Day 34: Multiplying with Scientific Notation

Quote of the Day: “Some people, when they do someone a favor, are always looking for a chance to call it in. And some aren’t, but they’re still aware of it - still regard it as a debt. But others don’t even do that. They’re like a vine that produces grapes without looking for anything in return...after helping others...They just go on to something else...We should be like that.” - Marcus Aurelius, Roman emperor

Question of the Day: Why is it that 40 times 10 to the 6th power is 40,000,000 and why is this incorrect with scientific notation?

Regular Math Objective: Multiply using scientific notation

Regular Math Standards: 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 

Regular Math Lesson Sequence:

1. QSSQ. I had the students answer the question which was why is it that 40 x 10 to the 6th power equals 40,000,000 is correct, but also incorrect. It was great conversation around scientific notation. 
2. Robert Kaplinsky lesson on How Many Stars in the Universe. It was fun to notice when I asked students to multiply the numbers in the video that they all defaulted to standard form. 
   
3. We did a chart of four different multiplication of exponents problems. In it students used two methods. If I could have this back, I would focus entirely on the method of having students multiply coefficients. It goes against the theory of letting students discover it for themselves, but in having the students do it both ways, they completely missed the convenience of multiplying coefficients and more importantly the base ten numbers. They also lost track of keeping the answers in scientific notation. 
4. The exit ticket came fast today. The majority of students could not complete the chart. 

Not surprisingly when my lack of directions on the ticket to leave lack directions the students calculate the answer in standard form. Note to next year: change the directions so that they say write in scientific notation. Despite that, the student above did use scientific notation on the second problem. Just had some issues with the decimal where the student was trying to slide the decimal over two spots with the base ten and in reality the number is actually less than one. Pretty normal error all things considered. 

This error of getting a coefficient greater than ten continues to haunt us. Past screaming and throwing things, I don't know how else to reteach except to say the same stuff again and again. I like this photo cause you can see me in the shadow taking the picture. Behind the magic if you will. 

The student in this answer does manage to get the coefficient between 1 and 10, but fails to change the exponent. What I am going to do to help clarify this issue is take the factors in a problem like 4 x 6 and divide one of the factors and ask students if I would still get the same answer if the other factor remained the same. 

Honors Math Objective: Multiply numbers in scientific notation

Honors Math Standards: 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 

Honors Math Lesson Sequence: It was very similar to regular math in terms of the objective and standard, but we got there a different way. First, since students had such a rough time on the exit ticket the previous day, I did something called "Wildfire." I had the students go throughout the classroom and ask around for help on their exit tickets. Virtually every student had something right and something wrong on this exit ticket so it was an appropriate way of trying to get students to understand their mistakes and teach what they thought they knew. I simply acted as another student so that my answers could be cloned for other students to teach. The activity took longer than I would have liked, but based on the dialogue I was having and the students were having it was necessary.

Next, I used this sheet which was required more independence and bridging connections between what they knew already and what they did not know. Students also took note of how the exponent changed when the number was greater than ten, but remained the same if it was less than ten. Unfortunately, with everything that we accomplished in this explore activity we did not have time for an exit assessment.