During this lesson, students will be exploring the concept of expressing two fractions, originating with different denominators, as two fractions sharing a common denominator. Students will be using their basic multiplication skills to produce these new denominators. It is important that students have prior knowledge of their basic facts as well as an understanding of the meaning behind terms such as "factors" and "common factors".
Upon completion of this lesson, students should have at minimum an introductory understanding of the following Michigan GLCE for mathematics:
N.ME.05.11 Given two fractions, express them as fractions with a common denominator, but not necessarily a least common denominator.
Learning Resources and Materials
To complete this lesson, the following learning recourses and materials are needed:
-Plastic overlays and transparencies
-A variety of manipulative pieces broken/shaded into parts that represent ½, 1/3, and ¼
-Computers equipped with the Inspiration software
Development of Lesson
To prepare my students for learning, I will start off by asking questions related to a real-life situation that will grab their attention and have the begin thinking about fractional concepts.
"How many of you have ever had pie for dessert at Thanksgiving dinner or for another occasion? Did you have the whole pie to yourself? More than likely you shared that pie with other hungry guests. Therefore, your slice of pie was a fraction of the whole pie."
"Lets say you shared that pie with 3 other people, meaning your piece was ¼ of the whole pie. Now, lets talk about my Thanksgiving pie experience. Imagine if I had the same sized pie, but instead of cutting my pie into fourths, mine was cut into eights, and instead of eating one piece, I ate two. Which one of us ate more pie? Lets demonstrate this situation using our manipulatives on the overhead projector."
To start off, I will begin with the lecture-style format. I will be using the overhead projector and manipulatives to demonstrate the content being taught. Unlike the traditional lecture format, I will be asking questions and involving students in the explanation process in order to assess their levels of comprehension.
Once the lesson is explained, I will break the students up into small groups (4-5 students) to practice finding common denominators of pairs of fractions. The students will be working in their groups to solve written problems, with help of manipulatives, as well as creating a document using the Inspiration software to map out which fractions are equivalent to each other. Students will be reminded to recall the common factors the two denominators share as a focus for solving their problems.
Groups will be assigned to form based on heterogeneous skill levels. In this case, I believe it would be best to have higher-level students help out those who may need further explanation. While doing this, those higher-leveled students will be solidifying their knowledge of the content while teaching their peers. By using both a lecture format and small groups, both direct instruction and cooperative learning will be delivered to students.
For students that may need accommodations/adaptations, spend time working with those students and their small groups to further clarify the content while the other groups are working on their assignments. Manipulatives provide enhancement for visual and tactile learners, while the lecture part of the lesson accommodates auditory learners. For those students who may need step-by-step instruction, a worksheet with step-by-step example problems can be distributed on an as-needed basis.
To assess students' level of understanding, ask questions and setting up prompts during the interactive lecture at the beginning of this lesson. Prompt students by asking questions like "What's the next step?" in order to promote group response. While students are working in small groups, make sure to check on each group and have students demonstrate and explain the process they are going through to you. Towards the end of the lesson, have each student complete a few problems (individually) of your choice and explain the steps (in writing) they took in order to reach their solution.
To wrap up this activity, have students write a reflective statement in their journals, math logs, or on a loose-leaf piece of paper simply stating any concepts they have learned or are now clearer after completion of this lesson. Allow them to also express any questions or areas that may need more attention given to them as well. As an instructor, collect these reflective statements and see in which areas your students are confident and in which areas they seemed to be confused or find difficult. Take these accounts into consideration when teaching future lessons and revisit any troubled areas before moving on in the unit.