How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown? For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››
I was delighted that Daniel recently posted our Binomial Multiplication sketches in Web Sketchpad format. I thought about those sketches when I noticed a fairly new myNCTM thread on "When and How do we phase out the body in math education?" This thread raises a very important question for us as … Continue Reading ››
The four Web Sketchpad activities below from our Dynamic Number project provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.
Dynamic Algebra Tiles, Part OneIn the first websketch, … Continue Reading ››
In my previous post, I wrote about cross number puzzles—puzzles that mix arithmetic and logic to introduce students to place value, commutativity, and the addition and subtraction algorithms. Now, I'd like to present a variant of cross number puzzles that adds some algebra to the mix. Below (and here on its own page) are … Continue Reading ››
We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››
In the interactive Web Sketchpad model below (and here on its own page), ABCD is an arbitrary quadrilateral whose midpoints form quadrilateral EFGH. Drag any vertex of ABCD. What do you notice about EFGH? The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics … 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 ››