Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will develop and use an algorithm for solving all types of fraction division problems.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with the basic multiplication and division facts; know how to multiply fractions; know how to change a mixed number to an improper fraction; know how to change an improper fraction to a mixed number; be familiar with modeling and representation techniques for math problems.
Guiding Questions: What are the guiding questions for this lesson?
Are students thinking about an algorithm as they reason through fraction division?
Are students able to explain how and why fraction division works through models, manipulatives, and verbal expression?
Teaching Phase: How will the teacher present the concept or skill to students?
- After the bell work and class discussion, teacher will place 3 more problems on the board, such as:
- 7 divided by 1/3, 12 divided by 3/4, and 5 divided by 1/4
- Students will work in pairs to solve these problems, with the teacher monitoring how the students are solving, whether using the standard algorithm or using models or logical reasoning. As teacher walks around, note special papers that would serve as excellent examples for their reasoning, correctness or incorrectness.
- After an appropriate time (use a timer), teacher will call back the students to a whole class structure and discuss the problems. Present student papers that you noted were of interest and discuss what is happening with the problems. See if some students changed the fractions to decimals before they divided, or if they used an interesting model. Steer the students towards why and how the answers worked out and keep them on that trail. Do not give away the algorithm too soon, as we want students to understand the logic of fraction division, not just the rote mechanics.
- Present more complicated problems and follow the suggestions above.
- 1/2 divided by 2/5, 3/4 divided by 2/3, 5/8 divided by 1/4, 3/5 divided by 5
- Present more complicated problems and follow the suggestions above.
- 3 1/2 divided by 1/2, 5 2/5 divided by 2/3, 4 3/5 divided by 2 1/2, 5 2/5 divided by 6
- Discuss these problems as described above. Students should be heading towards the algorithm that division involves multiplying the first number by the reciprocal of the second number. If more examples are needed for students to see this, give more examples and demonstrate models as necessary.
- Once students understand the how and why the algorithm works, they should be encouraged to use the algorithm for the sake of mathematical efficiency.
- In the above problems, be sure to discuss how a whole number is essentially a fraction with a 1 in the denominator (many students forget this), and that mixed numbers need to be changes to improper fractions before working with them.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will be provided with worksheets from CMP2 Bits and Pieces II Additional Skills and Practice, but other worksheets with fraction division problems can be used. Try to make sure the worksheet contain all types of fraction multiplication problems utilizing fractions, whole numbers and mixed numbers. When students are working on the worksheets, walk around the class monitoring for completion and correctness of work. Encourage students to show all their work. It is crucial that work is shown so that mistakes can be pinpointed and corrected before the incorrect thinking gets too far.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
A possible activity can be the Kagan structure called Pairs Check. See PairsCheckworksheet.docx.
More independent practice activities can be additional worksheets, or index cards with more fraction division problems.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will be required to write the algorithm for dividing fractions in their notes to avoid any confusion or forgetfulness.
There are many ways students remember the algorithm for dividing fractions. One of the most common is "Dividing fractions is easy as pie; Flip the second fraction and multiply". These kinds of reminders should be used with the caveat that students should know why the algorithm works and that "flipping" the fraction means using its reciprocal.
Algorithm for the notes:
- Keep the first fraction, switch the divide to a multiply, and use the reciprocal of the second fraction. Multiply as usual.
- If there is a mixed number in the problem, change it to an improper fraction.
- If there is a whole number in the problem, make it a fraction by putting a 1 in the denominator.
- Students can also be split into groups of 2 to 4 to make creative posters of the algorithm in their own words and examples.
Many students this age are familiar with the Miley Cyrus tune "Party in the USA". My class sings these words to the "Party in the USA" tune:
- So I put my hands up I'm dividing fraction, Keep Switch and Flip.
- Keep Switch and Flip; Keep Switch and Flip
- So I put my hands up I'm dividing fraction, You know I'm gonna be OK
- Yeah.....Keep Switch and Flip; Yeah...Keep Switch and Flip
(This means keep the first number, switch the divide to a multiply, and use the reciprocal of the second number. For "Keep" the hand movement is both hands palms out like meaning "stop"; for "Switch", the hand movement is making an X by crossing the forearms; for "Flip", the hand movement is a hand rotation almost like the signal for traveling in basketball.)
Students will be assessed using fraction division problems as a PairsCheckworksheet.docx . Further impact of dividing fractions will be assessed in other lessons using more complex examples and story problems.
The bell work will be an activity for writing what all students know and remember about dividing fractions. The students will be encouraged to come up with examples or key words or phrases they may already know. After a 3-4 minute period, students will pair up and share their responses with a partner. Teacher will call on partners for their feedback. Teacher will assess the breadth and depth of students' prior knowledge and proceed accordingly.
At this point, teacher may use one of the examples students mentioned or place a predetermined example on the board, such as 7 divided by 1/2 and ask how this would be solved. Students will be given time to think and share ideas with partners. Students will be asked to share ideas with the class. Some students may mention thinking about how many halves are in 7, or if there are 7 candy bars split into halves, how many pieces there will be. Encourage students to draw models of their thinking or use fraction strips. Students may even remember the algorithm for dividing fractions from previous experience.
Feedback to Students
Students will receive feedback throughout the lesson. During class discussion after the bell work, students will be called on randomly and/or raise their hands to answer questions about the problems placed on the board. Students will be monitored while working independently and in pairs for correctness of their procedures and their work. Students will be called back to a whole-class discussion and checking for understanding.