Category Archives: Geometry

Making a Kite

A few weekends ago I took my kids to a great kite festival in a near-by small town.  It was amazing!  There were huge kites, small kites, kite flying demonstrations, and even professional kite flyers!  Although the kite festival was really fun, there was one, small snag.

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The organizers of the event advertised that kids would be able to make their own kites.  This was the big draw for my kids, so as soon as we got out of the car, we made a beeline for the kite making station!  Imagine our excitement when we were the second family in line!

Then, imagine our frustration as we continued to stand in the line for the next 30 minutes.  The problem?  The kite builders were trying to have each of the children literally build. a. kite.  They had purchase dowel rods and parachute fabric. The idea was this . . . use a saw to cut the dowel rods.  Then, use a very teeny, tiny drill to drill holes at the ends of said dowel rods.  Next, tape the dowels together in a “+” and string tread through the holes to make the outline of the kite.  Finally, cut a piece of parachute fabric to cover the dowels and the edge of the kite and sew a hem around the entire perimeter of the kite with needle and thread.

Now, I have to say the up side of all of this?  The kites were legit kites . . . they probably would have actually flown!  The down side?  Every single child in line was under the age of 10 (interpretation–no one could do this on their own).  The station was set up so that only one child at a time could make the kites.

Finally, I leaned down to my kids and said . . . “Let’s go to a craft store, I’ll get the stuff to make the kites and we can do this at home!”

I made this offer numerous times, and about the 4th or 5th time I offered/begged them to get out of line, they finally agreed!

Now, we were going to make our own kites!  I headed to a craft store to get the supplies (which, by the way they don’t have parachute fabric!) and ended up with three, 36″ dowel rods, some fabric, and kite string.  We were ready to start making the kites!

Now, when you use the term “kite” it can mean many, many things.  There are kites like the kinds we saw flying that day, there are geometric shapes called kites, and there are kite graphs.  For this post I’m talking about kites that fly, but that are also in the shape of the geometric figure called a kite.

The definition of a kite is: a convex quadrilateral with two adjacent, congruent sides (length a) and two other congruent, adjacent sides (length b).  A rhombus is a special case of the kite.  The diagonals of a kite and perpendicular to each other, and one of the diagonals bisects the other diagonal.

I couldn’t make a rhombus kite, because I only had 3 dowels and two kids who wanted kites of their own.  And, it’d be really nice to only have to cut one of the dowels, instead of all 3 of them. Meaning, I’d like each of the kites to have one of the diagonals be length 36.”  The length of the other diagonal was up for debate, however . . .as long as it was at most 18″.  So, here’s what I knew . . .

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blue = dowel rods

red = string

So, I’m wondering . . . given these parameters what would you design the kite to look like?  How could you minimize the amount of string needed?  What about the amount of fabric needed to cover the entire kite?

 

Happy Pi Day!

How could a blog devoted to all things math not have a post on Pi Day?  Truthfully, I had big plans for today . . . starting with the Pi Day cookies I wanted to bake and bring to work:

This is as far as I got making Pi cookies for today.

This is as far as I got making Pi cookies for today.

#pidayfail

Honestly though, I’ve been running around like a crazy woman these last few weeks and just didn’t have enough time to get my self together to have a meaningful Pi Post today!  It seems as though the day as been jinxed.  You saw how well my Pi cookies turned out, then I went to the store to buy a pie to bring to work and they didn’t have any!  My husband did come through for me though and snagged this awesome Pi shirt from his junior high school (Thanks awesome junior high teacher!).

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Since I don’t have a great Pi Day post for you today, I thought I’d round up some of my favorite Pi activities from around the web . . . former students of mine will know some of these activities well 🙂

A great Pi Day cartoon:

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Pi set to music.  ( know there are lots of these around the web, but I have found this one to be the best!)

The argument for Tau Day (with two pies . . . I’m in!)

My favorite activity to do with students on Pi Day . . . although I’ve heavily adapted it!

Happy Pi Day one and all!  I’m off to round up some pie for lunch 🙂

How Tall is That Tree?

One of my most favorite lessons to teach is featured in this month’s issue of NCTM Middle School Mathematics (February, 2014).  If you’re a member of NCTM, click here to check it out and download the handy classroom printables.  If you’re not a member, click here to join NCTM; then click here to read the lesson and download the handy printables (or, you could make friends with someone who is already a member of NCTM . . . like maybe your department head and talk them in to letting you read the lesson!).  However you get your hands on it, I hope you enjoy!

Here’s a little excerpt from the full text:

“The American Forests organization documents the largest trees int he 50 states and the District of Columbia.  Each state, responsible for locating its largest trees to add to the national database, has its own method for measuring and locating tall trees.  Some states rely on amateur tree hunters for nominations.” (MMS pg. 386)

Turn your students into amateur tree hunters in this lesson!

Math for High Ability Learners–at the University of Iowa

Just a quick note to let you know that I’m teaching Math for High Ability Learners, a 3 week virtual workshop offered at the University of Iowa beginning January 21.  The workshop is worth 1-hour of graduate or undergraduate credit from the University of Iowa.

To register for the course click here.

The focus of the course will be designing mathematics lessons to meet the needs of both the typical and the high-ability learners in K-12 mathematics classrooms.

To get a better idea of the coursework here’s the syllabus:

MHAL Spring 14–Syllabus.

I hope you’ll join me!

 

Reblogged from The Atlantic: The Myth of I’m Bad at Math

Today I’m reblogging a post I saw in The Atlantic this morning.  I’m reblogging it because I think the authors, Miles Kimball and Noah Smith, do a great job of articulating a sentiment that I think many, many mathematics teachers share.

(And because they talk about Terence Tao, and any true Math Warriors fan knows his importance in the world of mathematics!)

Enjoy.

 

 

Talking the Talk and Walking the (Math) Walk

A few days ago I was poking around my alma mater’s website (Go Panthers!) and came across this math walk:

unimathwalk

(This math walk was originally posted at: http://www.uni.edu/math/sites/default/files/pdfs/unimathwalk.pdf )

I thought it was such a cool idea that I wanted to create a math walk of my own!  (So I did).

I know that not all of you will be walking around Iowa City or The University of Iowa’s campus, so I thought I’d bring the math walk to you.  I’d encourage you to:

1. Try my virtual math walk

and then . . .

2. Get some friends, or a class, or your family and create a math walk of your own.  When you do, send it to me (katherine-degner@uiowa.edu) and I’ll post the math walks on my blog.  Soon no one will be able to walk around without “thinking math.”  Wouldn’t that be great!

My University of Iowa/Iowa City Math Walk

I work at the Belin-Blank Center, on the University of Iowa Campus . . . which is here:

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So, I headed out of the building toward the Pentacrest (more on that later) and the Old Capital.

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I got no more than half a block when I ran in to this!

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The official name of the sculpture is “Ridge and Furrow,” although many people at the University of Iowa refer to it as the “brain sculpture.” (For obvious reasons!).   It was carved by artist Peter Randall-Page.  The artist says that it is many up of one, continuous ridge flanked by v-shaped furrows.

1. The description made me think of the mobius strip.  In other words, think of this as one great big twisty infinity symbol (which is a mobius strip, just FYI).  I’m also wondering if we could cut the continuous ridge and stretch it out into a straight line, how long would it be?  How could you estimate this?

As I headed toward the Pentacrest, I couldn’t help but notice the bricks I was walking on.

They looked like this.  I also noticed they tessellated the plane.

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2. Which made me wonder, how many other ways could I arrange these standard sized bricks so that they would continue to tessellate the plane?  And, what wallpaper pattern does this tessellation belong to?  Which really asks, “What type of symmetry is being used to create this pattern?”

In the middle of my math walk many classes let out and I was flooded by students.  And I saw these two:

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3. Which made me wonder, what are the chances of that happening?  (In case you can’t tell from the picture, the two men are dressed exactly.the.same. blue t-shirts, khaki shorts).  This question takes the form of “if you have 3 pairs of blue socks, and 2 pairs of green socks, what are the chances that . . .”

I was headed to the Pentacrest because I knew about a secret on the Pentacrest.  I thought I was the only one that knew, until I found this.   Anyway, “what’s the secret?” you might ask.  Well, the University of Iowa Pentacrest is home to the largest walnut tree in the state of Iowa!  Here it is:

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This leads me to my next (maybe obvious? question).

4. How tall is the tree and how in the world do you measure it?

As promised at the beginning of the post, I have a little bit more to tell you about the Pentacrest.  First, you may or may not know that penta- means 5.  This might lead you to believe that the Pentacrest has five buildings.  And if that’s where your thoughts lead you, you’d be right!  The Pentacrest is a little piece of lawn which houses 5 university buildings (one of which is the Old Capitol).  I tried to take a picture of the Pentacrest, but the truth is the professional photographers, that took ariel pictures just do a much better job.  See:

pentacrest_slideshow

Do you also see how it kind of looks like a pentagon?  No, not THE Pentagon (which is a regular pentagon), but it does kind of look like a pentagon, except that the Old Capital isn’t a vertex.  Anyway, this leads me to my last question on my math walk:

5. Is there a way to get to each of the 5 buildings using the sidewalks provided, such that I go to all buildings and walk on each sidewalk exactly once?  (Kind of reminds you of the Bridges of Konigsberg Problem, doesn’t it?)

Whew!  You made it!  Happy math walking!

P.S. Once I started “math walking” I just couldn’t stop, so I snapped these pictures as I was walking home from work:

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I’m wondering:

6. What percent of the house is covered in ivy?

7. Is that an equilateral triangle?  How could we find out?