To start the class we will review what we covered in the previous lesson (Converting Fractions). We will review their findings with the fractions and discuss the distinctions between terminating and repeating decimals. The entrance ticket will be to answer the following question: What is the difference between a terminating decimal and a repeating decimal? As students respond, I can check their writing to see if they can express a distinct difference between the two. If I notice some struggling students or incomplete answers we can talk about them as a whole group. I can ask other students to explain steps or discuss their own answer to help clear any confusion. We can put select answers under the document camera to share with the class. We can improve responses that need additional work.
In the lesson today, we will work with fractions using the same denominators we used in the previous day’s lesson but with different numerators. After our fraction discussion, we will talk about the definition of rational numbers. Students should be familiar with the definition of rational numbers. After working with the fractions during the previous lesson, they should now recognize and understand all parts of the definition. They will have worked with ratios written in the form of a/b, where b does not equal 0. They will also have determined both terminating and repeating decimals when the algorithm is applied to convert the fraction into a decimal. This whole class discussion will lead us into the group activity.
For the group activity, students will work in their groups to discover patterns in the fractions they are converting while practicing mastery of the algorithm (MP7). Student groups will receive denominators and will convert the fractions into decimals using numerators greater than one. For example, if a group is assigned the denominator 8, they need to convert the fractions 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8 . We will use the discussion questions we used in the previous lesson to guide their thinking as they work on the conversions. Do students see that denominators that are composed of certain factors terminate at a certain place? How did they decide where to stop dividing? How did they decide when a decimal was repeating? Were there any fractions that made them divide more than they thought they would? What patterns do you see as you are converting your fractions? After students finish the conversions, they can check their work with a calculator. To share their work, each group will pick one fraction they thought was easy to convert and one fraction that gave them trouble or they didn't like. Either using the SMARTboard or the document camera, each group will come up and demonstrate what they did with the two chosen fractions. I will use the discussion questions they were given to probe their thinking.
To end the lesson, I will assign the homework and give students time to begin the assignment in class. The assignment is similar to the previous day’s assignment but they will use numerators greater than 1 when converting. I want to see that they can work through the algorithm, individually.
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. The denominators chosen must be any other denominator than the one they were assigned in class for group work. Included in their homework, students need to describe the patterns they see as they make the conversions.