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Posted on April 18th, 2014, by

Topic: Mixed Operations with Fractions

Grade level: 5

Objectives: the students will be able to have a practice of mixed operations with fractions and to develop fluency with fraction concepts.

Materials and resources: math books, pencils, paper, colored markers, fraction cards for the game and testing, online program to practice mixed operations with fractions.

Pre-activities: The group of students will review the rules of addition, subtracting, multiplication and division of fractions. In addition, the students will be given a number of questions about the above mentioned operations with fractions

  1. What is the meaning of dominator (a common dominator)?
  2. What is a numerator?
  3. How to find equivalent fractions?
  4. What is improper fraction?
  5. How to identify mixed numbers?
  6. How to compare fractions by finding a dominator?


  • The students will be able to solve different problems with fractions and to develop fluency in manipulation of fractions. They will work in pairs: one student reads a problem with the use of fractions and the second student solves this problem, then they change their roles. The teacher will check the students’ answers.
  • The group of students will use online program on the AAA Math Website to practice mixed operations with fractions. The link is here:
  • The students will have a test based on the use of all operations with fractions, including addition, subtraction, multiplication and division. In addition, this test will also include word problems:
  1. Lily and Dan are collecting stamps. Dan collected 3/8 as many stamps as Lily did. If Lily collected 1/2 of a collection of stamps, how many stamps of the collection did Dan collect? (3/8*1/2 = 3/16).
  2. Roy has 1/2 of a pound of seed left to share equally among 6 bird cages in the pet shop where he works as a salesman. How many pounds should he put in each cage? (1/2:6 = 1/2 : 6/1 = 1/2 * 1/6 = 1 * 1 /  2 * 6 = 1/12)


At the end of the lesson, the students will be given a set of review questions in the form of a test, and they will judge the quality of their peers’ work. Self-assessment can help to improve the students’ motivation. When students complete 10-15 problems, their answers will be checked. The informal observation will be based on the participation of the students in online practice that helps to develop fluency.

6.         Assessment and Evaluation Methods

In this instructional unit, it is required to use both traditional assessment methods and alternative methods. It is recommended to use traditional pen-and paper tests, true-false tests and multiple choice tests which provide an opportunity to check the students’ ability to add, subtract, multiply or divide fractions.  In addition, it is required to provide teacher observation of students, in structured or unstructured activities and evaluate the quality of student task engagement, especially in games and in practice with the help of online programs. According to Mustafa Dogan (2011), student self-assessment, with students judging the quality of their own and their peers’ mathematical understanding and progress(p.421).

B.        Report on the Instructional Unit

1.         Summary of the Instructional Problem

The 5-th grade gifted math students struggle with understanding and manipulating fractions. According to the new Common Core Standards for math they need to be able to developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions (Common Core Fifth-Grade Math Standards, 5 NF, 2010). To do this students must understand and identify improper fractions, understand identify mixed numbers, develop an understanding of common denominators and renaming and comparing fractions by finding a denominator, identify and rename equivalent fractions and order fractions of all types including improper fractions and mixed numbers.

1.1          Discussion of the Major Findings from the Needs Analysis Conducted on the Problem

The 5-th grade students of this group who have poor understanding of fraction concepts and serious problems with manipulation of fractions have an opportunity to use special manipulative and fraction models to apply their understanding of fractions. These tools can help them in developing fluency with fraction concepts. In addition, the students who had serious problems with fractions in the 4-th grade will be able to improve their motivation because the activities used in the instructional unit are very interesting and attract attention of the students of this age group.

1.2       Discussion of why the Determined Problem could be Addressed with Instruction

The determined problem could be addressed with instruction because the instructional unit is specially designed to help the students of the 5-th grade to develop fluency with fraction concepts. Good instruction helps the learners to develop more skills and abilities in solving different math problems and practice the appropriate mathematical rules. Moreover, instruction helps to develop communication and listening skills which can help students in future.

1.3       Discussion of the Major Findings from Learner and Task Analysis Conducted on the Problem

The major findings from the learners prove the fact that this instructional unit improved the learners’ outcomes and the topic Fractions is not so difficult for the majority of the students. All students in the group successfully solved math problems with addition, subtraction, multiplication and division of fractions in their tests. Most of them got high grades.

Task analysis proves the fact that the material was effectively chosen by the instructor in this unit. The students were given an opportunity to review previous topics, defined the major terms and were taught the major rules of operations with fractions

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