The Math Education Blog
In a prior blog post, I introduced my new puzzle, Arranging Addends, that mixes arithmetic with logical thinking to create an engaging playground for mathematical discovery. Let’s revisit this puzzle and introduce some new variations. Take a look at the puzzle below (and here), built with Web Sketchpad. Your goal is to arrange the circles...
Mirek Majewski was born in Poland and studied mathematics at the Nicholas Copernicus University in Poland with an M.S. and Ph.D. in non-classical geometries. He is a professor of mathematics and computer science at several universities – PNG University of Technology, Inter-University of Macau (now Saint Joseph University), Zayed University in United Arab Emirates, and New York Institute of Technology....
In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip’s path as you pull the pencil around the taut string. Guaranteeing that the traced path...
Several weeks ago, my friend Martin shared the following probability puzzle with me: Two points are chosen independently and at a random on a stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle? This is a classic problem, dating back...
Did you know that aside from being a source of news, The New York Times is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum editor, Dan...
In my prior post, I presented a “zooming” number line model that allowed students to estimate the location of a point along a number line and then repeatedly magnify that portion of the number line to obtain ever-finer estimates, accurate to tenths, hundredths, thousandths, and beyond. In a sense I got ahead of myself because I...
One of the aspects I like best about Dynamic Geometry software like Web Sketchpad is its ability to illustrate concepts that cannot effectively be represented with static media. Take, for example, a number line that we draw on a white board. Showing the number line labeled with integers is easy. Adding tenth-mark divisions to the...
With Web Sketchpad, it’s easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics. My goal was to design a lesson focusing on the triangle area formula, A = bh/2. In particular,...
In my prior posts ( When Factoring Gets Personal, Open the Safe, and Reasoning with Multiples to Find the Mystery Number), I’ve given examples of how learning about multiples and factors can be made more engaging through the use of puzzles. Now, to add to this collection, is the lock puzzle below (and here). The first page of...
The origins of this week’s Web Sketchpad model date back to the Connected Geometry curriculum from the mid 1990s. I was one of the co-authors of the curriculum, working at Education Development Center with a wonderful team of math educators (Al Cuoco, Paul Goldenberg, and June Mark, among others) to develop a habits of mind approach...