Blog, She Wrote: 10 Days of Science with Math

Showing posts with label 10 Days of Science with Math. Show all posts

Thursday, November 17, 2011

10 Days of Science with Math: More on Calculating Velocity

Here is the repost of our Finding Velocity results. This was a great lesson and it spawned two more activities using the LEGO Mindstorms nxt brick. E had to make a marble speed trap using the light sensor and a while later he made a speed trap using the ultrasonic sensor. The update there is that he was successful in measuring the speed of a large ball coming toward the robot- it needed an object bigger than a marble. The important thing to note here is that if you are willing to let your kids explore the answer to a question...there is no limit to the experiences you can have in your homeschool. Just be willing to help facilitate the journey...don't be intimidated by things you don't know and try not to get caught up in having everything "ready" before you launch into something. Sometimes that kills a thing before it even gets started!

Here is the much anticipated result of our marble investigation. I was delinquent in getting pictures to go with my results. I have to have the pictures! If you missed the first post on our most excellent math lesson, then go to there and read about it. It was good science!!

The first thing the kids found was that it was hard to get the marble to repeat a good run enough times to record it for five trials in a row. They tried to get the marble to go around the curve correctly each time to no avail. Finally, they ended up making a new chart to record the partial runs. We could calculate the velocity whether or not the marble went all the way to the end of the track.

The data chart-we recorded the time in seconds using a kitchen timer. Each of them took a turn helping to hold up the part of the track near the curve, timing, and letting the marble go.

Then we measured the length of the track at both the partial and final marks and I marked the yarn with the start and partial distance. That was important later on. E11 used a yard stick to record the full and partial length of the track. Then we had the mathematical task of converting the measurement to inches. Note, scientific work is generally done in cm, but I was working with a yard stick not a meter stick so I just went with English measurements this time.

The final calculation page. E11 and R9 used the formula velocity = distance/time to get their answers. The answer was in inches per second. Their marble was traveling 41 inches per second down the marble track.

Then I thought I'd give E11 the challenge of converting our answer from inches per second to miles per hour. That was fun! Yeah...I'm that kind of mom!

Some things to think about- first the kids wanted to give up on the full track runs, but I made them stick with it. E11 was especially annoyed and declared it was all ruined several times, but I reminded him about how scientists meet up with obstacles all the time. Dan helps to manage a university lab full of users who get frustrated the same way. Months of work will come to a crashing halt when they make a mistake or a tool is dirty and ruins a wafer or a tool is broken and breaks something they've worked hard on for a long time. There is a delay in forward movement. They have to begin again. That's how it is in the real world of science! Besides, E11 is a very bright boy who needs to work on perseverance when something is more difficult than he would like to battle.

Also, before we could do calculations, we had to deal with the raw data. We chose to find the median rather than an average in order to do the velocity calculation.

We had trouble importing the video from E11's camera into Picasa so for now the video of the run will wait. Next time... Aha! E11 just informed me that his camera card was not wiped so perhaps, with my help, we'll load up some video for you. That was part of the challenge that day.

All in all a fantastic activity for math and science. I wonder what we'll do next!
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Be sure to visit these brilliant women during our 10 days adventure between November 7th-18th! I love these ladies and we know you will too.

10 Days of Science with Math: Finding Velocity

**This is a repost of an activity we did in November of 2009- two years ago now. The title of the original post was "Measuring the Velocity of a Marble or How to Have a Rockin' Math Lesson". This is the perfect example of how to capitalize on the interests of your children as you develop your schooling/lessons.

As I was finishing up on my computer one morning last week, I was reflecting on what type of family math lesson we'd have for the day when I heard the kids in our playroom having a good time building and testing a marble roller coaster. The roller coaster rocks because you can watch the marble the whole time. It rides on top of a track. How is that not fun?

That's when it came to me...so I shouted downstairs...do you want to find out how fast that marble is going?

The reply came quickly and loudly, "YEAH!!!"

So, we gathered at the school table and did some brainstorming. The first thing I asked them is what they thought we might need in order to find out the speed. We quickly determined we did not have any equipment that could just measure speed. E11 remembered from our Explorers unit last spring (He read Carry On Mr. Bowditch) that we just needed to measure the time it took the marble to go a particular distance. Woohoo!

So we talked about how we might measure the distance of the track. They had a lot of really good ideas. R9 suggested that the distance between the rails of the track were the same and we could measure one and then count how many there are and multiply to get the length of the track. Then they thought instead of the individual rectangles, they could measure track spans and add them up. Of course allowances and special measurements would need to be addressed at the curved track pieces.

They came up with using a sewing tape measure which could bend and finally using yarn to mimic the track and then measuring the yarn length which is ultimately what they chose. Very interesting to watch this process. We did discuss later on which would be the most efficient and perhaps the most accurate method, but I let them explore because that's what it's all about.

The start of the track- it began high on the toy shelf and made a drop to a loop-d-loop.

This track ended in the "kitchen oven" where the marbles collected on cookie trays.

There was a problem with the track at the turn. Sometimes it's hard to get the marble to negotiate the turn in the track. In the end, we had to have two ways to write down our time- one for runs of the full track and one for runs only to the curve.

I had the kids take turns writing on the chalkboard the things we'd be measuring or finding out- in the case of the speed of the marble.

In the end they decided to go with using yarn to determine the length of the track.

In the next post, I will share the results and how the kids determined the speed of the marble. We had some good discussions about the realities of being a good scientist.

Stay tuned for the results of our challenge- more math with our science!

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Be sure to visit these brilliant women during our 10 days adventure between November 7th-18th! I love these ladies and we know you will too.

Wednesday, November 16, 2011

10 Days of Science with Math: Relevant Resources

Today I want to share with you another great resource for math in your science. I discovered Yummy Math sometime during the last school year and it is really good stuff! I like to just see what is up on the home page because it always has seasonal items and current events right there. However, you can always search the site for topics that relate to what you are studying right now.

This is primarily middle school math, but you could modify the activities for younger kids. Lots of pre-algebra skills and beyond. Last year my then 7th grader was graphing lines and conic sections...how can you go wrong with an activity that asks your student to graph the parabola he is going to make as he shovels snow in the driveway? How?

Here are a few fine examples so you can have a guided glimpse!

Hurricanes
Earthquakes- this one popped up after the funky east coast earthquake from August
Why Does It Stay in Orbit? a look at how the space shuttle stays in orbit in honor of Endeavor's last launch
The Geometry of Flooding

I could go on and on! Seriously, this is an amazing resource for applied math. You won't be disappointed when you go looking for something relevant for math in your science.

Thanks for stopping by. If you have another resource to share, please leave a comment. I'd love to hear from you!

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Tuesday, November 15, 2011

10 Days of Science with Math: Bird Count Data

Today I'm going to share a source of data with you. Sometimes having math with your science is just a matter of where to look for some data. You don't always have to generate it yourself!

Sites like eBird, Avian Knowledge Network, and The Great Backyard Bird Count all provide data sets on numbers of birds spotted. What can you do with this data?

you can calculate averages and medians
make graphs
make box and whisker plots
compare bird data - see if you can make conclusions based on what you find

It's important to note that the Avian Knowledge Network has large downloads of data, make sure you choose a chunk of data that you can work with easily. Even if you cannot use everything there, you can make your own data list of a manageable number of data sets for your student.

Just a note that eBird is a great way to tally and count birds daily at times other than the GBBC. What a great way to have kids make a data chart and use tally marks! Be sure to log in and give your information to eBird. eBird is just one of the ways you can be a Civilian Scientist with the Cornell Lab of Ornithology.

Tomorrow I'll share another source for data and it will have lots of math concepts included. Stay tuned!

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Monday, November 14, 2011

10 Days of Science with Math: Reaction Time

Today's science with math idea is a lab exercise on Reaction Time...the time it takes our bodies to react to a stimulus. Perhaps you've done this before or perhaps you've seen similar things at a science center. Our local one has a display, but it's computerized. This one is going to be old school. You'll need a ruler and a data chart.

How It's Done:

Two kids will need to work together at a time or you can be the helper. One person will be dropping the ruler and the other will be catching it. They face each other and the ruler will be held above the participant's hands at about eye level. The participant chooses which hand will do the catching- I suggest starting with the dominant hand. He'll be catching the ruler between his thumb and fore finger when it is released. Remember to hold the ruler so that it is dropping with the lower numbers going first.

The object is to catch the ruler and read out what number was "caught" on the ruler. If the ruler was caught and the number 4 is read on the ruler, then you record the distance on your chart. Prepare a data chart ahead of time by determining the number of trials you will do and you might want to do left and right hands to see if there is a difference.

Now if you are working with a large classroom of kids, then there's plenty of math to go around on this one. With just a few kids in the house, you may have to get creative on finding more numbers or you can just adjust the number of times you try. It's important to discuss what additional trials are for. Why do you want to do the experimental procedure more than once? How many is enough? What would a good scientist do? More than one go at the experiment will tell you if your results are typical or if one or another try was an outlier compared to the rest. In addition, it will tell you if your results are repeatable. When a scientist publishes a study in a journal, one of the highest compliments is whether or not the results can be replicated. In fact, a journal committee will want to know if the experiment was replicated. It greatly diminishes the work of a scientist if others cannot achieve the same results and it calls into question the reliability of the study. So, the number of trials is important. Discuss these things as you choose how to make the data chart.

Of course, there are ways to work with data and study it to see the trends and ultimately see whether or not there are relationships between variables, etc. Today we can look at taking the average reaction time. You can also teach median and mode and do something called box and whisker plots which basically allow you to look at the range of your data and see where most of it is clustered. All of these will introduce statistics to your children.

Source Wikipedia- an example box and whisker plot plotted on a graph

If you have more than one student doing this exercise, you can use the data from all the trials of several kids to do the statistical analysis. That's probably enough data since you are just starting out! Box and whisker plots let you look visually at the 25th and 75th percentile (the top and bottom of the box), while the middle of the box is always the median. The ends of the lines are usually the maximum and minimum values, but you can choose other parameters for them. In the example above, you can see how the plots help to see how data is distributed.

Once you've found these values and you look at your data, discuss with your children what trends you see. Perhaps there is a relationship between age and reaction time? Gender? Handedness?

If you have questions, please leave them in the comments! Stay tuned for another day of science with math tomorrow.

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Sunday, November 13, 2011

10 Days of Science with Math: Investigating Lung Capacity

Starting today, each of my posts will be activity ideas on using math with science. Today is devoted to experimenting with lung capacity. Obviously, this is a great lesson for those of you studying the human body and specifically the respiratory system, but really it's a great lesson on exercise and health as well. Feel free to use this any time not just when it fits in with your curriculum.

For this activity you will need:

a balloon (one for each child participating)
a ruler
a stop watch (for the exercise portion if needed)
data chart for recording information

What to do:

After you have stretched out a balloon and made sure your kids can blow it up easily, have a child take a deep breath and blow as hard as he can into the balloon to blow it up without taking another breath. Make sure the child holds the air in the balloon when he's exhaled completely.
Have another person shape the balloon in to more of a sphere shape and measure the diameter of the balloon and record it in a chart.
Determine how many trials you want to do at this level and do it again until you are finished recording.
Exercise! Beforehand, choose a standard exercise that the children will perform- could be 10 jumping jacks, running in place for a set time, etc.
Have the child take a deep breath and blow into a balloon again.
Measure the diameter of the balloon in a sphere shape. Repeat for the number of trials you've chosen.
Calculate the volume of a sphere.

Once you've calculated the volume of the sphere, you have the lung capacity of your lungs! You can compare the numbers before and after exercise and see how it affects lung capacity. This would be a great opportunity to follow the relationship in a graph. Be sure to ask your student which type of graph would display this information the best.

As with any math you do with science, it's really important to draw conclusions once you've put the data in a form that makes it easy to interpret the results. Do you see a relationship or not? Does this agree with what you expected to happen?

There is another way to do this lab exercise which involves displacing water in a 2 liter bottle that is put under water to fill. You insert a tube into the water and into the bottle and blow into the tube. The air going into the bottle will displace the water. Knowing that completely full there is 2L of water in the bottle, you can cap off the bottle and pour the water that is left into a graduated cylinder. This would give you an accurate volume as well once you subtract the difference. I like to keep things simple when I do experiments because less things can go wrong. That is sort of a rule of thumb I have just because I've had to hold down a large classroom of students with miserably horrible results. Whenever that happens, I find a better, more efficient way of doing the lab. If you want to mess with the liquid volume/air displacement method, just do a Google search on lung capacity activity and you'll find more specific instructions. I found many of them were qualitative observations only, but it's easy enough to get the numbers on this one if you choose. And I hope you'll choose since we want to do math in our science!

I'm sorry this #5 post is late...I hope to have another posted tomorrow sometime. Stay tuned for another fun-filled science with math activity!

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Be sure to visit these brilliant women during our 10 days adventure between November 7th-18th! I love these ladies and we know you will too.

Thursday, November 10, 2011

10 Days of Science with Math: Qualitative vs. Quantitative Data Analysis

Today I want to share the difference between qualitative and quantitative data and how that leads to math in your science!

Qualitative observations relate to or involve the quality or kind of something. In the popcorn experiment I mentioned yesterday, the taste of the popcorn, the relative size of the kernel before it was popped, and what the popped corn looked like in the end are all qualitative observations. We recorded what each person thought of the taste of the corn with a scale we'd made up (for example, "good, ok, bad"), but that is largely a subjective observation based on each person's taste. Likewise, we recorded what the kernel size before popping was using a "small, medium, large" scale. Again, it's an inexact measurement, but it helps to make these observations. We also looked at the relative size of the popped piece of corn. Was the popped corn "small, medium, or large"? We recorded our results in a data chart and it made us ask another question. Does the size of the kernel affect the size of the popped corn? We wanted to know if small kernels yielded small popped corn and vice versa. We made our predictions and then talked about how we could find out.

This is where quantitative analysis comes in. Quantitative Data is measurable and can be calculated for analysis. In our popcorn experiment, we needed to find a way to accurately measure the size of the popped corn without making relative observations. We decided we could measure the volume of the popped corn by filling a pitcher with the popped corn and using the cylinder shape we could calculate the volume of a cylinder. Remember, we'd used the same amount of kernels by weight for each variety. So, the only thing affecting the volume of the popped corn was the variety of corn- not how much corn we used (an important element of our fair test). Calculating the volume of a cylinder...that sounds like math...in our science!

Now if you don't know the formula for the volume of a cylinder, you are not alone. Neither do I have that on my brain all the time, but I know it can be found. The volume of a cylinder equals Pi times the radius squared times the height.

We had the kids measure the diameter of the pitcher and calculate the radius from there. Then once the popped corn was in the pitcher, they measured the height of the popped corn in the cylinder and that gave us h. They didn't do this all alone. We engaged in the activity with them and helped them along with the calculations. This was a few years ago when our oldest was the only one who could do the math once we had all the parts of the formula, but it was a great introduction to how to use math formulas and manipulate numbers.

The resulting calculated volumes of each type of popcorn enabled us to answer our question. Does the size of the seed kernel affect the final volume of the popped corn? But how could we answer this question knowing the volume of each one? Time for more math...this time a graph! Now we had an opportunity to discuss which graph would be the best for helping us to see a relationship. Pie graphs are no good here...how about a line graph? Well, line graphs are best when you have a quantitative value on both axes- numbers to put on each side. In this case, we had one qualitative observation and our calculated volumes. This was a job for the bar graph! On the X axis we could have the names of the popcorn varieties and on the Y axis we'd have a scale to use with our Volume values.

What follows is an interpretation of the graph. We had the observed sizes of the corn and put them on the x axis in relative order from smallest to largest. When the bars were put on the graph, it was easy to see whether or not there was a trend in the data. We were able to clearly see that yes! There was a relationship. It turns out it was a direct relationship and it was in a positive direction. The bigger the seed kernel, the larger the popped volume of the corn. The smaller the seed kernel, the lower the volume of popped corn. That was a satisfying moment indeed.

If you'd like to see pictures and more story of how we did The Great Popcorn Popoff Extravaganza go here. You'll see that we used some basic household items to do the job- like a kitchen scale and some bowls and a pitcher. A post of the results and graphs are here.

In summary, the more you can quantify the results of an experiement, the more credible your conclusions are because you have the numbers to back it up. Numbers and observations make the math in your science! Now that you have some idea of how to get started and what kind of data produces the math, it's time to get some more ideas. Starting tomorrow and for the rest of the blog hop, I'll be sharing specific activities you can do in your homeschool to practice using math in science.

If you have any questions, please ask. I'd be happy to entertain discussion in the comments. Thanks for visiting!

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Wednesday, November 9, 2011

10 Days of Science with Math: How to Design a Fair Test

I know some of you are probably asking, "What is a fair test?" A fair test is when you conduct a experiment under fair conditions. To have fair conditions you need to make sure you only change one factor at a time while keeping all other conditions the same. Another way to look at it is to think about your outcome...when you finish the experiment you want to know that the results are based on just one factor (because that is the one you manipulated) not that it could be based on a few or you aren't sure.

The first thing to do when considering an experiment is to make a prediction. Scientists call this a hypothesis and it's easy to have your kids try it out. I like to use "I think ________ because _________." statements. Not only do they make a prediction about the result of the test, but they have to tell you why.

Now it's time to set up the fair test. First, you want a control- this is the item that remains unchanged in your experiment. Then you can choose one variable at a time to change. Variables are the changing factors in an experiment- to be a fair test only one can change each time you do the test. Remember, the factor you change is the one you are looking for in the experiment.

Let's try out an example. A few years ago, my husband bought a whole bunch of gourmet popcorn and as we checked out all the varieties, my kids began to wonder which one would be the best. So, my husband and I (being the science people we are) suggested we find out- with that twinkle in our eye! We talked to the kids about how we'd find out and what would be the criteria for "the best". Taste and the size of the popped corn came to mind. This led to the Great Popcorn Pop Off Extravaganza . In order to keep things fair, the popcorn had to be popped the same way. We measured out the weight of the kernels and the oil to be the same for all varities. These were the factors staying the same. Our changing variable was the type of popcorn since that is what we were testing for- which one of these would be the best. We didn't want the results to be biased by using more oil with one type or using more kernels for another. The best tasting and biggest popcorn had to be the result of the type of popcorn alone. That is a fair test!

In summary, when doing an investigation/experiment:

change one variable
measure another variable
keep all other variables the same

Conducting a fair test is one of the most important ingredients of doing good, scientifically valuable experiments.

Now that you've done that fair test and you've collected data, it's time to find out what you can do with it! And that is where the math comes in! Join me tomorrow when I discuss qualitative vs quantitative data- how to collect it and what to do with it.

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Tuesday, November 8, 2011

10 Days of Science with Math: How Do You Start?

What better way to work on living math than to apply it to something else your students are working on? Today we are going to talk about how to go about choosing a topic for math in your science and how to implement it once you have something in mind.

First of all, I think it's important to note that science doesn't always come from experiments in a book and experiments don't have to be in recipe form to be good ones. Scientists have to design their own investigations- no one is there to give them the recipe if they are doing their own innovative work. As you lead your students through this process, remind them that scientists have setbacks as well.

So, what is an investigation? It's to observe or study by close examination and systematic inquiry. Start thinking about how you can engage your kids in some discovery without being intimidated by formal processes and planning. So many times I see homeschoolers shy away from science because they often think it has to be formal and all their ducks must be in a row. I want to dispel that myth!

One of the best ways to get started is to follow an interest. Be willing to say yes when your student asks if they can find out more about how something works or if they want to test a prediction they have. Plenty of information to support your search is only a click away and it doesn't cost a thing! Part of being informal is saying yes and going along for the ride and having your kids make their own data collection forms- this helps them to organize information and gives you permission to be spontaneous. Remember, none of this has to be perfect only functional. You'll learn from your mistakes as well.

What if your child isn't really all that inquisitive? That's ok! You can reach out to where their passions lie and try to draw them out that way. It may take kids a while to respond to this if you have always done everything "by the book". Giving them permission, and working through the process together will develop this skill. Be patient! In the meantime, try to work with a topic/subject that they are crazy about and go from there.

Our investigations aren't always an experiment from the start. Sometimes my ideas are sparked by listening to my kids playing (story on this later), sometimes we just need to do some research to answer a burning question. And sometimes I just hand them an experiment book based on a topic they are studying or something they've asked about and see what they can do with it.

Sometimes a whole unit is created based on the interest of a child. Put together ideas that come from what your child is interested in- it fuels their passion and allows you to work in some great science. For instance, after watching Punkin Chunkin last fall, we did lots of work with catapults. Lots of great physics and math come with studying catapults! We do a lot of this so stay tuned for more ideas.

I hope this post gets you thinking about some possibilities in your homeschool. Tomorrow I will talk about qualitative vs quantitative data analysis and how to design a fair test (experiment).

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Monday, November 7, 2011

10 Days of Science with Math

Heart of the Matter is hosting another round of their 10 Days Blog Hop that we did last February. This time they let us choose our own topics and I didn't hesitate to announce I'd be doing a series on using math with science. Oh no! Some of you are undoubtedly saying, but I'm not a science person! So, on day one of Science with Math I'm going to help those of you who are worried that this is not a good topic for you. It's ok if you are not a science person, you can do it! Here are a few tips:

•It’s ok to sit down and be a problem solver WITH your kids.

•Be a resource in HOW to find out something you don’t know.

•Model for them good problem solving behavior.

•Reach out to others who can help you move to the next step.

Present Your Kids with a Problem and Some Materials to rise to the Challenge

•Gives ownership to your kids

•Allows you to be the facilitator rather than always running everything (which is a great way to disguise that you don't know everything! Facilitating doesn't mean you have to be the expert on the topic. It means helping your students find the answers.)

•Can be related to their current studies- or not.

Once you realize you can still do great science even if you aren't super confident, it's easy to start using science to apply math. Over the next 10 Days, I'll be sharing some more advice on how to do science easily in your homeschool along with some specific lessons on using math in your science lessons. I hope you'll stop in each day and join me.(please pardon the rough formatting today!)

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