One of the goals for my high school is to develop a math/science partnership to help students make connections between the content areas. The commitment to this goal can be seen in our new building, where math and science classrooms are side by side rather than in different wings, as in a traditional facility. This opens up some unique collaborative opportunities for us since I now have daily access to the biological science teachers and the activities/labs they do in their classrooms.

Enter the AP Environmental Science (APES) teacher. She and I have collaborated before and actually took a week long workshop together last summer in an effort to see where our curriculums collided. Stat has the unique ability to fit in with so many curriculums that I could easily tie into just about any teacher's lesson plans if I truly tried. Anyway, earlier in the week, the APES teacher came to me with a lab she was doing that involved Chi-Square tests. Ultimately, the idea behind her lab was Natural Selection - the ability of a predator to find and kill their prey and the ability of the prey to hide from a predator. Her students had taken 3 types of beans and spread them into two differing habitats (aka the sidewalk and the grass) and recorded which prey was killed in each habitat. They organized the data into a table and that's where the Chi-Square Test came in. Now, I don't get to Chi-Square until April, but I had just finished contingency tables and segmented bar charts, so I was pretty bummed to miss out on such a neat collaborative activity.

Today was test day, so I went over to my APES neighbor and asked her for a copy of a couple of the labs she had mentioned so that I could read over them and jot down notes for next year. During our short chat, she mentioned another lab that she said she would find and bring over to my room. Low and behold if she didn't show up with this map:

With this lab, the students have to count the species of plants to determine the potential environmental impact of the plants. My students have already been through the idea that a census isn't usually practical and is oftentimes inaccurate. We have also discussed the different random sampling methods used to generate data. This lab will let them see a real example of cluster sampling and using that to estimate a population parameter. They will drop the yellow acetate square 10 times, count the various species in the square, find the average of their 10 trials, and then use a conversion factor to estimate the population parameter. The next day, each of my student pairs will get the data for one species, have to display it in both a histogram and boxplot, and then describe the distribution of their species. I'm thinking this will be a great summary of the material we've covered thus far.

If you have any other ideas on how to integrate math and science, please leave it in the comments... We're in the baby steps phase right now, but eager to learn more!

## Friday, September 23, 2011

## Wednesday, September 7, 2011

### What a great day!

Today was one of those days that you just feel good about. Lessons went smoothly, the a-ha moment happened at just the right time, and kids were engaged.

First off, let me preface this by saying that for the most part, I am enjoying teaching AP Statistics all day long. Sometimes I get into that "Did I already say that?" rut, but overall, it's fun to be sharing my passion for stat with the students. I kind of miss Algebra 2 and I definitely miss collaborating with my Algebra 2 buddies, but after a couple of years where stat got pushed to the back burner, it's great to have the time to really devote to engaging lessons and an active classroom.

Right now in AP Stat, we are deep into the Experiments chapter. This year I am trying to bring in more real life articles and having them analyze them. Last week we discussed the vocabulary of experiments and the required elements of experimental design, then ended the week by analyzing some articles. Each group got their own article and an analysis sheet. Working with their partner, they broke down the article using the language of statistics. That brings us to today.... When class started, each group (my kids are seated in pairs) had a copy of this article about the Placebo Effect. They had to read and discuss it with their partner, then write a summary of it in their warmup folders. Then we had a sharing session to see what they had found interesting in the article. That immediately got us thinking that if the placebo effect can be so powerful, how well does the REAL treatment have to perform to be considered the "winner". We had briefly talked about the idea of Statistical Significance earlier in the year, so I pulled out another psychological experiment (Zener Cards and ESP) and we tested our class for ESP. This lead us into a discussion of how many right answers they expected to get, how many they actually got, and if that was a big enough difference to convince them of our class's ESP ability.

Then the grand finale (and lead-in for tomorrow), I told them we needed to do some quick review of all of that vocabulary from last week. I pulled up the Fish Tank problem from the 1997 exam. (Can I just say I really *love* the Snipping Tool in Win7!) I asked the students to identify the experimental units, the explantory variable, the treatments, and the response variable. Then we designed a Completely Randomized experiment for the fish tanks. We sketched the experiment on the whiteboard, then talked about randomization. I had the groups discuss how they would assign the fish food and really had some great responses (spinners, dice, etc). When someone said "Put the numbers 1-8 in a hat and mix well", I played it up and said "OH MY GOSH! That's what I did too!!!" I brought out my paper bag with 8 poker chips and we assigned the treatments. In all of my classes someone then said "But wait!!! What about the Temperature issue???" That led to a great discussion on confounding variables and at the end of the hour, I left them with the task to determine how to assign the new and old fish food to the tanks with respect to the temperature issue. Tomorrow, their warmup will be to write down their method and we should be able to segue into blocking and why blocking reduces variability.

However, every great day usually has a bummer moment too. I plan to also talk about matched pairs tomorrow and wanted to intro it using the Boots problem, so when hubs was running errands after work, I asked him to check on some really cheap boots that I could use as a prop. For some reason, in past years, students have not really understood that the new water proofing method does NOT change the appearance of the boots, they look identical. I was hoping with the two physical sets of boots that the kids would get that you could assign one boot of each type to a person and see which one resisted water the best, but it was going to cost close to $50 for 2 pairs of boots and that was quickly vetoed!

Now to figure out the blocking dogs activity to see if I want to tackle that this week too. :)

First off, let me preface this by saying that for the most part, I am enjoying teaching AP Statistics all day long. Sometimes I get into that "Did I already say that?" rut, but overall, it's fun to be sharing my passion for stat with the students. I kind of miss Algebra 2 and I definitely miss collaborating with my Algebra 2 buddies, but after a couple of years where stat got pushed to the back burner, it's great to have the time to really devote to engaging lessons and an active classroom.

Right now in AP Stat, we are deep into the Experiments chapter. This year I am trying to bring in more real life articles and having them analyze them. Last week we discussed the vocabulary of experiments and the required elements of experimental design, then ended the week by analyzing some articles. Each group got their own article and an analysis sheet. Working with their partner, they broke down the article using the language of statistics. That brings us to today.... When class started, each group (my kids are seated in pairs) had a copy of this article about the Placebo Effect. They had to read and discuss it with their partner, then write a summary of it in their warmup folders. Then we had a sharing session to see what they had found interesting in the article. That immediately got us thinking that if the placebo effect can be so powerful, how well does the REAL treatment have to perform to be considered the "winner". We had briefly talked about the idea of Statistical Significance earlier in the year, so I pulled out another psychological experiment (Zener Cards and ESP) and we tested our class for ESP. This lead us into a discussion of how many right answers they expected to get, how many they actually got, and if that was a big enough difference to convince them of our class's ESP ability.

Then the grand finale (and lead-in for tomorrow), I told them we needed to do some quick review of all of that vocabulary from last week. I pulled up the Fish Tank problem from the 1997 exam. (Can I just say I really *love* the Snipping Tool in Win7!) I asked the students to identify the experimental units, the explantory variable, the treatments, and the response variable. Then we designed a Completely Randomized experiment for the fish tanks. We sketched the experiment on the whiteboard, then talked about randomization. I had the groups discuss how they would assign the fish food and really had some great responses (spinners, dice, etc). When someone said "Put the numbers 1-8 in a hat and mix well", I played it up and said "OH MY GOSH! That's what I did too!!!" I brought out my paper bag with 8 poker chips and we assigned the treatments. In all of my classes someone then said "But wait!!! What about the Temperature issue???" That led to a great discussion on confounding variables and at the end of the hour, I left them with the task to determine how to assign the new and old fish food to the tanks with respect to the temperature issue. Tomorrow, their warmup will be to write down their method and we should be able to segue into blocking and why blocking reduces variability.

However, every great day usually has a bummer moment too. I plan to also talk about matched pairs tomorrow and wanted to intro it using the Boots problem, so when hubs was running errands after work, I asked him to check on some really cheap boots that I could use as a prop. For some reason, in past years, students have not really understood that the new water proofing method does NOT change the appearance of the boots, they look identical. I was hoping with the two physical sets of boots that the kids would get that you could assign one boot of each type to a person and see which one resisted water the best, but it was going to cost close to $50 for 2 pairs of boots and that was quickly vetoed!

Now to figure out the blocking dogs activity to see if I want to tackle that this week too. :)

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