Educational Technology: Let's Help Students Become More Motivated to Learn!: Comparing Fractions with the Integration of Technology

Comparing Fractions with Technology

By: Jamie Balzarini

Purpose: In this lesson, we will expand on our knowledge of fractions that we have learned this past week. We will review past skills taught, as well as introduce the skill of comparing and ordering fractions. This lesson is useful because this skill is utilized in daily life without people recognizing that they are actually comparing and ordering fractions.

Grade Level: 5^th Grade

Subject: Comparing Fractions

Location: Hawkins Path Elementary in the classroom setting

Time Frame: 50 minute lesson

Level of Knowledge: Remembering, Understanding, Applying, Analyzing

Pre-Requisites:

Basic understanding of fractions
Knowledge of the factors/multiples of numbers
Ability to find common denominators
Ability to order numbers from least to greatest

Content Standards: Common Core and New York State Standards

Learning Outcomes/Objectives:

• Students will be able to write fractions from least to greatest and greatest to least.

• Students will be able to compare fractions.

• Students will be able to integrate the terms greater than, less than, or equal to.

• Students will be able to explain their process of comparing and ordering fractions.

Learning Activities:

Introduction of new topic: Hook

- In the real world, people are put in situations where they need to determine which fraction is larger/smaller. For example, when cooking or manipulating a recipe, one needs to be able to figure out if a measurement is equivalent, greater than, or less than other measurements.

- In this lesson, we will learn how to compare fractions.

Brief review of fractions *Remembering

- Teacher will review how to find common denominators as well as reviewing the skill of ordering whole numbers from least to greatest. This will act as a brief warm-up for the students.

- Teacher will explain that finding common denominators is a key component when trying to order and compare fractions. The teacher will then put up the following three problems for the students to independently practice finding common denominators.

- The teacher needs to make sure that this skill is mastered before moving on to the focus skill of comparing and ordering fractions.

Launch/2^nd Hook: The teacher will have the students look at the board, which contains three different fractions 2/3, 5/8, 1/4. Teacher will then ask the question: If you had to find the largest fraction of these three fractions, how might you do it? Take suggestions from the students and record them on the board.
Students will then write the new topic into their notebook as well as the notes the teacher puts onto the SmartBoard. (As a teacher, I like to have the students organize their notes for studying purposes. If everything is clearly labeled with the objectives, students know what areas they need to focus on when reviewing and studying.) (Remembering)

- The teacher will have the students write down two fractions: 2/4 and 4/6. The teacher will then draw a picture to represent each of these fractions. The teacher will explain that drawing a picture can help visualize the fractions, however, sometimes the pictures are too similar to visually compare them. This is why it is important to be able to find common denominators.

- The teacher will then present the students with the following situation: Mary and Julie are twin sisters and it is their birthday. At the party, there were two different types of cakes, chocolate and vanilla. Mary and Julie each got their own slice of cake. Mary got 2/5 of the chocolate cake and Julie got 3/7 of the vanilla cake. Julie was upset because she thought she got a smaller piece than Mary got. Is she right? How do I find out?

- The teacher will explain that drawing a picture would be difficult to answer this question because the pictures will be too close to tell. The teacher will then ask the students what the best process would be to compare these two pieces of cake, with hope that they determine that they need to find common denominators before answering this question.

- The teacher will then model how to find the common denominators for these two fractions. After finding common denominators, the teacher will show that the next is to compare the numerators. The teacher will explain that when writing their final answer, the fractions have to be in their original form.

- Students will copy following steps: 1. Find common denominator, 2. Compare numerators, 3. Order fractions from least to greatest or greatest to least, or compare the fractions. 4. Write the fractions in their original form when recording answer or write in the greater than or less than signs (<, >, or =)

- The teacher will also review two simple rules that will act as an addition resource for students when comparing fractions. (See image below)

Guided Practice (Remembering and Understanding)

- Teacher will then put the following problem on the board:

5/10 _________ 3/4

- The teacher will ask the student which fraction is bigger and how do they know. The

students will reiterate the steps they need to follow to complete this problem
- The teacher will then go step by step:

1. Write down the multiples of 10 and 4.

2. Find the least common multiple (LCM=20).

3. Change both fractions so that they have a denominator of 20

5/10 = 10/20 and 3/4 = 15/20
4. Compare the fractions.

10/20 is less than 15/20
5. Rewrite with original fraction and write in the inequality sign.
5/10 < 3/4

- After completing this problem, the teacher will survey students to see if any step is

unclear. Teacher will observe to ensure that students are recording the accurate steps before

moving on to independent practice.

Independent Practice (Remembering, Understanding, and Applying)

- Teacher will post the following four problems for the students to complete independently:

*Light blue highlight = work to solve problem

*Yellow highlight = answer

- Throughout the course of this independent work, the teacher will be observing the
students to see if there are any students who are confused, don’t understand a specific
step, or who failed to grasp the new concept taught.

- If the teacher finds that there are a handful of students who are struggling, the teacher
will pull a small group at the back table to work more closely with these students. At this
point, the students who were able to grasp the concept and are able to complete these
problems individually will be given an activity sheet that has a variety of comparing fraction
problems. This will support the lesson and give the students more practice with the topic.
(Click here to be directed to worksheet)

- After working with the small group (of struggling students), the teacher will go over the
problems with the students as a whole group before moving on to the technology portion of
the lesson. The teacher will be sure to choose students at random to ensure that all students
are paying attention and reviewing their work. The teacher also wants to be sure that
students are able to explain the process of solving the problem. This will show the teacher
that students are grasping the concept and able to apply the steps to different problems.

Technology Integration

- Students will then utilize their iPads to play the Comparing Fractions game:

http ://www.mathplayground.com/fractions_compare.html

(Remembering and Understanding)

**This site reinforces the steps that students learned during the lesson. They are to review the brief overview of steps and then play the game. This site provides a variety of problems that require students to compare students after finding a common denominator.

- Teacher will survey students to receive a rough estimate of student performance for this game. Based on student performance, teacher will either review topic again or allow the students to choose from the following online games (they will continue to use their iPads):

1. Comparing Fractions Soccer Game

(Remembering, Understanding, and Applying)

This is a fun game that allows students to practice the skill of comparing fractions. They have to decide if the two fractions given are greater than, less than, or equal to. From there they move the arrow to point in the right direction and they shoot the soccer ball into the net. If they are correct, the ball goes in, if not, the goalie stops the ball. A fun, engaging way to practice this skill with immediate feedback.

2. Comparing Fractions Game

(Remembering, Understanding, and Applying)

This is a game in which students have to compare fractions. They must find a common denominator and figure out which fraction is bigger or smaller. In some cases, the fractions will be equal. The students select the correct sign and will get immediate feedback from the computer. An alternative, engaging way to practice this skill.

- The teacher will demonstrate each game to ensure that the students understand what they have to do for each game.

- These sites are just a couple of examples of a variety of interactive math games related to compare and order fractions.

- They give students a fun and engaging way to practice this skill.

- Each site practices a different skill so it allows students to choose which game or skill they feel they need more work on.

- The website gives them immediate feedback so they are able to see where they went wrong and try to identify their mistake.

- These websites can be accessed on any piece of technology that provides internet access.

- Great tool for students who have computers at home and want to continue practicing these skills at home.

Assessment

Authentic: None
Formative: As a tool of formative assessment, the teacher will give the students a brief assignment for homework that evaluates the students’ ability to compare and order fractions (Click Here For Worksheet). This assignment is a quick way to see where students are at when it comes to understanding and application of skills.
Summative: There will be no form of summative assessment during the lesson. The teacher will, however, administer a unit exam after further instruction and at the completion of the unit. The teacher will use a unit exam that will cover all areas described and instructed throughout this unit of study of fractions.
Individual: Individual assessment is being done through observation and informal discussion. The students will be completing practice problems independently. At this point, the teacher is able to walk around and observe closely to assess those who are struggling and those who understand the concept. The teacher is also able to watch the students “play” the educational games. Their results are a reflection of their understanding of the concept.
Informal: The teacher will be informally assessing students throughout the entire lesson. The teacher can recognize if a student is struggling or not by the questions they ask and by their explanations. This informal is important for teachers because it can help them recognize the level of comprehension/mastery.
Formal: The formal assessment will be the homework worksheet the students are getting along with the unit test the students will take at the end of the fraction unit.

User Notes: It is beneficial if the educator familiarizes himself or herself with the technology that is integrated into this lesson. The more comfortable one is with the technology, the easier it will be to explain to students what they have to do. Additionally, before the lesson begins, the educator should ensure that the websites and links all work so that there are not mishaps when trying to open the sites.

Resources: All resources are included at the part of the lesson plan where the students would actually use the websites or technological tools. They are all hyperlinked so when clicked on, they will take the user directly to the sites.

Reference List:

Churches, A. (2009, january 4). Bloom. Retrieved from

http://post.blackboard.com/bbcswebdav/pid-1215260-dt-  content-

rid11574500_1/courses/EDU625.901198020059/EDU625.90119802

0059_ImportedContent_20121220101950/MasterCourseEDU625_

ImportedContent_20121019125930/bloom's Digital taxonomy

v3.01(1).pdf

Dunn, J. (2011, December 19). Study: ipad apps improve learning. Retrieved from

http://edudemic.com/2011/12/ipad-apps-learning/

Effects of technology on classrooms and students. (n.d.). Retrieved from

http://www2.ed.gov/pubs/EdReformStudies/EdTech/effectsstudents.html

Ferlazzo, L. (2011, May 7). Why is it important for students to learn about bloom’s