To keep dust from settling on previously learned skills related to exponents, I included several problems in Warm Up today that will require students to recall and apply rules of exponents. In addition, they will convert two numbers to scientific notation.
As students work, I circulate through the classroom with my observation clip board in hand taking note of any student who is struggling with either of these concepts. I am keeping a particular eye out for the common misconception of adding the same number of zeroes as the exponent instead of moving the decimal.
After completing the warm up review, I explain to students that today, I would like for them to do a Heads Together activity where they will work with a partner to create a set of written steps explaining how to take a number in scientific notation and expand it into standard form. Once they finish their set of instructions, I want them to give it to the other pair at their table to test out.
After 6 minutes, I ask volunteers to read their instructions while I follow along with a sample on the smartboard, intentionally feigning ignorance with any vague instruction. For example if directions given by a student say move the decimal six places, I ask, "Which direction do I move?"
Once I have finished following the first set of directions, I ask if any other group has different instructions for me to follow. If so, I model those instructions as well.
While this activity may seem counter-intuitive, I have found that when students are asked to analyze a process and then articulate it, individual sense-making improves long term storage of the concept.
To put their newly created instructions to use, I introduce Let's Practice! I provide five numbers in scientific notation for them to write in expanded form. After five minutes, I pull sticks (with names of students) to come to the board and share their answer. I ask them to use appropriate academic vocabulary (significant digit and exponent) as they explain their work. If they forget to do so, I remind them.
To provide additional practice in a more engaging format, for today's Work Time, I created 3 scientific notation puzzles for students to solve. I run them off on three colors of paper so they can be easily told apart. I then cut them up and put them into envelopes. When the pieces of the puzzle are properly matched and arranged, a rectangle is formed.
I begin the activity by giving each pair of students one puzzle. Students can use scratch paper to determine appropriate matches. When the puzzle is complete, I give them one of the remaining two to solve. My goal is for each pair of students to complete at least one puzzle during the 15 minute work period, but my stronger students will easily complete two or even all three.
After 15 minutes, I ask student pairs to share their strategies for solving the puzzles. Many groups use the strategy of starting at the upper left corner and working across. I applaud them for making good use of Math Practice #7: Look for and make us of structure.
For closure of today's lesson, I want students to create a Ticket Out the Door. I give each student a blank index card and tell them to create two numbers, one very large and one very small (smaller than 1). I then tell them to express each number in scientific notation. The student responses on these cards provides me ample evidence that students are ready to move on to applying basic arithmetic to numbers in scientific notation.