Scatter Plots and Best Fit Lines

This week, my math class studied scatter plots and best fit lines. This definitely is not the most exciting concept to teach, so I looked for other ways for students to become more engaged. Lucky me, I found several activities that were a big hit!

Scatter Plots

The first concept that students needed to learn was how to create a scatter plot. As eighth graders, students were familiar with creating a scatter plot from given information. However, I wanted to challenge them to look at the association of the graph. Is it linear or nonlinear? Positive, negative or no association?

Once the class felt pretty confident in identifying these types of associations, I gave them an activity that really peaked their interests: favorite foods! This activity is a word document created by Erica Chauvet from Trinity High School. 

First, students individually rank their favorite foods from 1 to 10. Next, students pair up and create coordinates based on what their favorite foods are in order to compare them. They plot their coordinates and look at the graph to see what type of association they have! Strongly linear graphs would demonstrate more similar tastes in food!

Best Fit Lines

The next step meant teaching students about the best fit lines. I knew this concept would challenge a few of my students, so I wanted to show them the concept of WHY this was important. I believe this game was one of my best finds yet! XP Math has several games for students in all grade levels, and Naruto: Line of Best Fit had students learning math without even knowing it! In fact, I had several kids go home and play that night on their own!

The idea of the game is to help Naruto capture as many scrolls as possible by moving the line. Students are then introduced to the concept of creating a line that will be in the middle of the most points possible-the same idea of a best fit line! When I introduced best fit lines the next class period, I actually continually referred to making their lines “like Naruto” and capturing as many “scroll” points as possible!

Taking It Further

I wanted to stretch some students even further in their thinking of these concepts, and I found one more activity that would help with this on Desmos.com. If you have never used this website for math activities, try it now! Teachers can give students a login code and once each individual logs in, the teacher can monitor the progress on their own screen! When I have students do an activity here, I know exactly which question each student is on AND can see their answers. There are options to “freeze” all students’ screens when you need to explain something or “pace” students so they can not go through the questions too quickly!

Anyway, there was an activity that related to best fit lines on Desmos as well. The activity got students thinking about residuals as well, which was above our 8th grade standards, but a great introduction to future math concepts!

If you teach a middle school math class, I encourage you to check out some of theses resources! Even if you do not need to teach scatter plots, these have great options for other math concepts as well!

 

 

Population Extinction Game

Last week I posted about how to simulate counting populations using the “Capture-and-Release-Method.”  (Click here to see!) This week, continuing on the population theme (and using dried beans in the classroom), I wanted to share a population extinction game!

I found this activity on tes.com, which is a site that contains many different lesson plans for teachers. And it is free to register! Click here to see the lesson (although you may have to sign up to actually see it).

The activity uses the Wild Atlantic Sturgeon as an example population, however you could adapt it to any type of animal you would like. The link directs you to the instructions for the game, and a simple game board – a paper with boxes numbered 1-6. It also includes a chart where students can record their data.

Materials needed:

  • Instruction sheet, game board and data sheet (can be downloaded for free from the website!)
  • 20 small items of something (I used beans, but the instructions say paper clips)
  • A cup of extra items for each group (they may need more!)

Procedure:

  1. Give each group of students 20 beans (or whatever you chose to use) to start off with.
  2. Students toss/drop the 20 beans onto the game board
  3. Any beans that land on sections 1 and 3 are considered “extinct” and are removed from the game.
  4. Any beans that land in section 5 “reproduce” so you add another bean for each.
  5. Beans that land on any of the other squares are kept with no changes.
  6. Students record their numbers in the chart provided, then repeat steps 2-4 with any beans they have left for 10 total rounds.

Over time, students should notice the amount of their sturgeon slowly declining!

Discussion questions to use:

  • What years did you gain the most?
  • What years did you lose the most?
  • Did your population of sturgeon become extinct? Why are why not?
  • If so, how many years did it take?
  • Why do you think your population declined?

Capture and Release! Estimating Population

Just how do scientists know how many deer live in an ecosystem? How did they figure out the number of giraffe live in the African savanna? Where do ecologists get these numbers from?

These are some of the questions that my class discussed while studying changes in population and population density. Students guessed how this was accomplished: using satellites, sending people out to look around a lot, catching some of the animals and then bringing them back to the wild, looking at a small area, then estimating.

Although some responses seemed more on track than others, I wanted students to simulate one way scientists do this! The capture-mark-and-release method is the one we chose to try. And because I already had a bag of dried beans from a different lesson, that is what we used as our population!

Materials 

  • Dried beans (these represent the “animal”. You can also use dried pasta, packaging peanuts, or another low cost, small item that can easily be marked)
  • A bag or other container
  • Marker

Set up:

Before beginning the activity, I had divided up the beans into cups for each group of 2 to 3 students. I did not count the number, but used a few handfuls.

I created a chart for students to use like the one below

Estimating Populations Chart

Procedure:

  1. Students first grab a handful of beans from their cup and mark each one that they removed with a marker. Count how many beans were marked and record this on the chart.
  2. Return the marked beans into the container and shake the beans.
  3. Grab another handful of beans from the container.
  4. Count how many total beans are in the new sample, and then how many marked beans were in the sample. Record both numbers on the chart.
  5. Using the formula below, students calculate how many beans are estimated to be in their container.
  6. Repeat steps 3-5 again, recording the numbers on the chart.
  7. Once students have recorded the data, the group can make one final estimation of how many total beans they believe to be their container.
  8. Finally, students count the number of beans they have and compare this number to their estimations!

How does this simulate what scientists do?

Those that study population densities of different organisms will often use this method of capture-count-and-release. A group of organisms is captured and marked with a device or tag. Later in the year, or the following season, scientists will capture another group of that organism and see how many have been previously tagged. If there are only a small number of tagged organisms, scientists assume there is a larger population. If many of the organisms already contain tags, then the total population may be quite small. By using the bean simulation, students can begin to understand this process!

Questions to discuss:

  1. Compare the bean simulation to real life. What is alike and what is different? You might bring up that beans do not die or give birth, so the population will remain static (as long as no beans get lost under the table!). Live organisms always have changing populations, so this would affect the number of organisms in an ecosystem.
  2. How precise is this method? When students compared their estimations to the actual number of beans, they found that some groups were pretty close in their estimation, while others were not. We noticed a pattern of groups that had marked a higher sample initially also had more accurate estimations!
  3. Can this be used for all organisms? When I asked this question, students in my class determined that this would be very difficult to use for types of insects or other very small creatures. Larger animals would work better!

Reaction Time – Testing Your Nervous System

In the course of our human body unit, we have just wrapped up the nervous system. Part of the discussions included how our brain can send and receive messages to other parts of the body through neurons. Sometimes, these messages are sent almost immediately, without us really thinking about the process (think about when you touch a hot stove!). Other times, our brains take a little longer to process what needs to be done.

To demonstrate this point, the class did a quick reaction time lab. I first found this lab at TheHomeschoolScientist.com and I’m so glad I did! It was a blast!

For the lab, all you will need is a ruler or meter stick, and a conversion chart like this one:Image result for reaction time table If you don’t have a conversion chart ready, simply use the inch marks as your indicator!

You can get the entire lab and worksheets for free by visiting TheHomeschoolScientist.com and signing up!

Round 1

  1. The student being tested holds their hand out, ready to catch the ruler.
  2. Another person in the group holds the ruler with the end of the ruler (the “zero” inch mark) right above the blindfolded person’s thumb
  3. The person holding the ruler will drop the ruler without warning, and the student being tested must grab the ruler as quickly as possible.
  4. Check what inch mark the top of the student’s thumb is resting on.
  5. Record the number, then use the conversion chart to see the reaction time (if using the conversion chart)
  6. Repeat this process two more times. Students then find the average of all three trials.

Students had a great time watching each other try to catch the ruler as quickly as possible!  

If your students seem ready for the next challenge, gather several blindfolds and have students test their reaction time in a slightly different way!  

Round 2:

  1. One person in the group is blindfolded and holds their hand ready to grab the ruler
  2. Another person holds the ruler with the 0 inch mark right above the blindfolded person’s thumb
  3. The person holding the ruler counts, “1, 2, 3, Go!” and drops the ruler on “Go”
  4. The blindfolded student listens for “Go” and grabs the ruler.
  5. Another group member takes note of how far down the ruler went and sees at what measure the student’s thumb is near and record the time using the chart.
  6. Repeat this process two more times. Students then find the average of all three trials.

**If you do not have anything to use as a blindfold, just have students put their heads down on their desks and close their eyes. This can be way easier than messing with making the blindfolds just right around kids’ heads.**

Follow up questions to ask students:

  1. Which method did you have the quickest reaction time?
  2. Was this the better method for everyone in your group? Explain.
  3. Why might some people’s reaction time be faster than others?
  4. What errors may have occurred that would affect the outcome of this experiment?

Blender Muffins

I happened to stumble upon these blender muffins when my son wanted to “cook” with me. He loves baking cookies, muffins, or anything else that uses my stand mixer. We also had a few bananas that desperately needed to be used. This time, I found a recipe that uses the blender. Intriguing!

Turns out, this recipe was super simple, gluten free (there is no flour!) with mostly healthy ingredients. And of course, pressing buttons on the blender was a huge hit with my son! He asks to make these blender muffins often!

The original recipe can be found here at Iheartnaptime.net 

I made a few changes and added whatever mix-ins we had to the muffins. Chocolate chips and blueberries made the list, but really, any type of nuts, berry, or even adding some peanut butter would work!

The recipe makes about 12 regular size muffins.

Ingredients:

  • 2 ripe bananas (I usually keep overripe bananas in the freezer. Once thawed, these make excellent, moist muffins!)
  • 2 cups old fashioned oats
  • ½ cup unsweetened applesauce
  • ¼ cup Greek yogurt
  • ¼ cup brown sugar
  • 1 egg
  • 2 tbsp honey
  • 1 ½ tsp vanilla
  • 1 tsp baking soda
  • 1 tsp baking powder
  • ½ tsp salt
  • ½ tsp cinnamon

Mix-in options – almonds, walnuts, blueberries, raspberries, chocolate chips, butterscotch chips, peanut butter chips, raisins, coconut, etc.

Directions

  1. Place bananas, oats, and applesauce to the blender. Pulse for a few seconds until oats are slightly more smooth. Add all other ingredients and blend until well combined and mostly smooth.
  2. Add in any mix-ins that you would like and stir with a spatula (so the mix-ins don’t get crushed up!)
  3. Pour batter into muffin liners two thirds to three fourths full. You can add more mix-ins to the top of the batter if you would like! The muffins will rise as they  bake, but flatten out once they come out of the oven.

Bake muffins at 400 degrees for 13 – 15 minutes, or until a toothpick comes out clean.

While you can eat the muffins right out of the oven, they freeze well too, which makes a great grab and go breakfast on those busy mornings. Make sure you allow the muffins to cool completely, then put them in a Ziploc bag or wrap with a few pieces of plastic wrap. You can thaw in the fridge or by zapping them for a few seconds in the microwave.

Enjoy!

Lung Capacity Lab

Want to know how much hot air middle school students have? Try this lung capacity lab. Students will be able to see how much air their lungs can hold!

The human body unit is once again upon us! Because I’m using a new curriculum this year, I’ve made some adjustments to how I go about teaching. However, a few labs are tried and true that I will definitely keep! This was one of them. It is so easy. Grab a balloon and a ruler for each student, and you’re set!

Warning:

Giving middle school students balloons does have some risks. Be prepared to hear many balloon squeals and other noises that sound like body functions. I warned the students in advance that no balloons should be released across the room.

Now to the lab:

Once students have received their balloon, they will use it to measure how much air their lungs hold. We compare the difference between vital capacity and tidal capacity of their lungs.

Vital capacity – the maximum amount of air the lungs can hold.
Tidal capacity – the normal amount of air that your breathe in and out.

Procedure:

 

  1. Students take a deep breath and blow up the balloon as much as they can with that one breath. Hold the balloon (do not tie it!) and measure the diameter with a ruler, recording this length.
  2. To find the volume, you can use the formula for the volume of a sphere (although the balloons aren’t perfectly sphere, this gives a pretty close measurement). Or, I give my students a graph that they can use to estimate the volume like this one, which is found l here at Biologycorner.com.
  3. Repeat this two more times, then find the average of all three.
  4. Next, students take in a normal breath and breathe it into the balloon. Be careful not to push too hard! This should be a normal breath.
  5. Record the diameter and then find the volume either using the formula or the graph.
  6. Repeat this two more times and then find the average diameter and average volume.

The average adult male has a vital capacity of a little more than 3000 cm3 and the average female’s vital capacity is about 2700 cm3. Of course, this also depends on height, weight, health and several other factors.

You can have students compare their lung capacities to their classmates. You can also ask follow up questions such as:

  1. What would you expect a professional athlete’s lung capacity to be? Why?
  2. What would you expect the lung capacity of someone who smokes to be?
  3. How might a musician’s lung capacity compare to others?

What a great way to lead into talking about health concerns and the importance of exercise!

Radioactive Pennies

Teaching chemistry in middle school is difficult. You can’t see atoms and you can’t feel electrons moving around.The material leans toward the abstract, even though atoms are what make up all concrete objects! To make it worse, this unit comes during the mid-winter, still not close enough to spring break time of year.

I always try to use hands-on simulations or interactive labs to help students connect to the information. (For example, these cereal Bohr model projects). Radioactive elements are another great one to simulate (I mean, you have to simulate it… highly radioactive elements are frowned upon at school). Radioactive Pennies a mini lab that can bring the concept to life. This lab uses probability and flipping coins to simulate what happens to elements that undergo radioactivity. Each round represents a half-life of the penny element. So after discussing what happens when an element becomes radioactive, students participate in this!

Materials Needed:

  • 50 pennies per group
  • Ziploc or paper bag
  • Blank graph

Instructions for Radioactive Pennies

  1. Students put all the pennies into the bag, shake, then dump them out onto the table
  2. Any pennies that land on heads are the ones that have changed elements. Put these in a pile to the side.
  3. Place all the tails back into the bag to be dumped again
  4. Repeat the process until all the “element” has changed
  5. Students record how many pennies landed heads after each round and create a line graph plotting the number of heads each time on the y-axis and rounds on the x-axis.

    This shows how many pennies were heads after each round

Comparison to a half-life of an element

Students should notice a pattern of about half the pennies being flipped to heads each round. Of course, it is not always half, but this idea is the same as an element’s half-life. It takes each element a certain amount of time to fall to half its size. It takes one round for the group of pennies to fall to half its size. From this, you can predict about how long it would take for all the pennies to flip, just as scientists can predict about how long it takes for certain elements to “fall apart.”

 

Science Fair

Every year, our school has a different academic theme. Every 4-5 years, it is science’s turn. And this was the year. This also means this is the year I am in charge of many extra activities for our students to participate in. This past week, our school held a science fair. This was an evening open house event for parents to come and see the different projects students have been working on (some since September!)

Putting together a night like this was not easy, but overall, I would say it was worth it. Both students and families enjoyed seeing the different projects and taking part in different STEM activities.

Here are some ideas that helped make our science fair a success this year:

Start planning early!

We began having meetings in October to plan for an event taking place at the end of February. My committee consisted of 3 other teachers and myself, which is not large by any means. However, 6 weeks before the event occurred, we had ideas for all activities, an outline for the night and each person knew which items they would be responsible for. We did end up making a few changes in the days before, but this were not a big deal since everyone knew their responsibilities.

Inform teachers of expectations

We made informational packets for each grade level teacher to inform them of guidelines for student projects. Obviously, the guidelines for 1st grade looked very different from the 8th grade. Our goal was for students to learn at their own level. Some classroom teachers allowed their younger students to simply research a science topic and write it, displaying what they learned on small posters. Other teachers in the middle grades walked through the scientific process by doing a whole class experiment. Students were responsible for collecting their data during the school day, then they did their write ups and posters in class with teacher supervision. Middle school students were responsible for coming up with their own experiments. Although I walked them through each step throughout the year, most of the work was done by themselves. They displayed their work on trifold display boards. Differentiating the projects in this way made sure students were learning at their level! Students also were very proud of their final projects

Include activities for the family

From the very beginning, we promoted our fair as a family event. We encouraged families to come together to see the student experiments! Creating simple stations for students and families to “do science” together helped! We decided three activities were enough to provide variety, but still not overwhelming for us to plan and staff.

  1. Snowman Paper Challenge – using 2 pieces of plain paper and a small amount of tape, families had to create the tallest snowman, making sure it still had the shape of a snowman
  2. Density Exploration – We had three different liquids in beakers with a variety of different small objects. Participants predicted if they thought the objects would sink or float and then tested it out!
  3. Oobleck! – This station was by far the biggest hit. Participants could mix up their own batch of the mind -boggling non-newtonian fluid and play around with it. Parents and students alike had fun with this one!
Announce Winners!

During the day, our middle school projects were judged by volunteers associated with the school. These judges all had science backgrounds and used a rubric to score the different projects. At the end of the night, we announced the winners to the families! Students won a ribbon as a prize and I also gave them a “100 Grand” (since no prize money was involved). Even though the prizes were not huge, the build up to who the winners might be was very exciting for both students and families!

There are just a few basic tips that helped our science fair night be a success!

Music to My Ears

This is an activity I almost didn’t do with my class. I found this great resource for sound and pitch on PBS Design Squad and liked it, but wasn’t sure if I woudl do it. One of my classes this year has been somewhat of a challenge for me. They struggle with socializing. Although that is not anything new for middle school, this class seems to be the extreme. We’re working on it, but it makes me a little hesitant at times to try new activities when a lot of instructions may have to be given.

String Thing Game

I found this cool inquiry activity online and knew it was perfect for investigating pitch. But did I really want the students to work together on the Chromebooks to see what kind of noise they could make? It was a Friday after a pretty crazy week and to be honest, I did not have any other activity prepped, so this was it. And it was amazing! The student pairs worked quietly, stayed on task and LOVED doing it. Of course there was noise in the classroom – it is a sound game – but it was that awesome hum of productiveness. It was music to my ears!

String Thing Game, created by PBS Design Squad, has students explore how changing the length, tightness and type of string creates different pitches. Students can manipulate the features and to create different sounds and pitches. First, I had students just explore. How could they make a sound lower? What happened to make a sound higher? There are also demo songs where students can see all the different strings. Once they played on it for several minutes, I gave them the worksheet that the site created which asks specific questions on how different sounds are made. Finally, students attempted to make a song or tune online.

I originally had planned to only do this for 10 to 15 minutes, but when I observed how well the students were doing, I let them continue working until the end of the class! I even had students come up to me the following Monday to say they had played it at home. Win!

Build an Instrument

On Monday, I had students work in the same groups to create their own musical instruments and Build a Band, using their knowledge from the game. Cardboard boxes, rubber bands and wooden dowels were the only materials needed. I challenged them to create a song using four “strings”. Some groups immediately knew the song they were singing and could adjust the bands accordingly. Others decided to put the bands down, and then try to come up with a song. Although rubber bands are a little tricky to keep “in tune” because they can stretch or become looser, most students recognized how to adjust the pitch. I’m not saying that all the songs were perfect, but when the groups “performed” their songs, most students could figure out what tune was being played.

The class had so much fun with this activity – they could be social and musical at the same time. Yet they were still learning! Thanks PBS Design Squad! I’ll definitely be looking to them for more lessons in the future.