Robotics and Programming with Snap Circuits

This semester, we're studying Robotics and Programming. The spine for this unit is the Girl Scout Robotics badges for Cadettes and Seniors, and the Cadette/Senior/Ambassador Think Like a Programmer Journey. Our main manipulatives are LittleBits, Ozobot BIT, and Sphero, although we're bringing lots of other tech into the unit, as well.

Here's what we did for Step #2 of the Cadette Programming Robots badge:

• Simple Sensors with LittleBits

This Snap Circuits activity also meets the requirement for Step #2 of the Cadette Programming Robots badge. For us it's an extension and enrichment, but if you didn't have access to LittleBits but wanted a click-to-assemble option, Snap Circuits are readily available and more affordable. Here are some of our favorite sets:


Since my kids have been playing with Snap Circuits since they were preschoolers, this project was a review of what makes a circuit and a chance for the kids to reinforce the concept by applying it to Snap Circuits. They've been making circuits with Snap Circuits for MUCH longer than they've known what a circuit is, so the activity is a helpful reminder that although some of the vocabulary is new, they're long familiar with the physical setup.

And besides, any excuse to play!

As usual, Will set about making the most elaborate circuit she could manage, and Syd set about making the most annoying circuit she could manage. Somehow she figured out how to turn the fan into a helicopter that would launch itself after a completely unpredictable time pretending to be just a simple fan.

If you don't get hit in the face with something unexpected, then your kids probably aren't having enough fun!

Story Time: Last week, the kids and I volunteered at the Children's Museum in a new-to-us capacity, as volunteers for their regular homeschool classes. We helped with a morning and afternoon session of an engineering workshop, and it was super fun and I hope they invite us to do it again.

As part of the workshop, Will led an activity about determining the correct surface for structures, I led an activity about human inventions that were inspired by nature, and Syd led an activity on communication challenges. Syd's activity was actually identical to one of the suggested activities in the Multi-level Cadette/Senior/Ambassador Think Like a Programmer Journey that we're also working on in this unit, so it was pretty cool that she not only did it, but LED it for two hours!

Anyway, after our part of the workshop was finished, the leader invited us to stay for the all-group activity. She guided all the kids through making light-up LED keychains using pre-cut clear acrylic forms, button batteries, and an LED. We got to scratch decorations into the acrylic, then insert the button battery and LED  into pre-cut holes. After all of our circuitry work, my kiddos immediately knew how to get the LED to light up, of course, but what came next was even cooler.

The leader gave us circle stickers and instructed everyone to use those to tape the LED and battery to the acrylic keychain. She noted that this would make the LED stay lit constantly until it burned out or the battery died, and if we didn't want to do that we could just peel the sticker off and stick it back between the lead and the battery.

Workable, but awfully inefficient, don't you think? I thought that surely I could figure out a better method, and with a little futzing and troubleshooting, I managed to tightly roll a sticker and stick it to the battery so that it pushed the lead away, but not so far that I couldn't simply press the lead back to the battery a little further down. I covered the whole thing with a sticker and there! I'd made my own pressure sensor! Now to light up my keychain, all I have to do is push the sticker button.

All excited and proud of myself, I turned around to show my kids, in case they wanted to do it, too, only to find that they both wanted to show me how they, too, had each turned their LED keychains into pressure sensors that would light up only when they chose. AND each kid had done it in a different way!

If they understand circuits well enough to create their own physical modifications to a circuit to solve a problem, then I think that they understand circuits.

So you know what we're going to do next in Robotics?

We're going to build a functioning hydraulic arm out of Girl Scout cookie cases!

Montessori Pink Tower and Cuisenaire Rod Extensions for a Sixth-Grader

When Syd's sixth-grade Math Mammoth curriculum covered exponents, she and I (and her sister, on occasion...) did a lot of hands-on sensorial work with exponents. It's easy to forget that even bigger kids benefit from hands-on math, but when you set something down in front of them and watch them become totally immersed in it, you're unlikely to forget again.

Soon after seeing how invested Syd was in working all the Montessori pink tower extensions, and how quickly she moved through them, I asked her if she wanted to join me in creating some extensions for the pink tower and Cuisenaire rods. Both sets of manipulatives are keyed to the centimeter, and so we found that they worked quite well together!

Here are some of the combinations that Syd and I found:

For some reason, Syd really enjoyed making a pattern with the pink tower, and then repeating it with the Cuisenaire rods. It's none of my business why or what she's getting out of a particular experience--the fact that she's happily engaged and invested in her work is proof enough that there's something of value in it for her.

We made a log cabin quilt block!

You can play a lot with perspective when you explore these two materials together. Each Cuisenaire rod is only one centimeter wide, so many of the patterns are best seen looking straight down from above.

I thought that this diagonal patter that Syd made was extremely clever. You can see that she doesn't have it quite worked out in this photo, but I can tell that she's noticed that two pink tower blocks can share a Cuisenaire rod. 

I think she might be exploring along the same lines here, as she's omitted the centimeter cube that she was originally using to cap all the corners of her creations.

This was just a "play" day for us, but you could make this activity more academically rigorous, and in some cases cross-curricular, by adding more investigations to it:

• Children could be the ones in charge of photographing their designs.
• Children could diagram their designs on graph paper. To continue extending it, they could add photographs of the completed designs, write a description or instructions, hand-paste or use a graphic design program to make a book, and then bind that book themselves.
• Children could use clip art versions of pink tower blocks and Cuisenaire rods in a graphic design program, designing patterns that are impossible to create in real life.
• Children can design and perform STEM challenges, such as creating the tallest free-standing tower or the longest possible bridge with supports.
• Combine these materials with the decanomial square to explore cubes, or add more pattern possibilities. Bonus points if you use foam core and/or foam sheets to make your decanomial square pieces one centimeter thick!

Most outside resources for these materials focus on extensions best suited for young children, but here are a couple that I've found that are sophisticated enough to intrigue an older child:

• Build a tower, an inverted tower, and connecting towers from Cuisenaire rods. You can challenge your fine motor skills with this one! This takes some serious problem-solving, and you'll be well-suited for architecture or engineering afterwards.
• Long division with Cuisenaire rods. This is how I modeled long division when the kids were first learning it, but it's a useful--and mind-blowing!--model to use anytime to make the connection that MATH MAKES SENSE.

Hand-Dyed Wooden Beads and Blocks in Pumpkin+Bear

"Aww, look!" I thought. "The chicken wants to seee what I'm doing out on the deck on this gorgeous afternoon!"

"Isn't she pretty?"

"HEY!!! Those are not berries!"

So there you go. My hand-dyed wooden beands and blocks are so pretty that chickens think they're berries.

I can't even tell you when I dyed these--a couple of years ago, perhaps?

We were doing several projects that involved hand-stained wood, and I was working out just the perfect technique to share over at Crafting a Green World.

While working out the technique to my satisfaction, I made waaaaaay more dyed wood pieces than we needed for the projects.

Apparently, I just squirreled the surplus away in my stash, because I am actually a hoarder.

I rediscovered them the other day while I was cleaning and decided I might as well peep into that plastic drawer in the closet--I'm still finding containers that I haven't unpacked after our move (which was four years ago now, for those of you playing the home game), so perhaps that drawer could contain my wedding ring, or my folk music anthology!

It didn't.

What it did have, however, were projects that I'd meant to list/relist in my Pumpkin+Bear shop. Some were projects that I used to have listed but wanted to rephotograph or rework in some way, and some where projects that I wanted to list in Pumpkin+Bear, but I'm guessing the light was poor on the day that I wanted to photograph them, or I got busy, and set them aside, consequently forgetting all about them.

Of course.

Fortunately, last week we had our first sunny, above freezing days in FOREVER, and there was nothing I wanted to do more than spend the afternoon out on the deck photographing stuff.

These cubes are 1/2" across, nice and light and brightly-colored now.

These beads are 3/4" diameter, with a 3/8" hole.

The kids actually use our stash of undyed wooden cubes as a sensory material. I pour them out onto a tray that sits on our homeschool table, and off and on all week I'll notice a kid fiddling with them as she thinks or reads. They're stackable, arrangeable, and they just feel good in your hands.

Syd really wants to turn some of these beads into Camp Halfblood beads, so that's a project we'll be taking on before too long.

I've used these stained beads to make magnetic mosaic tiles for our giant metal memo board. I'll probably use some of these to make more, and I'm tempted to upcycle a metal tin from somewhere and make a travel-sized version.

Of course, if you bought these from me, I'm sure I'd find something else to happily hoard and/or occupy my time with...

Homeschool Science: How to Make a Molecular Model of Photosynthesis

The kids and I are using CK-12's 9th/10th grade Biology textbook as the spine for this year's biology curriculum--for Will, who is in the eighth grade but who is taking high school-level coursework, this will be recorded as Honors Biology on her transcript.

In addition to that textbook, we're using The Illustrated Guide to Home Biology Experiments as our lab manual, and of course we've got a plethora of other reading/viewing/listening resources and hands-on activities to enrich our study.

We're progressing through the book a LOT more slowly than I thought we would, but that's okay, as biology is in both of the kids' areas of interest, so we might as well be thorough and enjoy ourselves, and unlike AP European History, which Will and I are also enjoying, there's no deadline for finishing, so I'll be happy simply to have us finish by next September, when Will will begin 9th grade coursework.

All that is to explain why after almost two months of study we're only in chapter 4, lol! And we've taken nearly a month to get through chapter 4, as some of the labs that I wanted the kids to do called for special supplies that I had to order. But finally we've got our elodea cuttings, our bromothymol blue, our hydrochloric acid, our test tube stoppers, and our heat lamp bulb, and so so our study of photosynthesis and cellular respiration is finally almost complete.

This molecular modeling of the process of photosynthesis is a hands-on enrichment activity that I had the kids complete after reading the chapter, but before we did our first experiment on actual plants. Modeling the process helps your kid see that it really is just a math formula, not magic: carbon dioxide plus water plus light energy equals glucose and oxygen.

Oh, who am I kidding? Science IS just another name for magic!

Got some molecular modeling tools? You can make the magic happen yourself!

To model photosynthesis, you'll need your favorite molecular modeling kit, or a DIY version. We have Zometools, and last year I bought the Molecular Mania set when we were doing a brief chemistry study. I like the Zometools set because it includes color-coded buckyballs and molecule building cards, but since we have the larger set, too, when I needed more of a particular element all I had to do was lightly spray paint one of our regular white buckyballs and there you go! Paint a ball red and it still works with the regular kit, but now it also represents oxygen!

Here is the chemical formula of photosynthesis:

6CO₂ + 6H₂O + sunlight ------> C₆H₁₂O₆ + 6O₂


To model photosynthesis, then, each kid needs to build six carbon dioxide molecules and six water molecules:

In Zometools, carbon is black, oxygen is red, and hydrogen is white. I told the kids not to worry about single or double bonds, since I just wanted them to witness the conservation of matter throughout the process itself.

We used our imagination to add sunlight, and then the kids then had to figure out how to use what they already had to build glucose: C₆H₁₂O_6:

This is Syd's version of glucose:

I didn't ask them to put it together the "right" way, because I didn't want them to have to research an answer. Just getting all of the correct elements collected into a glucose molecule was enough for me.

Nevertheless, look what Will came up with, all on her own!


Well, the dog may have been giving her tips...



But check out the symmetry of her glucose molecule!

It's really not that far off!

As you could see in the lower half of Will's photo above, when you've finished reassembling the water and carbon dioxide molecules into glucose, you'll have some oxygen atoms left over. This is the waste product, but oxygen doesn't like to be a single atom--it likes to have an oxygen buddy, so give all of your oxygen atoms an oxygen buddy:

And you'll have a perfectly even number!

It's ready to be exhaled, so that humans can inhale it and exhale carbon dioxide, which is what plants inhale so that they can exhale 02, so that humans can inhale it.

P.S. If you don't want to buy a molecular modeling kit, that's cool. I've actually collected links for some nice-looking DIY molecular modeling sets, so here they are:

• I haaaaate the idea of Styrofoam balls, but it would be cheap!
• Gumdrops and marshmallows could work--you'd just need to color code the elements.
• You've probably already got what you need for this LEGO version.
• This biochemistry teacher uses pipe cleaners, beads, and paper clips.

How to Divide Fractions with Cuisenaire Rods

Although by now my kids well know that with almost every math problem there's an algorithm hiding in there somewhere, and that the algorithm will be even quicker and easier than the model and so they want to know it RIGHT NOW, I still try to whip out the mathematical models whenever possible, and especially whenever a kid is having trouble remembering or utilizing the algorithm. If, for instance, a kid can't consistently remember the algorithm for dividing fractions, that's because she doesn't understand dividing fractions. If she understands how it actually looks to divide a fraction, then she'll have a better idea of the answer that she's looking for, and that will likely remind her of the algorithm that she needs to use to get that answer.

You know how when you're trying to spell a word that you don't fully know how to spell, or trying to grammar check some tricky grammar, you often know when that word or sentence "looks" right, or when it doesn't? That's because you've read so much that you understand how words and sentences are formed, even if you don't completely remember the algorithm for your particular word or sentence. It's the same with math. If you understand how to physically divide fractions, and you're presented with, say, the expression 1/2 divided by 1/3, then even if you don't completely remember the tricky algorithm involved (which is to invert the divisor and then multiply), you should at least know that the answer isn't 1/6. You'll probably, in fact, be able to look at the two terms and know that the answer will be greater than 1,  and that might be enough to remind you of the algorithm.

Here, then, is a quick-and-easy way to model fraction division using Cuisenaire rods. It takes longer than simply calculating using the algorithm, but it makes dividing fractions make SENSE, which, if you learned how to do it using only the algorithm, is a pretty big deal and might blow your mind even now.

Take this problem:


Syd's math curriculum asks her to work the following: 2 divided by 5/6. I asked her to interpret it in this way: "How many times will the fraction 5/6 fill into two wholes? Or, how many 5/6s are in two wholes?"

Step 1, then, is to wrap your head around one possible interpretation of a fraction division problem: how many times will the divisor fit into the dividend? You can work some whole number problems to illustrate that interpretation, if you like. How many times will 7 fit into 35? How many times will 10 fit into 120? You can even work those with the Cuisenaire rods first, using the method that I'm about to show you, to prove that the problems are essentially no different.

Step 2 is to set up the problem with Cuisenaire rods. Since we're being asked to divide 5/6, then the whole is clearly 6/6, or a six bar, and there are two of them, so set up two six bars. You need to divide that by 5/6s, so gather up some five bars to represent that, and some single units in case you're figuring out remainders. The five bars make up 5/6 of the six bars, and those singles will represent fractions of the five bar. One single unit is 1/5 of a five bar.


That alone is going to tell you that if you do have a fraction remainder, it's going to be in fifths. The remainder, if you have one, is always going to have a denominator the same as the numerator of the divisor, because that numerator is what you're actually dividing. It's not something you notice when you divide whole numbers, because when you divide whole numbers in our society, you're using the Base Ten system, and so denominators are ALWAYS in tenths (or hundredths, or thousandths, etc.). Not so when you divide fractions!

Step 3 is to notice how many of the five bars, which are 5/6 of the six bar, it takes to equal the two six bars, which are each 6/6. When you line them up together, you can see that to equal two whole 6/6s, it takes two whole five bars and two single units. Those two units represent 2/5 of the five bar.

2 divided by 5/6 = 2 2/5

Note that this model takes a LOT longer to explain than it does to do. I'd recommend just modeling the actions with the kid, not necessarily all of my blather that engulfs the simple and clear actions with a bunch of verbal baggage. The kid can see perfectly well what you're doing, and doesn't have to hold all the explanations in her mind for her mind to *know* it, if that makes sense. It's the way that when you read to a kid, you're not all, "Here's the subject of the sentence. It's a pronoun, but that's just because there's a noun that we just saw in the previous sentence, so we don't want to see that again so soon. And here we have a helping verb, which comes before the action verb. You know that next you'll see the direct object, unless you have an indirect object first. Oh, no, actually we've got a prepositional phrase next! How fun!", but nevertheless the kid internalizes all of those patterns well enough that when she's old enough, she'll know that something is wrong with a sentence that lacks a verb.

If your kid is just beginning to learn dividing fractions, you can do lots of these models, as many as the kid can stand, before teaching the algorithm as the tricky shortcut that gives you the same answer. Syd, however, had already been presented with dividing fractions, and was just struggling to remember the algorithm, so every time she completed a problem using the model, I then had her rework the problem with the algorithm to show her that they give the same answer, and to reinforce the connection between the two. It still takes more time and more practice until the algorithm is second nature, because it is NOT an intuitive one, but it all goes easier when it makes logical sense!

Homeschool Math: Zometool Geometry

We've been using Will's recent geometry unit in Math Mammoth to do a lot of enrichment with Zometools, which are a practically perfect geometry modeling manipulative.

Although I loved geometry as a kid, the modeling of two-dimensional and three-dimensional figures is clearly a place where my own education was lacking, so I've been relying on other Zometool resources to mentor us all.

Zome Geometry gets very quickly out of our depth, as there's very little of the hand-holding that I've come to expect in most teacher's manuals (in fact, when paging through it I feel like young scholars of old must have felt upon being handed an edition of Euclid's geometry and told, "There you go! Read up!"), but the beginning units are well suitable for doing some interesting modeling of two- and three-dimensional figures.

So that's what we did!

We're first meant to make these stars and calculate the interior angles. After you've done a few of those, it's easy to create your own formula for calculating the interior angles of a circle.

Now we're trying to use the star models to make regular polygons. This only works for some of them, and for others, you have to delete some of the spokes.

Will got involved in her own extension activity.

It turned out really cool!

On another day, we were asked to use our polygons to construct both prisms--easy!--and antiprisms--SUPER hard, as we didn't have any hand-holding!

I struggled and struggled and struggled to construct an antiprism from my pentagon model. I found many interesting symmetrical constructions, but no antiprisms!

Will struggled and struggled and struggled as well, first to create antiprisms from her squares, and then, after she gave up on that, to contruct antiprisms from triangles.

She got really frustrated before she finished, but finally...

And this girl mostly did her own thing, but at least she was at the table with us! I have come to believe that the ten-year-old schoolwork stubborn streak is a REAL thing, now that my second kid has it, too.

We're playing around with Zometool geometry some more today, but now that Will has moved on in her Math Mammoth to integers and Syd to graphing, our math enrichment will look very different next week.

Life-sized Battleship, perhaps?