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Fractions Greater Than One


Plan Author: David Riddick
Date Created: 5/11/2003 10:04:44 AM PST


Dyer St. Elementary

Grade Level:

31 Students. 20 boys and 11 girls. 10 E0s; 10 RFP's 10 ELD4-5: 1 ELD2. GATE class - advanced learners

Subject Area(s):

Students will have an understanding of different ways to show the same value of a fraction greater than one.

Students will learn two different ways to write fractions greater than one, Improper Fractions and Mixed Numbers.


CA- CCTC: Aligned CSTP's and TPE's

• Standard : CSTP: Standard for Understanding and Organizing Subject Matter for Student Learning
TPE: A. Making Subject Matter Comprehensible to Students
CSTP Description: Teachers exhibit strong working knowledge of subject matter and student development. Teachers organize curriculum to facilitate students’ understanding of the central themes, concepts, and skills in the subject area. Teachers interrelate ideas and information within and across curricular areas to extend students’ understanding. Teachers use their knowledge of student development, subject matter, instructional resources and teaching strategies to make subject matter accessible to all students.

• CSTP Key Element : Developing student understanding through instructional strategies that are appropriate to the subject matter.

 Question : help all students develop enthusiasm for and a deep knowledge of the subject matter?

CA- California K-12 Academic Content Standards

• Subject : Mathematics

• Grade : Grade Five
By the end of grade five, students increase their facility with the four basic arithmetic operations applied to fractions, decimals, and positive and negative numbers. They know and use common measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass to solve problems. They use grids, tables, graphs, and charts to record and analyze data.

• Area : Number Sense

• Sub-Strand 1.0: Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers:

 Standard 1.5 (Key Standard): Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

Cognitive: Students will learn improper fractions have the same value as mixed numbers.

Observable behavior: Students will independently convert improper fractions and mixed numbers.

Criteria: Given a Fraction handout, students will demonstrate ability to answer fraction questions with a value greater than one, with 70% accuracy.

Prerequisite Background Skills/Knowledge:
Students should be cognizant that a division algorithm follows these steps: divide, multiply, subtract, compare and bring the next number down.

Vocabulary / Language Skills:
Listening: Students listen to verbal instructions given during directed lesson. ELD students are given help by peer tutors as teacher speaks.

Speaking: Students participate in directed lesson by raising hands and answering questions.

Writing: Students write answers on paper provided.

Reading: Students read the math textbook directions, material on overhead, and chalkboard.

Vocabulary: mixed number, improper fraction, denominator, numerator, simplest form,

1) Pencil & Paper
2) Worksheets
3) Transparencies
4) Transparency pen
5) Chalk
6) Math textbook

Classroom Management:
During directed lesson, students are seated in assigned seats, which are 2-person desks.

During independent lesson, students who understand the lesson will be allowed to tutor students who are struggling.

During assessment, all students must return to their seats. As students finish, they must stay in their seats. They may write or read as they finish.

Procedure: Open

As an attention getter, I call on students who have transitioned well into math to be the first volunteers to work on the chalkboard.

The class is already divided in half. I call on students from both sides of the class to duel one another for extra-credit points.

The problems the students will solve are an introduction to the new lesson, and review from previous lessons.

Procedure: Body


1st: Point our standards we are working on (posted.

2nd: Establish a sense of academia by introducing vocabulary for this lesson. Review the background vocabulary they need to know, and deepen their understanding by providing examples of a mixed number and an improper fraction.

3rd: I will make a comparison of a fraction to a school bus. The denominator will be the seats on the bus. The numerator will be the students who need to ride the bus. In this example, there will be more students than seats available on the bus. Creating an improper fraction.

4th: I will show the students their are two ways to write this improper fraction. 1) As an improper fraction 2) An a mixed number.

5th: To promote high level and/or open-ended questions, I will ask when do we use an improper fraction? When do we use a mixed number?

6th: I will model how to convert mixed numbers to improper fractions, and improper fractions to mixed numbers. To keep the interest going, I will ask for student volunteers to write and solve problems on the overhead.

4th: As students answer the problems, I will walk around the room to keep the other students on task.

5th: I will ask for student input on how the student volunteers are answering the questions.

Guided Practice:

I will write problems on the board, the students will work with a their table partner to get the problem correct. Tables who work the best together will get extra credit.

To check for understanding, I use non-verbal hand cues to assess for confusion and clarification.

Independent Practice:

Students will practice their learning independently answering questions in the text and preparing for a quiz. The quiz will be a 10 problem quiz on P. 299 Set I.

Procedure: Close

To close the lesson and summarize what was learned, students will reflect in their journals what they learned and vocabulary introduced. I will hand it over to the class to discuss what they learned, giving them time to process their learning.

Students will answer 10 fraction questions of a value greater than one, with an accuracy level of 70%.


The objective of the lesson was achieved. I know the objective was achieved because the students were able to answer the fraction questions with an accuracy level of at least 70%.

I correctly anticipated the students would have difficulty equating improper fractions and mixed numbers as the same value. I made visual diagrams to show that both definitions had the same value.

On the other hand, I did not anticipate the students would have such difficulty with the calculations of converting a mixed number to an improper fraction. These calculations brought a great deal of confusion to the students.

If I were to teach this lesson again, I would have given the higher achieving students a greater opportunity to experiment with what a fraction greater than one can represent.

Higher achieving students could make diagrams or present real world situations in the form of a skit or commercial ad to demonstrate what a fraction greater than one would look like in a real life situation. (Ex. A commercial for a Pizza company offering one full pizza and a half)

The lesson was relevant and worthwhile for the students because it gave them insight of what a fraction greater than one represents. In the future, I will enhance the lesson by allowing the high achieving students the opportunity to create math reasoning scenarios. I believe this will allow me to meet the standard for Understanding & Organizing Subject Matter for Student Learning. I want to help all of my students develop enthusiasm for and a deep understanding of fractions greater than one.