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MthEd 377 Lesson Plan Cover Sheet Name: Jefferson Hall Date: 9/7/2005 Section 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 OR 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) 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. 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 Anticipated Student Time Thinking and Responses Your response to student responses and thinking Formative Assessment, Miscellaneous things to remember Launching the Lesson 1. Students should (2.) If this understand the concern numerator and arises, explain denominator. that it will be 2. Students may dealt with in not understand later lessons. that the parts (4.) Explain that need to be the area is equivalent to what add them determines together. the part and 3. Students should that the shape understand that is not the first teacher important. 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. Orchestrating the Task 1. Again, students (1.) On their may have boards, give trouble. With them making shapes examples of with parts that two different are different shapes with shapes. the same area 2. Students may to illustrate disagree about the concept. how to do it. (2.) Encourage 3. Students may them to work have trouble together and understanding ask the last problem appropriate where the leading Encourage students to be creative in their solutions and to try to get a solution that the other group will not. Lesson Sequence: Learning activities, tasks and key questions (what you will do and say, what you will ask the students to do) Anticipated Student Time Thinking and Responses numerator is greater than the denominator. 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. Your response to student responses and thinking questions to get them back on task. (3.) Explain that fractions can represent nonwhole numbers greater than the whole. Facilitating the Discussion 1. Students should Concerns with have been able numbers greater to discover the than the whole basic principles should be of the fraction discussed and the through the principles should activity. be explained. 2. Students will Any other probably have a concerns should little trouble be dealt with as with numbers students ask greater than the questions. whole. Formative Assessment, Miscellaneous things to remember Lesson Sequence: Learning activities, tasks and key questions (what you will do and say, what you will ask the students to do) 1. Ask for students to explain what they understand about fractions as a way of expressing nonwhole numbers. Anticipated Student Time Thinking and Responses Debriefing the Lesson By this time students should have a fairly solid understanding of the basic fraction. Your response to student responses and thinking Where necessary, ask leading questions to help correct students understanding. Formative Assessment, Miscellaneous things to remember