Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 34730
Fractions: Let's Compare
In this lesson students use area models, number lines, and the benchmark fraction of 1/2 to compare fractions that are less than one and have
different numerators and denominators to solve real-world problems.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, LCD Projector, Microsoft Office
Instructional Time: 1 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: fractions, comparing fractions, compare fractions
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Number Line Fractions Comparison.docx
Using a Number Line Fractions Comparison.docx
Area Model Fractions Comparison.docx
Independent Practice Fractions Comparison.docx
Key Independent Practice Fractions Comparison.docx
Summative Assessment Fractions Comparison.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
compare fractions less than one that have different numerators and denominators.
explain their reasoning when comparing these fractions.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with the following terms, symbols, and concepts: whole, half, less than, greater than, equal to.
Students should have mastered MAFS.4.NF.1.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention
to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent
fractions.
Guiding Questions: What are the guiding questions for this lesson?
1. What does the denominator represent?
2. What does the numerator represent?
3. How can two fractions have different numerators and denominators, but represent the same part of a whole?
4. In this problem, what is 1/2 and how could that help you compare the two fractions?
5. What array arrangement would illustrate this problem?
6. How could you mark a number line to illustrate this problem?
page 1 of 4 7. What have you learned before that could help you answer this question?
Teaching Phase: How will the teacher present the concept or skill to students?
Note: This lesson builds on previous understanding and is taught as a whole class with combined teaching and guided practice.
Ask students if they have seen anyone comparing fractions. (science experiments, rainfall measurement, recipes, carpentry, etc.)
Tell students that today they are going to compare fractions.
Review the concept of always using the same "whole" when comparing fractions.
1. Hold up two same-shaped containers of different sizes such as a small and large drink bottle, cylindrical cans, beakers, etc.
2. Ask, "If you poured rice into 1/2 of the small container and rice into 1/2 of the large container, would the quantity of rice in each container be the same?" (No.)
3. Look puzzled and say, "But I filled each container halfway." (The containers are not the same size, so 1/2 would be different amounts.)
4. Say, "It is important to think of this, because although we filled both containers 1/2 of the way it was still a different amount based on the original size of the
container. When we are comparing fractions it is also important to consider the size of the whole. To compare fractions we must always use the same whole."
5. Assign partners based on the needs of your students.
Phase 1 - Area Model
1. Distribute gridded paper (from the Uploaded Files Section) and pencils (preferably a red, blue, and green). Distribute the Fractions Comparison Area Model
worksheet (from Uploaded Files section) or display it.
2. Read the introduction from the Fractions Comparison Area Model worksheet through question a. Provide time for students to draw 4 x 8 arrays on gridded paper to
represent the bases with and the representations for wholes of all green, all blue, and all red tiles.
3. See the answer Key Fractions Comparison Area Model. Tell students to answer question a. After sufficient time, tell them to discuss their answers with their
partners. Call on a student to share his/her answer and explain.
4. Tell students to answer question b. After sufficient time, tell them to discuss their answers with their partners. Call on a student to share his/her answer and
explain.
5. Continue this procedure through question i.
6. While students are working, circulate though the classroom looking at students' work and listening to conversations, so that you can provide feedback with guiding
questions and encourage students to revise their work, if needed, or offer affirmations for correct strategies.
7. Ask students for other strategies they might use to answer the questions.
Phase 2 - Number Line Model
1. Distribute the Fractions Comparison Number Line Model worksheet or display it, giving students the number line document, if needed. See the answer Key Fractions
Comparison Number Line Model.
2. Read aloud: Mr. Jones bought a long piece of ribbon for a decoration and needs 1/2 of it. His young child was playing with the scissors and snipped the ribbon into 3
pieces, such that one piece is 5/9 of the original ribbon, one piece is 7/18 of the original ribbon, and a very small piece is left over. Which piece is closer to 1/2, the
5/9 or the 7/18? Use a number line to show your thinking.
After posing each question below, give students time to think, ask them to share with their partners, and then call on a student to answer and explain.
3. Ask students how they might mark the number line to locate 5/9 and 7/18. (Make tic marks at 9 equidistant spaces between the 0 and 1; make tic marks at 18
equidistant spaces between the 0 and 1. Label the 5/9 and the 7/18.)
4. Ask students how they might decide which piece is closer to 1/2 and to explain? (5/9: measure the distance between the 5/9 and the 1/2 mark and the 7/18 and the
1/2 mark or recognize the distance in eighteenths.)
5. Ask students to compare 5/9 and 7/18 and record the results using symbols for greater than, less than, or equal to. (5/9 > 7/18 or 7/18 < 5/9)
6. Ask a student to explain his/her answer. (5/9 is more than 1/2 and 7/18 is less than 1/2, so 5/9 is greater; or 5/9 = 10/18 which is greater than 7/18.)
7. Ask students for other strategies for deciding which fraction is closer to 1/2, and which fraction is greater.
8. Ask students what is the same about some of the strategies students presented and what is different. You should hear ideas like:
The numerators are the same, so I just compared denominators.
The denominators are the same, so I just compared numerators.
Used benchmark fractions, such as 1/2.
9. Ask students to explain which strategy they think is the most efficient.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
See the Teaching Phase.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
1. Distribute the Independent Practice worksheet (from the Uploaded Files section), gridded paper, and a number line (or provide students with a straight edge to
draw their own, based on the needs of the class).
2. When students have had adequate time to complete the task, have them share their work with their partners and revise their work, if needed.
3. Call on a student to share a response.
4. Ask students who used different strategies to share until all strategies are exhausted. Encourage precise mathematical vocabulary. Elaborate on responses, if
needed.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Facilitate a class discussion:
1. Ask students where they have seen fractions used in the real world. (cooking, science experiments, weighing produce at the grocery store, measuring their height,
etc.) Say, "Sometimes we need to compare fractions to know which quantity is more or less."
2. Ask students what they did during this lesson to compare fractions. (Drew a gridded model, marked a number line, used 1/2, noted if the denominators were the
same in the gridded model or number line then the numerators could be compared to find the larger fraction. If helpful, display some solutions again to review.)
3. Ask students what is the same about some of the strategies and what is different. (Responses should include: The numerators are the same, so I just compared
denominators. The denominators are the same, so I just compared numerators. Used benchmark fractions, such as 1/ 2.)
page 2 of 4 4. Ask students to explain which strategy they think is the most efficient and why.
5. Remind students that when comparing fractions, we must always use the same whole. When students are ready, administer the Summative Assessment (from the
Uploaded Files section), gridded paper, a straight edge for number lines, and at least two different colored pencils.
Summative Assessment
Administer the Summative Assessment (from the Uploaded Files section), when students are ready.
Students who are unable to successfully complete the task using a strategy of their choice will need remediation.
Formative Assessment
The Illustrative Mathematics task Money in the Piggy Bank could be administered one or more days before teaching the lesson to assess students' prior knowledge
to assist in planning instruction.
Take anecdotal records to determine next steps for learning with re-teaching, reinforcement, or extensions.
Assess throughout the lesson by monitoring students' understanding with guiding questions and attention to students' responses.
Feedback to Students
Provide feedback during the Guided Practice and Independent Practice phases of the lesson. Circulate and assist students to clear up student misunderstanding and
encourage students to revise their work and be persistent, as needed.
Model precise mathematical terminology. Offer affirmation for students who have correctly answered the questions.
Acknowledge alternative solution strategies, but continue to model the area and number-line model, since these students may not appreciate the value of it yet.
When sharing between partners students will be able to compare their answers, collaborate, and revise toward having correct responses that they can justify.
Watch for the misconception that larger numbers in the numerator always indicate larger fractions.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Provide pre-marked number lines.
Provide pre-drawn arrays.
Provide translations, definitions, and/or examples of vocabulary that may be unfamiliar to any student. Based on the needs of the class, a word wall may be helpful.
Assign partners that would most benefit both students.
Extensions:
Fractions manipulatives from the National Library of Virtual Manipulatives
Suggested Technology: Document Camera, Computer for Presenter, LCD Projector, Microsoft Office
Special Materials Needed:
Students:
Class set of Fractions Comparison Area Model worksheets, unless it is displayed
Class set of Fractions Comparison Using a Number Line Model worksheets, unless it is displayed
Class set of Independent Practice Fractions Comparison worksheets
Class set of Summative Assessment worksheets
Number Lines, as needed
Gridded paper
Straight edge or ruler
Colored pencils; each student should have two different colors
Teacher:
At least two items of the same shape but different sizes to illustrate halves of different quantities
Answer keys
Gridded paper
Document camera and projector or overhead would be helpful, but is not required
Further Recommendations:
Avoid the use of mnemonic devices as a justification (multiplying fractions by fractions equal to 1 to get common denominators), since students should understand and
be able to explain their comparisons with an array or number line at this developmental stage.
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following Mathematical Practices:
MAFS.K12.MP.4.1 Model with mathematics, when students use number lines and arrays.
MAFS.K12.MP.5.1 Use appropriate tools strategically, when students use number lines and arrays.
MAFS.K12.MP.6.1 Attend to precision, when students compare fractions.
SOURCE AND ACCESS INFORMATION
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
page 3 of 4 Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.NF.1.2:
Description
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators
or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when
the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
page 4 of 4