This unit plan has been developed for fourth grade gifted and talented students who are operating at a seventh grade level in mathematics. The duration of the unit will last approximately two weeks.
This unit will teach students how to add, subtract, and multiply positive fractions and mixed numbers.
Goals and Objectives
- Each of the students will score at least an 80% on the unit test which focuses on the addition, subtraction and multiplication of positive fractions and mixed numbers.
- Students will be able to understand how operations relate to each other (multiplication equaling repeated addition).
- Students will know how to use estimation to verify their answers.
- Students will also be able to quickly estimate and determine how reasonable their estimate is in relation to the correct answer.
- Students will be able to choose, identify and use the correct operation (addition, subtraction, and multiplication) to solve a real-world word problem consisting of several steps.
- Students will have strengthened social interactions through a cooperative learning environment.
- Students will learn interdependence yet maintain individual accountability.
- Students will participate in an active learning environment that promotes life-long learning skills.
- Students will apply knowledge in real-world environments.
Prior to starting this unit on adding, subtracting and multiplying positive fractions and mixed numbers a pretest will be administered to determine the knowledge of the students.
Terminology will be addressed on the first day of the unit including the terms: fraction, whole number, common denominator, numerator, denominator, least common denominator, least common multiple, prime factors, and simplify.
Multiplying two fractions is the easiest of any of the operations. When multiplying fractions, you simply multiply the numerators together and then multiply the denominators together. Simplify the result.
When adding and subtracting fractions, the fractions being added or subtracted must have the same common denominator. When denominators are different, they need to be converted on each fraction into an equivalent fraction. This is accomplished by finding the least common denominator. The two new fractions should have the same denominator, making them easy to add or subtract.
The rule for adding fractions is that they each must have the same denominator. If they do not, find the least common denominator for the fractions and put each in its equivalent form. Then, simply add the numerators of the fractions. Simplify the result.
The rule for subtracting fractions is that they each must have the same denominator. If they do not, find the least common denominator for the fractions and put each in its equivalent form. Then, simply subtract the numerators of the fractions. Simplify the result.
A whole class activity will begin this unit to learn the terminology related to adding, subtracting and multiplying fractions. The terminology which will be explored will include fraction, whole number, common denominator, numerator, denominator, least common denominator, least common multiple, prime factors, and simplify. Additionally, examples will be shared on how to do the activities as well as how to do the mathematical operations.
Manipulatives will be used such as white and black fraction strips, color fractions strips, pizza fractions and circles (Super Teacher, 2012). Students will work in pairs or small groups in a cooperative learning environment. This strategy will be used as students work together in comparing and contrasting the similarities and differences. Students will also be asked to share their successes and disappointments (Thousand, Villa, & Nevin, 2007).
Worksheets, practice and homework will be used throughout the unit while students to help the students to understand the mathematical operations. The teacher will methodically push students to reach beyond themselves by asking probing questions while circulating through the classroom (Super Teacher, 2012).
Lastly, a game, entitled Lure of the Labyrinth, developed at MIT with gifted and talented students in mind, will be used in this unit. This game includes a wealth of puzzles to encourage the student in pre-algebra skills such as forming hypotheses and testing variables. encourages students in their critical thinking skills and real-world applications. This tool was created for middle school students which will encourage elementary aged gifted students to stretch academically in order to complete the puzzles including the mathematical operations of adding, subtracting and multiplying fractions.
The game setting, directed for pre-algebra students in middle schools to learn critical math skills in a digital puzzle setting, has them believe they are not studying. The game intrigues students and is linked to national mathematics standards. It encourages students to think like mathematicians while they move mathematical theory to application. It can be played both individually and in teams (Osterweil, 2012).
Resources and Materials
The following resources and materials will be needed for this unit:
- writing utensils.
- manipulatives such as white and black fraction strips, color fractions strips, pizza fractions and circles (Super Teacher, 2012).
- worksheets for in class work, practice and homework (Super Teacher, 2012).
- computers or technology lab.
- training opportunities in how to use the Lure of the Labyrinth game. This would include both time and technology required. Lure of the Labyrinth includes videos and training for teachers, explaining how the game can be integrated into the classroom. The Lure of the Labyrinth site includes details for success, lesson plans, tips and even support. Use of the site is free (Osterweil, 2012).
Evaluation will be completed through both formative and summative assessment methods. The formative assessment will occur throughout the instructional process, providing immediate feedback for students while the summative assessment will be completed as the unit concludes (Moore, 2012). Formative assessment will be achieved through worksheets, practice, manipulatives, whole class discussion and the Lure of the Labyrinth game. Summative assessment will be achieved through the end of the unit test and the Lure of the Labyrinth game.
The Lure of the Labyrinth will generate a report for instructors which compiles not just the amount of time and dates the student played the game but also the number of puzzles completed. It also gives the teacher a snapshot of the students’ successes and where the student needs additional instruction (Osterweil, 2012).
There are instructional concerns for gifted and talented students. Gifted and talented students experience high frustration levels as their fine motor skills do not match their reasoning skills. They also experience unique social-emotional difficulties such as intense emotional, psychological, social and intellectual over-excitability. These concerns are further exasperated through the mismatch between their skills and their instructional environment (Peterson, 2009).
The use of technology bridges the gap between the fine-motor skills of students and intellectual capability. It also reinforces learning through a variety of means which include visual, audio and even tactile learning styles. Lastly, by including the gifted student in a team setting to play the Lure of the Labyrinth game and working in a cooperative environment, the student will learn social skills which may otherwise be weak.
The teachers and teaching assistants along with the gifted and talented facilitator will assemble to determine how the students met their pre-determined objectives. Success will be determined through comparison of products and objectives. Students will be given an opportunity to write an evaluation of the project through the use of a graphic organizer. The team will discuss the successes and disappointments of the activity after evaluating all information. They will then discuss if the project should be used again and if so, what recommendations could be made to increase the efficiency of the unit.
Every student has a preferred learning style. However, it is important to expose students to different types of learning styles to give an opportunity for personal growth (Pritchard, 2009). Throughout the application of this unit, students will be exposed to cooperative learning which will help strengthen social interactions between their peers. Manipulatives are introduced to students to develop the mathematical operations for the tactile learners as well as the traditional method of using a pencil with a worksheet. Lastly, technology invites the students into a active and authentic learning situation to recognize that learning can be enjoyable (Moore, 2012).
Miller, E. (2009). The effect of training in gifted education on elementary classroom teachers’ theory-based reasoning about the concept of giftedness. Journal for the Education of the Gifted, 33, 65-107.
Moore, K. D. (2012). Effective instructional strategies: From theory to practice (3rd ed.). Thousand Oaks, CA:Sage Publications.
Osterweil, S. (2012). Lure of the labyrinth: for educators. Retrieved from labyrinth.thinkport.org/www/educators.php
Peterson, J. (2009). Myth 17: gifted and talented individuals do not have unique social and emotional needs. The Gifted Child Quarterly, 53, 280-283.
Pritchard, A. (2009). Ways of learning: Learning theories and learning styles in the classroom (2nd ed.). New York, NY:Routledge.
Renzulli, J., Siegle, D., Reis, S., Gavin, N., & Reed, R. (2009). An investigation of the reliability and factor structure of four new scales for rating the behavioral characteristics of superior students. Journal of Advanced Academics, 21, 84-113.
Super Teacher. (2012). Manipulative fraction tools. Retrieved from http://www.superteacherworksheets.com/fractions-basic.html
Thousand, J., Villa, R. & Nevin, A. (2007). Differentiating instruction: Collaboratively planning and teaching for universally designed learning. Thousand Oaks, CA: Corwin Press.
By Tracy Atkinson
Tracy Atkinson, mother of six, lives in the Midwest with her husband. She is a teacher, having taught elementary school to higher education, holding degrees in elementary education and a master’s in higher education. Her passion is researching, studying and investigating the attributes related to self-directed learners. She has published several titles, including Calais: The Annals of the Hidden, Lemosa: The Annals of the Hidden, Book Two, Rachel’s 8 and Securing Your Tent. She is currently working on a non-fiction text exploring the attributes of self-directed learners: The Five Characteristics of Self-directed Learners.