Clymore Elementary School

Mrs. Nienke Stilwell- Fourth Grade

Reviewed by Mrs. Stilwell on February 12, 2013

To be completed at 8:30 AM on February 19, 2013

TITLE/TYPE OF LESSON

  • Order Em Up
  • Comparing and Ordering Fractions

 

CONTEXT OF LESSON

  • The students have covered the basic concept of fractions in grades previous and had one day dedicated to reviewing previously taught material before introducing new concepts. Prior to teaching this lesson, the students practiced reducing fractions and creating equivalent fractions. This is an appropriate time to introduce this lesson because the students have worked with number lines and grids, but they typically do not incorporate both in one lesson, nor have they placed fractions on a number line. This concept will help students to understand how fractions relate to one another so that students are able to add and subtract fractions at a later date. Practicing the placement of fractions on a number line provides students with a simple way to estimate if their answers are correct or incorrect after they add, subtract, multiply, or divide.  Additionally, placing fractions on the number line after ordering them will help students be more familiar and comfortable with doing the same action with decimals in upcoming lessons.

 

LESSON CONCEPTS

  • This lesson will show students to use grids to compare fractions to one another and determine which one is bigger or smaller than the other.
  • This lesson will give the student an opportunity to find equivalent fractions and reduce fractions that are not in their simplest form.
  • This lesson will give the student an opportunity to order fractions according to their relation to the numbers zero and one and their relations to each other on a number line.

 

LESSON OBJECTIVES

  1. The student will compare fractions.
  2. The student will represent equivalent fractions.
  3. The student will order fractions.

 

ASSESSMENT OF LEARNING

  1. To assess objective one, I will ask each student to answer the questions on their notes that I also post on the doc camera. These questions will be comparing two fractions to see which fraction is larger, in other words closer to one on the number line. The student will indicate the answer by circling which fraction is larger. This activity will help the students to order the fractions later on in the lesson and I will know if the student met my objective if the correct fractions are circled. I will collect the notes and document the information during recess that day and give the notes back to them at the end of the day.
  2. To assess objective two, I will ask students to show their work in transforming fractions into simplified or expanded form. I will ask that also the students place the fractions that are equivalent on top of one another on the timeline. For example, I may give one group the fraction 1/2 and the fraction 5/10. If the group has two or more grids stacked on top of one another on the number line, they will have met my objective. This will show me that they understand the concept of equivalent fractions. I will document the information on my documentation chart after collecting the number lines at the end of the lesson.
    1. A. To assess objective three, I will watch the groups order the fractions (represented on grids) on the number line and I will record on the attached observation form which students correctly order the fractions. I will review the posters as my artifact for objective three and I will take a picture of each of them so that the students are able to post their work in the classroom.
    2. I will assess objective three near the end of the lesson as well when individual students order one fraction on the class timeline. I will assess this by documenting the accuracy of the placement of the fraction on the same documentation chart. If the student orders the fraction correctly, they will have met my objective, and if they fail to place the fraction in the correct place, they will have failed my objective.

 

LESSON CONCEPTS LESSON OBJECTIVES PLAN FOR ASSESSMENT
What do you want the students to learn as a result of this activity? How will the students demonstrate understanding of the concept? How will you assess student learning of the concept?
Concept 1:

This lesson will show students to use grids to compare fractions to one another and determine which one is bigger or smaller than the other.

 

 

 

 

 

 

 

 

 

 

 

 

 

Concept 2:

This lesson will give the student an opportunity to find equivalent fractions and reduce fractions that are not in their simplest form.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Concept 3:

This lesson will give the student an opportunity to order fractions according to their relation to the numbers zero and one and their relations to each other on a number line.

The student will:

1.The student will compare fractions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.The student will represent equivalent fractions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.The student will order fractions

 

1. To assess objective one, I will ask each student to answer the questions that I post on the doc camera. These questions will be comparing two fractions to see which fraction is larger, in other words closer to one on the number line. The student will indicate the answer by circling which fraction is larger. This activity will help the students to order the fractions later on in the lesson and I will know if the student met my objective if the correct fractions are circled.

 

2. To assess objective two, I will ask students to show their work in transforming fractions into simplified or expanded form. I will ask that the students place the fractions that are equivalent on top of one another on the timeline. For example, I may give one group the fraction1/2 and the fraction 5/10. If the group has their work shown of how they converted the fraction and they have two or more grids stacked on top of one another on the number line, they will have met my objective. I will document the information on my documentation chart after collecting the number lines at the end of the lesson.

 

3. a. To assess objective three, I will watch the groups order the fractions (represented on grids) on the timeline and I will record on the attached observation form which students correctly order the fractions. I will review the posters as my artifact for objective three and I will take a picture of each of them so that the students are able to post their work in the classroom.

b.I will assess objective three near the end of the lesson as well when individual students order one fraction on the class timeline. I will assess this by documenting the accuracy of the placement of the fraction on the same documentation chart. If the student orders the fraction correctly, they will have met my objective, and if they fail to place the fraction in the correct place, they will have failed my objective.

 

 

RELATED VIRGINIA STANDARDS OF LEARNING

4.2          The student will

a)   compare and order fractions and mixed numbers;

b)   represent equivalent fractions

 

MATERIALS NEEDED

  • 3 large poster boards cut in half vertically with timeline on each (provided by me)
  • Markers (provided by students)
  • Pencils (provided by students)
  • 1 sheet of 100 grids per group in baggie pre-cut (provided by me)
  • 1 sheet of 100, 10, and 1 grid (provided by me)
  • 1 sheet of notes per student (provided by me)
  • 1 glue stick per student (provided by student)

 

PROCEDURE

 

BEFORE Anticipated student responses
The students began their fraction unit by reviewing what they learned about fractions from years prior to 4th grade. In the days leading up to this lesson, the students worked on finding equivalent fractions and simplifying fractions to their simplest form. They are familiar with this process and have represented mathematics problems on grids before, but they have never shown a fraction on a grid. My goal is to bridge the disconnect between a fraction and how it looks represented on a base 10 or base 100 grid and how that is shown on a number line.

 

Draw a large number line across the entire length of the white board with three marks representing zero, 1/2, and 1 for later on in the lesson.

 

Have worksheet, sheet with fractions, supplies, and tens and hundred’s grids already cut out and ready.

 

Hand out the notes worksheet to each student.

 

Introduce the lesson.

 

 

 

 

Display a copy of the notes worksheet on the doc camera.

 

 

Ask students to answer number one on the notes worksheet.

 

 

“Could you figure out this problem without coloring in the boxes?”

 

 

The teacher will show this example using the base ten grid.

 

 

Ask student to repeat answer.

 

 

 

 

 

 

 

 

“Now try ordering the next three fractions from least to greatest.4 9,   7

5     5    5

Choose a volunteer to write their answer on the board.

 

 

 

 

Try the third problem on the notes.

4  or  4            6  or   6              3  or  3

5       8           10       8              5        6

 

 

 

 

 

 

 

In the last problem, place the fractions in the correct order on the number line.

 

3         2         5        9       2

4         4        10      10      8

 

 

 

 

 

 

 

Model the Activity: Place the sheet of paper on the doc camera and show the example of shading 2/10 to 20/100 on the tens and hundreds grid.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Teacher: Today, we will be learning how to compare and order fractions. Today we will be using grids and number lines to compare and order fractions.

 

 

Teacher: We will begin by answering a few questions about comparing and ordering fractions on our worksheet.

 

Teacher: Which is larger? 2/4 or 3/4?

Student:  Colors in boxes.

Student 2: 3/4!

 

Student: Yes. Just look at the numerator.

Teacher: It is easy to compare fractions that have the same denominator. Now, compare the numerators. Whichever numerator is bigger is which fraction is larger.

 

 

 

Student: 3/4

Teacher: How do you know that 3/4 is larger than 2/4?

Student: Because the 3 is bigger!

Teacher: That is correct. 3/4 is larger because both fractions have the same denominator and the 3 is larger than the 2.

 

 

Teacher: I would like one volunteer to write their answer on the board.

Student: Raises hand.

Teacher: Chooses student and explains the correctness or incorrectness of the student’s answer. These were not very difficult to order because they had the same denominators.

 

Teacher: Asks student to raise their hand to provide answer for number three.

Student: Provides answer and says 4/8 is bigger than 4/5 because the 8 is bigger.

Teacher: That is incorrect. If the numerators are the same, then you only compare the denominators. The larger the denominator is, the smaller the piece; therefore, 4/8 is less than 4/5 because the 4 pieces in 4/5 are larger than the 4 pieces in 4/8.

 

Teacher: We are going to shade each fraction on a tens-grid, so we can compare them.

Student: How do I put 9/10 on the number line, it is too big?

Teacher: Is 9/10 bigger than one?

Student: Yes!

Teacher: Let’s look again. Is the fraction closer to one or zero?

Student: 1 because 9 is close to 10.

Teacher: Great observation! Yes it would be very close to 1!

 

Teacher: This is a whole. It represents “1”. This is a tens grid- it has ten equal parts. I will shade 2 parts out of ten to represent the fraction. What is my fraction?

Student: 2/10

Teacher: That is correct. I shaded 2/10 parts of the whole, so my fraction is 2/10

This square is a hundred chart. Now it is divided into 100 equal parts. What is the fraction that is being represented now?

Student: 20/100.

Teacher: That is correct!

 

Teacher: Could I have a volunteer to show me how to represent 6/10 on the tens grid?

Student: Shades 6 out of 10 strips.

Teacher: Could you explain your answer to the class, please?

Student: Sure, I shaded 6 strips for the 6 and there are ten strips total, so this is 6/10.

Teacher: Nice work. We are all going to practice using these tens grids now.

DURING  
 

Divide the class up into groups of 4 students. This will be about 5 groups. Follow the groups sheets provided to place the students in their developmentally appropriate group.

 

Give each group a list of about 10 fractions and a baggie of tens grids.The list of fractions is attached to this lesson plan. Provide the students with colored pencils or markers, glue, and a half poster board.

 

Give the students instructions.

 

 

 

 

 

 

 

 

 

 

 

The students will work in groups to complete the activity while the teacher circulates around the room. Students may have questions as they are working.

 

Students will move into their groups.

 

 

 

 

 

 

 

 

 

 

Teacher: Color in the amount of tiles that fit your fraction and place it where it belongs on the number line. Do not glue it down until you have placed all of the grids where you think they belong.

 

Teacher: Once you think they are correctly ordered, glue them down and write the fraction next to the grid. Then, raise your hand and the teacher will come by to check the work.

 

 

Student: How do we color this one? The denominator is 5 and we have 10 tiles.

Teacher: What could you do to fix this problem?

Student: Make the denominator 10.

Teacher: How would you go about doing that?

Student: I would see that there are 4 out of 5 and see how many that would be out of 10.

Teacher: I really like the way you working through this problem. Great work! What would your answer be if you have 4 out of 5 and you need to show it on a tens grid?

Student: I think it would be 8 because it is doubled.

Teacher: Excellent job!

AFTER  
 

Ask the members of each group to explain their number line to you (the teacher) and assess the number line for correctness.

Other groups with either be finishing their work as a group or working on the additional challenge (decimals-.5, .67, .2, .99, .54, .1, .25, and .75. ).

 

 

 

 

 

 

 

 

 

 

Once each group is finished, draw names from the class set of popsicle sticks to write one fraction on the giant class number line with a dry erase marker.

Repeat this step until every student has added one fraction to the class number line.

The teacher is responsible for making sure the mathematics is correct and that the student’s reasoning matches their equations.

 

 

“When looking at this number line it is important to remember to look at the numerator and denominator before deciding which fraction is bigger or smaller and where to place the fractions on a number line.”

 

 

You may now put your supplies from math away and get ready for Language Arts.

 

 

 

Teacher: It looks like you have completed the activity, explain to me why you ordered the fractions in this way.

Student 1: We started with 1/2 because we knew where they one went and then we put the ones we knew on the graph.

Teacher: Starting with something you already know is a great idea. How did you know where to place the rest of the fractions?

Student 2: We found equivalent fractions and reduced some of the fractions so we could color the right amount of squares.

Student 3: And then we saw which ones were bigger and smaller and put them on the graph.

Teacher: Great job working through those problems!

 

Teacher: Brandon, you are up.

Student: OK!

Teacher: Please add the fraction 5/10 to our timeline.

Student: Adds the fraction.

Teacher: Why did you choose to put 5/10 there?

Student: Because 5/10 is equivalent to 1/2.

Teacher: Thank you, Brandon.

 

 

Teacher: What are these fractions called when we have more than on fractions on the same part of the number line?

Student: Equivalent fractions!

Teacher: That is correct- we have several equivalent fractions.

 

Teacher: Thank you for participating and for being good listeners.

 

 

MODIFICATIONS FOR STUDENTS WITH SPECIAL NEEDS

  • My class does not have physical disabilities or English language proficiency difficulties. There are students however that struggle in mathematics and fall far behind others when introduced with new material. Many of those same children also have ADD or ADHD, so in order for them to finish around the same time as the rest of the class, they will need to have fewer problems to complete.
  • Remedial Problem: For students with special needs I will provide the students with simple fractions such as 1/2, 1/10, 8/10, and 5/10 so that the lesson is developmentally appropriate for them. Students in this group will simply have to look closely at the numerator and shade the correct amount. Their challenge problem will be 1/2 being that the denominator is not 10. I will give those students a smaller amount of fractions so that they do not reach a frustration level and so they have more time to complete the number line.
  • There are four students in the class that have recently passed the gifted test and will find the activity to be very simple. In order for them to not be bored and to engage in challenging mathematics for the entire class time, they will need supplemental, developmentally appropriate problems to work on.
  • Challenge Problem: I anticipate that the gifted group will need the additional challenge, but I will bring a few copies in case other students find the activity to be too easy. For an additional challenge I will give the group decimals to include on the timeline. Decimals include .5, .67, .2, .99, .54, .1, .25, and .75.The group will have to switch their thought process back and forth between decimals and fractions and they will have to understand the concept of decimals and their relation to other numbers on a timeline.

 

WHAT COULD GO WRONG WITH THIS LESSON AND WHAT WILL YOU DO ABOUT IT?

  1. Lesson- Students may now remember how to simplify fractions, so if this is the case I will demonstrate a mini lesson on reducing fractions. During the mini lesson I will discuss the idea of greatest common factor and least common multiple so that the students have a clear idea of how to simplify.
  2. Lesson- Students may not understand the concept of shading the grids during the first two examples as a full class. If this is the case, I will provide the students with 2 more examples to clarify the concept.
  3. Lesson- Students who struggle with math may have trouble understanding the concept of a fraction in which case I will have manipulatives prepared so that the students can see the problem visually.
  4. Attendance- My class tends to have a poor attendance rate, so if this is the case I may have to have one less group as to not have a group of two students.
  5. Behavior- If a student chooses to not participate or acts in an inappropriate manner during the lesson I will ask the student to report to the writing table and journal about his/her behavior. The students should be used to this procedure because my cooperating teacher uses this method.
  6. Technology- The doc camera may not work in which case I will draw on the Smartboard. If the Smartboard is not working I will draw on the dry-erase board and have copies of the grids to attach to the board.
  7. Time- If my supervisor is not able to make it on time or if there is a change in plans determined by my cooperating teacher, I will help my cooperating teacher go over homework until I am able to teach my lesson. If I am short on time I will limit the amount of fractions we display on the timeline as a class.
  8. Emergency Drill- If there is an emergency drill or any other type of emergency I will immediately stop my lesson and take the appropriate action determined by the school.

 

REFLECTION

**To be completed after the lesson**

 

PAPERS THAT I WOULD BRING FOR THE LESSON

 

 

GROUPS FOR LESSON

 

 

Group 1:

Grace

Samantha T

Jarred

Heather

 

 

Group 2:

Bradley

Nathan

Abi

Morgan

 

 

Group 3:

Tori

Makiah

Sam

Samantha M

 

 

Group 4:

Jordyn

Zac

Kaden

Courtney

 

Group 5:

Timmy

Marisa

Logan

Tara

 

 

 

 

 

 

 

 

FRACTION OPTIONS

 

1/4

 

3/4

 

1/5

 

2/4

 

100/100

 

3/6

 

2/10

 

30/100

 

4/5

GUIDED NOTES FOR LESSON

 

Name: ___________________________________________           Date: _________________

 

Comparing and Ordering Fractions

 

1.         Which fraction is larger?  2  or  3? Circle the larger fraction.

4       4

 

2                                                                                                   3

4                                                                                                   4

 

 

   
   
   
   

 

 

2.         Order the following fractions from least to greatest.

 

4,          9,         7

5          5          5

 

 

3.         Compare the following fractions by circling which fraction is larger. Be sure to pay attention to the denominators!

 

 

4  or  4                                                 6  or  6                                     3  or  3

5       8                                                10      8                                     5       6

 

 

4.         Order the following fractions on the number line. Which numbers are closer to zero, 1/2 , or one?

 

3                                  2                                  5                            9                            2

4                                  4                                 10                          10                           8

 

 

 

1/2

1

0

 

 

 

Data Collection Form

Student Name Indicate how many comparison questions the student answered correctly Indicate if the student has represented equivalent fractions by writing an X or a ü Indicate how many fractions the group ordered correctly Indicate if the student ordered the given fraction correctly on the board with an X or ü
Group 1        
GN

 

       
ST

 

       
JH

 

       
HM

 

       
Group 2        
BS

 

       
NS

 

       
AD

 

       
MS

 

       
Group 3        
TG

 

       
MC

 

       
SA

 

       
SM

 

       
Group 4        
JM

 

       
ZR

 

       
KW

 

       
CM

 

       
Group 5        
TH

 

       
MJ

 

       
LM

 

       
TB

 

       

 

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