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 ››
Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other.
Believe it or not, you can stick a pin straight through both maps … Continue Reading ››
Arrays can be enormously helpful tools for helping young learners to visualize multiplication. Early work with arrays also sets the stage for more advanced mathematics, like binomial multiplication
. In this blog post, I present several interactive arrays built with Web Sketchpad as part of the Dynamic Number
The interactive array model below (and … Continue Reading ››
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 ››
The picture below on the left shows a right triangle JML
with altitude KM
. This altitude is defined as the geometric mean
. Using similar triangles, you can prove that JK
². Another way to think about this construction is shown below on the right. Start with segments JK
and … Continue Reading ››
Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem
presented the image below with two squares, ABCD
sharing a vertex. Given that AE
= 5, what is the length of DG?
My first thought was that surely the problem was … Continue Reading ››
Estimation is an important mathematical skill, yet we rarely ask students to make estimates that relate to fractions. As part of the Dynamic Number
project, we created a "mystery" fraction challenge that presents a green point somewhere between 0 and 1 on the number line. The point's location can be represented as a fraction with … 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 One
In the first websketch
, students … 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 ››