Scale of the Universe

Lesson objective: students can plot data of varying magnitudes on a semi-log scale.

This is a lab day, and students log on to find this website: http://htwins.net/scale2/lang.html

They then pick 12 objects of various sizes and write down their names and sizes in meters.  The interactive website displays data between the two extremes shown below, and naturally student choose some from each side of the spectrum, which makes it hard to graph using a base 10 scale

As students enter I hand them this worksheet that will guide them through the activity.  After they pick their 12 objects they plot them on semi-log scale graph paper.

Logarithmic Lions

Lions: 1,2,...many, logarithmic thinking.

This lesson was designed after a national geographic article I read some years back, and I wish I had a copy or knew the name of the article.

Here's the lesson:



Show this flip (its in Smart Notebook, sorry ActiveInspire).  Each student has to write down the number of predators they see, but I only show the slide for a fraction of a second.





Which leads to the idea that the human brain was wired to think logrithmically.  Evolution favored those who could discern the difference between 1 lion, 2 lions and 3 lions, but no favor is granted to those who can tell the difference between 9 and 11, as they are dead meat anyways.

This intro is a fun activity and is a non-threatening way to show semi-log scales.

Formal introduction to logarithms

Learning target: students can apply logarithms

DAY 1

1st I throw this puzzle at them, and they try to solve for the unknown with guess and check.  I give them about 5 minutes, which allows them to get close on about 3 or 4 of them.  One student may even figure out the relationship between 3=10^x and 30=10^x.

Common questions:
"Can we write on this?"
"How close do we have to be?"
"Is there an easier way to do this?"

then I introduce the common log as a way to undo a base, while first reminding them that they just learned how to undo a power (raise to the reciprocal power).

I solve 1=10^x by taking the log of both sides, and show how things reduce.  Then students find the rest of the values by using the log function. 

Then we talk about how this is all in base 10 and the 10 is not written but is implied.  Someone, almost on cue, asks "how do you solve if the base isn't 10?"  which leads us into the notes on uncommon logs.  I hand out a slip (calculator instructions) that students glue into their notebook, and go over this process.  then we do one example, base 3.

At this point I don't have time to prove the rules so I show them were they come from and we write them down in our exponent booklet. for example 2^3*2^5=2^(2+3)=2^8 leads to the log property log(a*b)=log(a)+log(b)

Exit slip: expand this logarithm

Day 2: We talk about how the scale they used in the Moore's law activity is a logarithmic scale, increasing by exponents. then we look back on the logarithmic lions, and talk about how the scale is adjusted.  then its back to logarithms rules in their booklet.  I will on the side also introduce natural logarithms but we wont work much with them.  Homework time.  This introduction on day 2 was too boring, and needs to be beefed up.  Also, I should have done a few more example on the homework packet before letting students loose.