Day 33: Scientific Notation Mistakes

Quote of the Day: “Provide employees with what I call ‘Goldilocks tasks’ - challenges that are not too hot and not too cold, neither overly difficult nor overly simple. When what they must do exceeds their capabilities, the result is anxiety. When what they must do falls short of their capabilities, the result is boredom. But when the match is just right, the results can be glorious.” - Daniel Pink

Question of the Day: Why is 12 x 10 to the third power not scientific notation?

Regular Math Objective: Write numbers in scientific notation; determine why a number is not in scientific notation and change it so that it is in proper scientific notation

Regular Math Standards: 8.EE.3 Use numbers expressed in the form of a single digit multiplied by an integer power of 10 to estimate very large or very small quantities, and express how many times as much one is than the other. 

Regular Math Lesson Sequence:

1. Visual Pattern #32
2. QSSQ
3. Review Exit Tickets (so many students put 12 instead of 1.2)
4. Correct the mistakes. I got this idea from the Math Assessment Project

Here were the four problems:

3 times 10 to the negative 3 = .0001

This was designed to get kids to stop thinking that since the exponent is three we put three zeroes.

40 times ten to the sixth = 40,000,000

This was put on there to revisit our question of the day. I screamed at students in a ridiculous monologue upfront on the question of the day that they would fail to execute on this exact idea later in class. Sure enough they forgot even though I screamed at them. The great news is that now they are really registering this idea. 

0.5 times ten to the negative second = 0.005

Again students were unable to recognize that the number that is the coefficient needs to be under 1. I failed to call it a coefficient today so we need to drill that in tomorrow.

4 x 10 to the negative second < 8 x 10 to the negative fourth

Students were actually able to quickly point out that the inequality should be flipped. I know. That's pretty much the only way to fix the mistake (well not the only way but you know what I mean). What was cool though was that they got the why in there too.

Honors Math Objective: Write numbers in scientific notation; determine why a number is not in scientific notation and change it so that it is in proper scientific notation

Honors Math Standards: 8.EE.3 Use numbers expressed in the form of a single digit multiplied by an integer power of 10 to estimate very large or very small quantities, and express how many times as much one is than the other. 

Honors Math Lesson Sequence:

1. Exponents Exploration. The link is a Google Doc. I messed up question 1 as I wrote the numbers backward, but other than that it was pretty effective way to show students that they just multiply whatever the coefficients are and then multiply the differences in the exponents as a base ten. The harder part was when there was a coefficient that was larger and an exponent that was smaller. Something like 7 x 10 to the 3 versus 4 x 10 to the 5. I had students just do the  math all the way out in standard form, some estimated, and others use division. I honestly was just hoping that they could do the estimation and know to take the base 10s and divide by the number that separated the coefficients. 
2. Exponents Exploration II. 
3. Exit Ticket from MARS. See the pictures below. The results were less than desirable. Tomorrow we will just have to build off of this.