This post presents virtual dances based on geometric transformations. As a penguin travels around a polygon, you, as a frog, must match its movements, but with the added challenge of dancing as a reflection, rotation, or dilation of the penguin’s path.
Category Archives: Assessment
Transformation Games
This post presents an abundance of games that find their inspiration in three geometric transformations: reflection, rotation, and dilation.
Dynagraphs of Linear Functions
This post provides three interactive examples of dynagraphs–a powerful representation of functions that emphasizes the behavior and relationship of a function’s independent and dependent variables.
A Bevy of Rhombus Constructions
In how many ways can you use dynamic geometry software to build a rhombus that stays a rhombus when its vertices are dragged? This challenge, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties … Continue Reading ››
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 ››
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 ››
Find the Secret Number
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 … Continue Reading ››
Deducing the “Mystery” Fraction
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 numerator between … Continue Reading ››
Algebra Cross Number Puzzles
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 ››
Cross Number Puzzles
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 ››