In my previous post
, I presented a number line model for adding fractions. Now, I'd like to offer an updated Web Sketchpad fraction model below (and here
) with two new pieces of functionality:
- You can subtract as well as add fractions.
- You can divide the number line into equal parts and choose the … Continue Reading ››
In previous posts, I've presented fraction-related websketches from the Dynamic Number
project. Several of these activities—specifically Dividing and Subdividing
and Deducing the Mystery Fraction
—focus on a number-line representation of fractions. Below (and here
) is another such websketch, with students constructing segments of fractional length that can be placed end to … Continue Reading ››
Mathematics is a wonderful game. It's one that can stretch students' minds and expose them to the beauty and unexpected delights that lie behind every good problem.
I've always gravitated to colleagues who share my love of math's playful, game-like side, so I quickly made friends with Toni Cameron when we met at P.S. 503 in … Continue Reading ››
This month's post is based on a problem that appears in Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American
. Below (and here
) is a Web Sketchpad model of an orderly forest. There is a tree at every point whose x
- and y
-coordinates are both integers. These are the green points. You … Continue Reading ››
Given a strip of paper, how might you divide it into fourths without using a ruler? Undoubtedly, you'd fold the strip in half and then in half again to locate the quarter marks. Now suppose that your goal is to divide a strip into sixths. You might start by folding the strip into thirds and … Continue Reading ››
On the NCTM discussion site myNCTM, there's currently an extended discussion about "Division and multiplication of fractions." As the discussion has continued, I've grown concerned with what I see as a fundamental problem with the way we often introduce multiplication as repeated addition: "Multiplying 4 by 5 means we're combining five groups of four items. … Continue Reading ››
We created the Web Sketchpad game below (and here
) as part of our Dynamic Number project. It challenges elementary-age students to uncover the value of a secret number by collecting and analyzing clues that narrow its range of possible values. The game familiarizes students with inequality signs, introduces the use of x
to represent an … Continue Reading ››
A recent post on the my NCTM discussion group
asked about tools to help students visualize and understand addition and subtraction of integers.
I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … 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 project.
The interactive array model below (and here
) … 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 ››