CTD Parent Seminar April 27, 2013 in Evanston

(now that the workshop has been completed, I've added several links that touch on the kinds of activities we did today)

Geoboard Workshop

Introduction:  Back-to-back activity

• communicating mathematically
• listening, following instructions
• geometric shapes
• coordinate systems -- locating a point in a  plane using two pieces of information

Squares on a geoboard (see also this page)

• measurement:  area of square, rectangle, right triangle; length of line segment
• problem solving strategies--solve a simpler, similar problem; change your point of view
• extensions: representing irrational numbers as lengths; discovering Pick’s Theorem; Pythagorean Theorem

  

Fourths on a geoboard

• fractions
• areas of irregular shapes
• line symmetry
• rotational symmetry
• congruent regions
• equal regions
• vocabulary:  vertical, horizontal, congruent, equal, reflection, rotation, line of symmetry, angle of rotation
• extensions: halves, eighths

Dynamic Geometry Follow-Up

Just to show what you can do with dynamic geometry software, here are some illustrations using the free software, Cinderella.

The task is to draw any quadrilateral, ABCD; locate the midpoints of the sides; connect the midpoints of the sides consecutively to obtain quadrilateral EFGH. Drag free points and make a conjecture about EFGH.

Here are three pictures of what happens when you move what is free to move. First, the diagram at the start:

Next is a picture showing what happens when the original quadrilateral is dragged to make it convex:

Finally a shot of what happens when the dragging makes ABCD into something we wouldn't even call a quadrilateral:

What appears to be true about EFGH in all three illustrations? How could you prove it?

Amazing Geoboards!

The geoboard is pretty much my favorite manipulative--there is so much mathematics that can be addressed using this simple tool.


My newest student is a gifted 6-year-old and the first manipulative I introduced him to was the geoboard. He had used one before, but I assured him we would be doing activities with it unlike any he had done at school.

By the end of the first hour, he was happily finding the areas of squares on the geoboard, and NOT just squares of size 1, 4, 9, and 16!

(There are FOUR other squares whose areas are whole numbers.  Give it a try. Email me with your results.)

During the second hour we collected data about the areas of shapes classified by the number of boundary pegs and the number of interior pegs. Over time, we'll work our way to Pick's Formula. (A mathematical discussion is presented in Chapter 2 of Strange Curves, Counting Rabbits, & Other Mathematical Explorations.)

By the end of the third hour my student had discovered a tessellation,

 but was more interested in creating more of his own designs.