Kindle Apps We're Playing - DragonBox Alegebra and Geometry

We currently have three Kindles in our house.  T received one for Christmas, last year. I purchased a second, as my "big expense" for this coming school year.  Then, A won one from our library's summer reading program, and all those Kandinsky cookies, and craft stick bridges we worked on through the summer ended up paying off doubly.  We had the fun of the projects, and the three girls swept the prizes, A with the Kindle, C with a cart of blocks, and E with an all day ride pass for the county fair.

The fair started the day we moved, so that pass went to a very grateful friend, but we've been making good use of the blocks, and the Kindle.  With school coming on, and our life in boxes...

...finding a few good educational apps has been a high on my priority list.  The catch being, of course, that my children absolutely despise any game with even the smallest hint of a suggestion, that it might be educational.  The only educational game they've ever willingly played, and truly enjoyed just for the sake of the game, and despite its educational value has been Cosmos Chaos!...

...a truly enjoyable, and completely educational, vocabulary game for Nintendo DS.  And, actually now that I think about it, it was really only D (age 11) who really liked that one.

That is not to say that I have given up, or that I can never get the children to try out a new educational game for me - just that I usually try not to use those two words together when presenting it to them.  Which is how I found myself purchasing We Want to Know's DragonBox Agebra 5+, a game promising to secretly teach basic algebraic concepts to children ages six and above.

DragonBox Algebra 12+, basically the same game as DragonBox 5+, but with more levels and operations to learn.

And DragonBox Elements, leaving algebra behind, and moving on to geometry.

First off, let me say, I love these games.  When I say that, I mean as a player, rather than I as a mother.  To see what they were like, I grabbed up one of the Kindles, and played my way through DragonBox 12+, and partway through DragonBox Elements.  They are fun, logic puzzle type games, and since I enjoy logic puzzles, I enjoyed the games.

Do they teach algebra and geometry secretly?  No.

It's hard to teach something secretly when you tell the person you're teaching, over and over again, what it is you're planning to teach "secretly".  In the intro, the ads, and every write-up from the game company, they mention that they are teaching children algebra secretly.

As soon as my children read those words - they were done.  These were clearly educational games, and they didn't want to play - without a little convincing, anyway.

Do they teach the concepts of algebra and geometry, secretly or not? Not really.  More than teaching, they are games that allow students to play with algebra and geometry.  Which to my way of thinking is much more valuable than a game integrating algebra and geometry into the play, anyway. 

There is not a lot of instruction.  Students must fumble there way through, and figure out what is expected, and how to accomplish the goals through trial and error.  This can lead to a lot of frustration, but also some real breakthroughs in mathematical thinking.

However, if you're looking for a game that students can play through, walk away from, and be able to pass a textbook style algebra test - these are not the games you're looking for. But, they do come with downloadable teacher's manuals (on the website), and printable worksheets to help you, as the teacher, walk your students from the games through into actual math terminology, and concepts.

Did my children enjoy the games, once they got past the educational aspects, and agreed to play them? Some did, and some didn't, but they were all willing to play through to the end of whichever game I gave them.

To begin with, I gave DragonBox Algebra 12+ to D (age 11), and asked him to try it out for me.  He likes math quite a bit, but does not like to be frustrated.  So, in order to convince him to push through his frustration to the breakthrough moments, I bribed him with a Lego set he's been wanting (not that I recommend bribing your children, just because I bribe mine on occasion).

He then sped through the game, and even requested DragonBox Elements.  He found the second game entirely frustrating, and with no further bribes being offered, gave it up after the second level (hence, the reason I don't recommend bribing your children).  Now that I know there is a manual for that game as well, I think I will print it for him, and see if the explanations there can help to alleviate some of his stress with the game.

E (age 9) who loves to compete with her brother, was happy to play through DragonBox Algebra 5+, without a bribe.  She really wants to make it through 12+ too, but so far has needed quite a bit of help in order to make through the higher levels.

I suggested to my teens (ages 13, 15, and 17) that they play through the Algebra 12+ game as an intro, or review to Algebra (depending on their age) at the beginning of this school year.  They have been faithfully playing through the levels, and seem to be "getting it", but I wouldn't say they love it.  In fact, when I asked them what they thought of the game, they answered with an, "It's okay."

They're no Cosmos Chaos, but for "educational" games, they're alright. The graphics are cute, the levels increasingly difficult, the instructions scant, but understandable, and with the additional resources on the website, I'd say it's they are a good concept, and worth the five to ten dollars we paid for the apps on Amazon.

Oh, and no, I am not being paid for these opinions - they are just for your information, one parent/teacher to another.  Really good apps and games are few and far between, and I'm happy to mention any we find along the way.

Summer Fun 2014 - Lego Challenge - Building a Model Without Buying the Set

From time to time I like to pull out a manual from one of our long dismantled, and well scattered Lego sets, and send the children on a scavenger hunt through their toy box for the pieces to put the set back together.  This weekend, I upped the difficulty of the challenge, by printing instructions from the Lego website, for a set we don't own, asking the children to try, and create the model (in this case model 6615 - the Lego Eagle Stunt Flyer pictured above in red, with photo credit to lego.wikia.com) from the Lego blocks we already have.

At first, the children declared the task impossible.  We don't own an airplane set.  We would never have the right pieces.  Surely, I wasn't suggesting taking apart any of their precious creations to build something new (get these kids some Kragle already)?

Undaunted, I started building myself, with the few scrap pieces they were willing to let me use.  It wasn't long before I was joined by a newly formed team of master builders searching for pieces, offering advice, and ready with criticisms for each new substitution we had to make.

"Our" plane didn't turn out exactly like the picture, but the children were pretty impressed with what came out of their scrap blocks.


The thinking involved in the process was very much the "this is what I have - that is what I need - so how do I get from what I have to what I need?" kind of thinking used in high school geometry.  But, don't tell the children that.  They're already scanning through the Lego website for the next impossible model to build.

Summer Fun 2014 - Marshamallow and Toothpick Geometry - Finding the Cubes in a Hypercube

I did a little bit of research, and it turns out the octagon full of squares, and triangles, and stars which the girls had so much fun coloring in with sidewalk chalk paint...

...is really the outline of the shadow of a tesseract - not the glowing blue cube from The Avengers, or the 5th dimensional wormhole Meg Murray travels through in L'Engle's  A Wrinkle In Time, but a 3-dimensional representation of a 4-dimensional hypercube, "that is to a cube, as a cube is to a square".  I'm totally not making this stuff up, either.

What we found really interesting though, is that what all that gobbledegook means, is that besides being filled with squares, and triangles, and stars, our painted picture is also filled with cubes.  Can you see them?

We couldn't see any cubes at first.  So, we built a couple 3D models out of toothpicks and marshmallows, that we could hold, and turn, and flip around...

...by starting with two cubes...

...and then connecting the respective corners - "front top left" to "front top left", "front bottom left" to "front bottom left"...

...and so on, until they were all connected and...

...we could smoosh, and pull...

...and flatten the shape, looking for the cubes.  How many can you find?

We found eight.

And, if I understand correctly, eight is the total.  Can you see them now?

It's great to be a homeschooler.

Resources:

A Wrinkle in Time by Madeleine L'Engle.

Flatland, a Romance of Many Dimensions by Edwin Abbott Abbott.

Carl Sagan's Comsos - Tesseract.

Wikipedia - Hypercube and Tesseract.

Animated Hypercube by Nicholas Mee.

Gingerbread Geometry

Our groundhog might have predicted an early spring just yesterday, but we had more snow on the ground today, than we've had all winter so far.

Normally, we make gingerbread men to celebrate the first "real" snow of the season.  We gave up this year before Christmas, and made them with only a skiff of snow of on ground.  Even so, with the children out playing, and the snowflakes falling, I couldn't resist rolling out one more small batch of gingerbread.

Since I hated to lose the entire school day to a February snow, and since we (or at least I) have been in a mathy mood this month, I cut out 2''x2'' squares instead of men...

...scoring them into quarter inch squares (more or less) before baking...

...for a frosting covered, gingerbread geometry lesson to go along with the obligatory mugs of hot chocolate, when the children finally came shivering back inside.

I gave them each a baggie of frosting, and let them pipe along the scored lines while we talked about perimeter and area of the squares.

We frosted a few of the extra squares together to investigate the surface area of a six sided cube...

...and piled up a batch of Pfeffernüssen-ish gingerbread cubes (made with the left-over dough)...

...for a quick lesson on volume, as well.

It's great to be a homeschooler on a snowy day.

Snowbleck - Simple Snow Day Ratios

Ironically, while the eastern half of the country has been bracing against arctic blasts, Montana has been unseasonably warm.  We've had to make the most out of every snowflake.

So, today, with our latest flurry falling, but melting fast, I decided to extend the fun with a messy-play-meets-math-lesson type of activity - snowbleck - like oobleck, but made with snow instead of water.

The first step in making snowbleck is to collect, and melt a cup of well packed snow, to determine how much water it contains.

Our snow today contained 1/2 cup of water for every cup of snow.  A ratio of 1:1/2 snow to water (convenient for a simple lesson).

Oobleck is made with a 2:1 mixture of cornstarch and water.  We had 2 cups of cornstarch, so we needed one cup of water...

 ...or two cups of snow.

The girls mixed the snow with the cornstarch...

 ...melting it in their hands...

 ...transforming our math lesson, into a science lesson, into ooey-gooey fun.

It's great to be a homeschooler.

A Skip Counting and Fancy Nancy Vocabulary Apple Harvest

I decided to slip in a couple of last apple themed lessons for my youngest, before turning the page on the calendar to pumpkins and the like.  It was super simple with the help of a "count by fives" apple printable from Doodle Bugs, which I cut out and paper clipped to our fall leaf list tree...

...for C to harvest and place out in order on the table, as she counted by 5s.

Then, I reset the tree for a Fancy Nancy vocabulary, pick and match-up, activity using an apple template from dltk-kids.com, modified in Paint to add the vocabulary words...

...and their definitions from...

...the back of Jane O'Connor's Fancy Nancy Apples Galore.

It's great to be a homeschooler.

9 Piece Square Puzzle Cookies

Gearing up for "school", we've been playing with a number of geometry/logic/spacial reasoning puzzles, like Thinkfun's IZZI© puzzle shown below.

In fact, that particular puzzle was the inspiration for yet another cookie project.  Staring at the black and white squares, I just couldn't help but be reminded of chocolate and vanilla cookie dough, and finally couldn't resist baking up a couple of cookie puzzles to add to the game table.

The 64 black and white IZZI tiles were a little more project than I wanted to take on just now (maybe this winter).  So, I settled instead for a 3x3 square style puzzle, like I've made out of cardboard for the children in the past.

Half a batch of sugar cookie dough (click here for the recipe) - with half left plain vanilla, and half with baker's cocoa added...

...is enough for two puzzles rolled 1/4 inch thick...

...and cut to be 4 and 1/2'' square.

Transfer the cut squares onto a large, greased cookie sheet, and then score the dough to divide each square into 9, 1 and 1/2'' squares.

Use tiny cookie cutters, or cut geometric shapes out of each square with a butter knife, crossing the scored lines in a pattern (so below the bears are all cut in half at the arms in the middle of squares, and the hearts are divided into quarters by the corners of the squares).

Pop the cut shapes out, and swap them with pieces of the alternate dough cut from the other square, or from the leftover scraps.

Finish cutting the small squares apart along the scored lines.  Spread them out on the pan, using a ruler to double check they are all still 1 and 1/2'' square.

Bake the cookies for 13 minutes at 350°F.  Allow them to cool completely before removing them from the pan.  Serve the scrambled puzzle on a plate...

...and challenge children...

...to solve the puzzle (with clean hands, of course)...

...before eating the cookies.

There might be more than one solution too, which is okay, as long as each of the small squares matches up on all sides with the sides of all the other squares it is touching.

It's great to be a homeschooler.