How Do I Solve for m?

Since we were on the subject of manipulating equations this week, I thought I'd share this other tidbit with you...

I've had plenty of students who could recite F=ma and could readily solve for F, given m and a.  But, given F and a, they lacked the understanding of how to solve for m. 

This little trick solved a lot of problems (and even students capable of solving for m enjoyed using this). 

Draw a triangle and divide the triangle into three parts by drawing a T in it (see below).

Now fill in the variables.  In the case of F=ma, the F goes on the top and m and a each go in a bottom section.

To use....
Use your finger to cover the variable you're solving for an "read" off the equation. 

If you're solving for F, cover the F and you'll notice the m and a are next to each other, which means they need to be multiplied to get F.

If you're solving for m, cover the m and you'll notice that you're left with F over a, so you'll need to divide F by a get get m.

And finally, if you're solving for a, cover the a and you'll notice that you're left with F over m, so you'll need to divide F by m to get a. 


Much like the popsicle stick, this trick can work for any three variable equation like density and speed. 

As long as you can remember one iteration of the formula, you can recreate the triangle!

Manipulating Equations

In an ideal middle school classroom, all students would understand how to manipulate simple equations and be able to explain what happens to one variable when another is changed.  But, the reality of the classroom often means doing what you can to help some struggling math students work their way through equations in science class.  For those students, these simple manipulatives may just provide the crutch they need. 

This idea for these popsicle stick manipulatives, to help your students better understand what happens to the different variables in a formula, came from the Bond with James blog, and I found it through Pinterest. 

In its original form, this manipulative is used to help students better understand the ideal gas law.

But, since I never did a whole lot of instruction on the gas laws, I immediately began thinking of the equations I did use with my students that fit this pattern (i.e. three variables). 

The equations that came to mind were:
Newton's second law: F=ma
Density = mass / volume
Speed = distance / time

The manipulative is simple a popsicle stick,  labeled with m (mass), F (force) and a (acceleration).  The biggest trick is get the right letters in the right spots. 

Once the stick is set up, you can put it to work.  For our first scenario, lets say we want to know what happens to an objects acceleration if we decrease its mass, but keep the force constant. 

Because you're keeping the force constant, you'll place a finger over the F.  The stick now pivots around that point. 

Move the m end of the stick downward, to indicate a decreasing mass and observe the a end of the stick rising. 

Therefore, when the force is kept constant while the mass decreases, acceleration will increase. 

For another example....
What happens to the acceleration of an object when we keep the mass constant, but apply less force to the object?

Place your finger over the m, because mass remains constant.  Move the F downward to indicate a lessened force and observe that a also moves downward.

Therefore, when an object maintains a constant mass, but a decreasing force is applied, the acceleration will decrease. 

Here's a manipulative stick for the density equation:

It's used in the same way....
What happens to the density of an object if its mass remains constant but it's volume increases?

Place your finger over the mass, raise the volume end of the stick and observe the density end. 

If an objects volume increases without changing the mass, the objects density will decrease.      And while I don't have a picture of one.... a stick for the speed equation would have distance in the middle and speed and time on either end.      Hopefully with enough practice, your students will begin to internalize these ideas.  And when that happens, they will have a much better understanding of whether or not their answers make sense. 

Grade Levels for Science Activities

I wanted to talk briefly about assigning grade levels to the activities I share.  More specifically why I don't do it. 

I know there are people who would like to be able to search the activities by grade level and at one point I thought about adding labels along those lines.

But then I realized those labels wouldn't do much to narrow down your search, as I'm a firm believer that the bulk of the activities I share can (and should) be done with a very wide range of students.

Let me give you a few examples...

I originally learned the Heart Mambo at a Life Science Institute for middle school science teachers I attended.  In its original form, it is clearly meant for 7th grade (give or take...) students to learn the path the blood takes through the circulatory system, with a fair amount of detail (names of the specific arteries and veins through which the blood passes at each point in the cycle). 

A few years later, I was asked to provide a science activity for my son's preschool class as part of their study of body systems, particularly the heart.  I used the same premise, but greatly simplified things.... There was a large heart in the middle and two loops - one going to the lungs and the other going to the body.  They walked the loop and named the places they were passing through.  In addition, I had them pick up construction paper oxygen molecules at the lung and deposit them at the body. 

And while I haven't had opportunity to work with older students, I think plenty of them would enjoy the addition of some kinesthetic activity to their reading and lectures.  I would anticipate adding additional pieces of information, such as the valves. 

A really, really simple activity is the Sticky Web. Totally appropriate for students as young as preschool learning about spiders and their webs.  

But... I did the exact same activity, without any modifications, with my middle school students.  It took less than 5 minutes, but it was hands-on and got them involved.  And it doesn't even matter if they'd done it before - each time they do something they get something different out of the experience, based on their accumulated knowledge up to that point.   

I encourage you to find ways to use these activities to meet the needs of your students and your situation.  If you see something you'd like to use and aren't sure how to adapt it to your situation, shoot me a message and we can brainstorm together.  Also, if you're looking for activities that you can use to teach a particular skill (as opposed to a content area), let me know and I'll try to lend a hand with that as well. 

Weathering: Plant Roots

 

Plants, specifically plant roots, are one source of weathering.  Cracks in driveways and sidewalks often provide evidence of this, but it's simple to watch it take place within your classroom. 

You'll need some Plaster of Paris*, seeds** and a small disposable cup or cupcake paper.

Mix the plaster according to the package instructions (usually 2 parts plaster to 1 part water).  Pour the plaster into your vessel. 

Poke two or three seeds into the plaster.  Place in a spot where it won't be disturbed while the plaster sets and the seeds germinate (there's enough moisture in the plaster for the seeds to begin germinating, no need to add anything). 

Within a day my seeds had swollen and begun to germinate.  The force the seed exerted was enough to crack the plaster. 

Now think about what happens in a driveway or sidewalk... a crack forms in the surface, seeds blow or fall into the crack, a bit of rain falls and the seeds begin to germinate.  The force of the seed germinating and the roots taking hold forces the more cracking.  Now there's a larger crack into which more seeds can gather and cause further cracking.  If nothing is done to curb the problem, eventually the sidewalk or driveway will be dessimated. 

*FYI Plaster of Paris does have a limited shelf life.  If it gets too old, it won't set up properly and you'll have a crumbly mess.

**I've mentioned it before, but dried beans (like you'd use to make soup or baked beans) will germinate.  They're cheaper to buy in a large quantity than garden seeds and they can be found easily year-round.

Playing Catch-Up

Happy New School Year!

Our household started back this week, so I'm hopeful once we settle into the new routine, I'll find more time to work on the blog and put into play some of my many ideas. 

I know some of you are returning to the blog after a summer hiatus, so I thought I'd take a minute to highlight a few things you might have missed over the summer. 

Science Matters can now be found on Facebook.  If you use that form of social media, I'd love to have you join us there.  It's currently a small following, but I hope to increase the things going on over there, especially as we grow in numbers.  There may even be some special opportunities available to Facebook friends!

I've also started a Science Matters Pinterest account.  There you'll find all the activities in the Science Matters archives, organized by topic.  It seems to be well-received and I'm enjoying the visual index of activities. 

And finally, for the rest of the month, you can enjoy a 15% discount when shopping at Pow! Science.  The discount code is  SCIMATTER0913, can be used as many times as you like and applies to any size order.