Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.On page 1 of the websketch below (and here), begin by asking students to drag point … Continue Reading ››
For the past five years, Scott and I have featured interactive Web Sketchpad models in nearly all our Sine of the Times blog posts. As much fun as it's been to build "websketches" to share with you, we've really wanted to put the creative power of Web Sketchpad into your hands. And now, finally, that's possible. Today … Continue Reading ››
In his 1947 book, One, Two, Three...Infinity, physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle.
Among a pirate's belongings you find the following note: The island where I buried my treasure contains a single palm tree. Find the tree. From the palm tree, … Continue Reading ››
The picture below on the left shows a right triangle JML with altitude KM. This altitude is defined as the geometric mean of JK and KL. Using similar triangles, you can prove that JK × KL = KM². Another way to think about this construction is shown below on the right. Start with segments JK and … Continue Reading ››
At the 2017 NCTM Annual Meeting I was invited to do a short Wednesday-afternoon presentation on Function Dances in the NCTM Networking Lounge. (Here's the handout from the presentation.) The idea of function dances is to get students (or in this case teachers) moving around, acting as the independent and dependent … Continue Reading ››
In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››
Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square? I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››