Lesson 1 of 12
Objective: Students will convert a rational number to a decimal using long division and know that the decimal form of a rational number terminates or eventually repeats.
To start the class, each student, using long division, will convert each of the following fractions into a decimal. Students will work individually for 4-5 minutes. As students are working, I can walk around and look at their progress. The progress that I see will help determine the groups created for the next segment of the class. Students will be grouped according to their ability. Students who are able to use the algorithm without any problems will be grouped together. Students who may need assistance will be grouped together. This way, there is no group leader who is showing everyone else what to do. Students who are struggling can work together, with my help, to find the solution. As groups compare their work, I want to make sure that students know the steps in the algorithm and have an understanding of the places in the decimal. I also want to hear in their discussion that they are comfortable with using the algorithm. Is anybody running into a struggle about the order of the steps? Can you show a classmate how to do the division? Does anyone need the acronym to help remember the steps? Once students have completed this section of the lesson, we will have a whole class discussion about benchmark fractions. Can my students describe benchmark fractions? Why are they referred to as benchmarks? What are they used for? What is their familiarity with the concept? Once we have discussed benchmark fractions and their understanding of the concept, I want them to recognize the relationship between the unit fractions and the corresponding decimals.
To continue the lesson, I will ask students to make a generalization about which denominators will result in a terminating decimal and which will result in a repeating decimal. Students will convert the next set of fractions into decimals using long division. We will finish the list of unit fractions up to the denominator 12. Students will work in the group to convert the fractions then check their work with a calculator. As students work in their groups, discussion questions and statements will be on the board for the groups to consider. I would like for students to make the connection between terminating denominators and the factors of powers of 10. Do students see that denominators that are composed of certain factors terminate at a certain place? During the discussion, if students don’t arrive at that conclusion, I will guide them toward seeing the connection. I want them to see the relationship between the division and place values in our decimal system.
I will ask volunteers to model the division on the SMARTboard to show what the long division looks like, step-by-step.
For homework, students will choose 5 fractions with denominators from 3 to 11, but have numerators that are greater than 1. They will do the long division algorithm for each of the 5 fractions to generate the decimal equivalent. Of the 5 fractions, students need to ensure they have one terminating decimal and one repeating decimal.