Sep 262014
 
Visual Patterns no 115 300x78 Visual Pattern Site by Fawn Nguyen

pattern no. 155 from Fawn Nguyen’s site visualpatterns.org

When I taught 7th grade for six years visual patterns were used to start the school year because they did so many great things for students. They were engaging to the students, visually stimulating, allowed all students easy entry to the math involved, worked great for student projects, and addressed many math standards. Here’s a site with a lot of patterns you can use in your classroom, along with commentary for teacher use.

As of the date of this post (Sept 2014) there are 145 patterns, along with the Equation Key. Fawn Nguyen is the host of the site, and teachers/others are encouraged to submit patterns for others to use. She has another site, Finding Ways, that in her words: “is where I tell stories that are mainly about teaching and learning mathematics in the classroom.”

Take a look and be prepared to find some nice patterns to use when teaching linear functions.

Sep 252014
 

Malin Christersson Digital Math Malin Christersson Digital Math for GeoGebra EnthusiastsMalin Christersson’s site, Digital Mathematics, is a great place to spend some time for GeoGebra enthusiasts. It has some of the best tutorials on the web, organized into seven clusters. Malin provides clear and detailed explanations, some with embedded videos, that help the new as well as experienced user to get more out of GeoGebra. Malin also has provided further work in the areas of Non-Euclidean Geometry, Latex/LyX, Geometry, Functions, Trigonometry, Calculus, Statistics, Linear Algebra, and Fractals.

From the site:
“This is a collection of material that I have used when teaching or giving workshops about GeoGebra. All pages are written in HTML5 and styled using CSS3. They are fully functional only if viewed from a modern browser, e.g. Google Chrome or Firefox. The GeoGebra worksheets on this site can be found at MalinC’s GeoGebra-book. When GeoGebraTune is down, the worksheets on this site will not work. Since this web site relies heavily on lengthy Javascript calculations, it may be worth pointing out that Google Chrome is faster than the other browsers when it comes to Javascript (no, I don’t work for Google, and I personally prefer Firefox, but I have made several tests to check out browsers when it comes to Javascript, and Chrome is best).”

I’ve learned a lot from reading Malin’s work and suggest the site for all those who are serious about GeoGebra. It makes me want to delve deeper into the mechanics of this great educational software, and points out one of its open-source strengths: that of people all over the globe sharing what they know and love.

Sep 242014
 

Dissect the circle into four parts of equal area by drawing three curved lines of equal length.
– idea from Arithmetrics, by Jerome S. Meyer, pg 88
Move slider halfway to reveal a hint if you’re stuck.

Questions for you or your students:
1- Why are the 3 curved lines of equal length?
2- How do you show that the 3 curved lines make equal areas?

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

here.

Sep 232014
 

Van Aubel’s Theorem describes a relationship between squares constructed on the sides of a quadrilateral. In Martin Gardner’s “Mathematical Circus,” pg 179, he shows generalizations of this theorem. This one is for triangles. Starting with a triangle, construct a square on each side. In this case Van Aubel’s Theorem says that the line segment between the centers of two of the squares and the line segment between a vertex of the triangle and the center of its opposite square are of equal lengths and are at right angles to one another.

Draggable points are colored red.

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Yin and Yang Extended

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Sep 232014
 

Here’s the familiar yin-yang figure in a circle of radius 1. If you continue subdividing the diameter of the large circle into semicircles, this wavy line approaches the diameter as a limit. It’s tempting to say that this wavy line then has a length of 2, but of course, its length is still π. Starting at the top and moving downward, any path (mix and match) also has length π.
– idea from “Wheels, Life and other Mathematical Amusements“, by Martin Gardner, pg 54

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 232014
 

How many rows with 4 plants per row can be made with different numbers of trees?
Interesting questions to pose about graph theory for classroom exploration -from Time Travel and other Mathematical Bewilderments, by Martin Gardner, pgs 280-290

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 232014
 

Here’s an interesting problem to pose for classroom discussion and exploration: How many rows with 3 plants per row can be made with different numbers of trees?

-from Time Travel and other Mathematical Bewilderments, by Martin Gardner, pgs 280-290

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Sep 212014
 

Each row begins with the number 1 at the left. Skip counting by 2, 3, 4, 5, and so on gives the rest of each row. The diagram can be continued as far as desired.
Adding the numbers in each L-shaped region forms a well known mathematical sequence; what pattern shows up?
Another mathematical pattern is formed by the numbers along the diagonal? What pattern is this?

– idea from Math Puzzles & Games, by Michael Holt, pg 27

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Van Aubel’s Theorem

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Sep 212014
 

Van Aubel’s theorem describes a relationship between squares constructed on the sides of a quadrilateral. Starting with a given quadrilateral (a polygon having four sides), construct a square on each side. Van Aubel’s theorem holds that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another. Another way of saying the same thing is that the center points of the four squares form the vertices of an equidiagonal orthodiagonal quadrilateral. The theorem is named after H. H. van Aubel, who published it in 1878. There is a proof of the theorem on the cut-the-knot.org site in an entry called Squares on Sides of a Quadrilateral – What is this about? A Mathematical Droodle.

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.

Cevian Triangles

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Sep 212014
 

A cevian is a segment drawn from a vertex of a triangle to the opposite side. In this case the point on the opposite side is a trisection point. These cevians create seven triangles, and each triangle has an area that is a multiple of 1/21 of the area of the original triangle.
Can you find the area of each region?
– from wikipedia: Giovanni Ceva (December 7, 1647 – June 15, 1734) was an Italian mathematician widely known for proving Ceva’s theorem in elementary geometry.
– idea from 1000 PlayThinks, by Ivan Moscovich, page 128

The downloadable file can be found here.
My other GeoGebraTube apps can be found here.