With a few adjustments, we can make the Hundred Chart more intuitive and more useful for students. This post explains why the improvements are needed and describes how students can build a physical model that more accurately corresponds to the number

# Category Archives: Elementary Mathematics

# A New Twist on Arranging Addends

Of all the original games I've designed, Arranging Addends is among my favorites. On page 1 of the Web Sketchpad model below (and here), you're given five addends—1, 2, 4, 8, and 16—and asked to arrange them in the circles so that the sum of the numbers in each circle matches the values … Continue Reading ››

# Tanton’s Two-Pan Balance Puzzle

I'm a big fan of pan-balance puzzles in which you're given a two-pan balance and asked to use it to uncover a counterfeit coin or determine the weight of a coin. One classic example is the following puzzle:

*You have 12 coins that all look exactly the same. One is counterfeit and is either heavier … Continue Reading ››*

# Splitting Arrays

In last month's Construct a Building post, I presented any array model in which students construct the rooms and floors of a building as a way of representing multiplication. Now I'd like to follow up with a similar array model that allows students to take a problem they don’t know, like 8 × 7, and … Continue Reading ››

# Construct a Building: Modeling Multiplication with Arrays

When Scott Steketee and I developed activities for the Dynamic Number project, we thought about ways that dynamic array models could help children to conceptualize multiplication.

Rather than presenting children with arrays that were fully formed, we thought it would be instructive for them to build these arrays themselves. That design goal led to the … Continue Reading ››

# Adding and Subtracting Fractions on a Number Line

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 ››

# Adding Fractions on a Number Line

In previous posts, I've presented fraction-related Web Sketchpad models 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 … Continue Reading ››

# Early Childhood Math Routines

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 ››

# Beam of Light

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. … Continue Reading ››

# Dividing and Subdividing

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 ››