For today's Warm Up assignment, I have given students two problems that review the previously learned concepts of subtracting and multiplying with numbers in scientific notation. I wanted students to have the opportunity to determine strategies for each in preparation for today's lesson.
Once the five-minute timer sounds, I select student volunteers (from sticks in a cup) and then ask the class to verify each student's work.
Once the class has reached consensus on the Warm Up assignment, I quickly display the day's Learning Objective for the class. I remind students that we have already learned how to work with adding, subtracting, and multiplying numbers in scientific notation, and today we will learn how to divide numbers expressed in it.
Rather than telling or showing students an algorithm for dividing numbers in scientific notation, I will again show examples of simplified problems and explain that we are Identifying Patterns we see. After sharing the first two examples, I ask a pre-selected student (whom I chose based on what s/he wrote about in his/her journal) to share.
I then show the next two examples and ask if the patterns seen on the previous two problems still fit. I then encourage students to record a procedure in their own words for what is happening. This "recoding" allows students to think about what they are doing mathematically in their own voice so it is likely to make more sense to them in the future.
Once students have written their procedures in their journals, I reveal four problems on which students can practice. I reveal only two questions at a time so that I can watch for misconceptions and correct them before a student has completed too many problems. Once the class has practiced the first four problems, I reveal the second set of problems.
Once the majority of the class is confident in their ability to solve problems dividing numbers expressed in scientific notation, I distribute the Work Time Dividing Sci Not Cards to each students. On each card is a division problem, which they must solve. After solving all eight problems, I then want students to order the answers from least to greatest. This requires students to order numbers in scientific notation, which they can do employing a variety of strategies.
When the Work Time timer sounds, I bring the class back together for consensus building.
In Building Consensus among the students, I randomly select volunteers to share the answers they found from least to greatest and record them on the SmartBoard. I then ask if anyone found a different order. Typically, there are one or two cards that cause some critical discussion which leads us to the conclusion that we must write the answers in standard form in order to "prove" to others the correct order. This strategy allows students another opportunity to utilize skills learned previously in the unit.