MthEd 377 Lesson Plan
Cover Sheet
Name: Jefferson Hall / Date: 9/7/2005Section Title: Fractions and Mixed Numbers (2.2)
Big Mathematical Idea:
Non-whole numbers can be expressed by breaking areas down into parts with the same area. Shape are not important as long as the area is the same. The number of equal parts that it would take to make the whole is the denominator. The number of equal parts it takes to make the number you are representing is the numerator.
Why is this topic important?
Fractions are the simplest method of representing non-whole numbers. It is important to understand the basic concept of a fraction before you can learn how to perform arithmetic on fractions.
How does this lesson fit in to the overall unit? (i.e., How does this lesson build on the previous lessons and how do subsequent lessons build on it?)
This entire module teaches how to perform arithmetic on fractions. It fits right after module 1 which focused on arithmetic for whole numbers. The first section in the module taught about basic shapes to prepare for this section which represents fractions with shapes. The concept of a fractions, as taught in this lesson, is the basic method of representing non-whole numbers used in the remainder of the module. In essence, this lesson introduces the concept that the module is all about.
Grading rubric (for Keith’s use)
5 The Big Mathematical Idea addresses core mathematical concepts and is clearly articulated
5 Description of the importance of the topic is well thought out and relevant
5 There is a clear, insightful discussion of how this lesson fits in to the mathematical content of the overall unit
5 Lesson sequence is well thought out and detailed
5 Students' thinking is anticipated with forethought and detail
5 Reactions to students' thinking is mathematically oriented, insightful and detailed
10 3-5 reflection paragraphs demonstrate thoughtful reflection and are clearly articulated / 10 Met with Dr. Leatham and made appropriate revisions based on this discussion
30 3-5 page reflection paper demonstrates thoughtful reflection and is clearly articulated
Lesson Sequence: Learning activities, tasks and key questions (what you will do and say, what you will ask the students to do) / Time / Anticipated Student Thinking and Responses / Your response to student responses and thinking / Formative Assessment, Miscellaneous things to remember /
Launching the Lesson
1. Draw a circle on the board divided into five equal parts and ask how many parts its divided into.
2. Use this example to explain what a denominator is.
3. Shade two of the wedges in the picture and ask how many 1/5 parts are shaded.
4. Use this example to explain what a numerator is.
5. Ask for 2 volunteers to divide a geoboard into 2 equivalent halves and show the 2 example halves from the teacher sheet. / 1. Students should understand the numerator and denominator.
2. Students may not understand that the parts need to be equivalent to add them together.
3. Students should understand that the first teacher example is half the geoboard since the parts are the same.
4. Students may have trouble with the second example since the parts aren’t the same. / (2.) If this concern arises, explain that it will be dealt with in later lessons.
(4.) Explain that the area is what determines the part and that the shape is not important.
Orchestrating the Task
1. Divide students into four equal groups and give two groups form A of the worksheet and the other groups form B of the worksheet.
2. Have students use one geoboard per group and agree on the solutions to the given problems and then draw them on their handouts / 1. Again, students may have trouble. With making shapes with parts that are different shapes.
2. Students may disagree about how to do it.
3. Students may have trouble understanding the last problem where the numerator is greater than the denominator. / (1.) On their boards, give them examples of two different shapes with the same area to illustrate the concept.
(2.) Encourage them to work together and ask appropriate leading questions to get them back on task.
(3.) Explain that fractions can represent non-whole numbers greater than the whole. / Encourage students to be creative in their solutions and to try to get a solution that the other group will not.
Facilitating the Discussion
1. For each problem:
a. Have a person from each group (different person each time) draw their solution on the board.
b. Have them explain why their solution is correct.
c. After each round of solutions, open the class to discuss what they do and don’t understand.
2. After the last problem ask if anybody had trouble with the fraction larger than the whole.
3. Ask if there were any other problems that the class encountered. / 1. Students should have been able to discover the basic principles of the fraction through the activity.
2. Students will probably have a little trouble with numbers greater than the whole. / Concerns with numbers greater than the whole should be discussed and the principles should be explained.
Any other concerns should be dealt with as students ask questions.
Debriefing the Lesson
1. Ask for students to explain what they understand about fractions as a way of expressing non-whole numbers. / By this time students should have a fairly solid understanding of the basic fraction. / Where necessary, ask leading questions to help correct students understanding.