What is 4 divided by zero? Some students reason that you can think of it as long division and take out as many zeroes as you like from 4 without ever making 4 smaller. So maybe 4 divided by zero is "infinity"?
Wednesday, November 30, 2022
Why can't I divide by zero?
Wednesday, November 9, 2022
Rectangles and Triangles
Rectangles are so simple. Their angles are always 90 degrees. But triangles come in all different shapes. So how do you find the area of a triangle?
Check out this musical video about the area of triangles: Rectangles and Triangles
Saturday, October 22, 2022
Map Folding Problem
The lines in the map above show how it was folded. Dotted lines show a “valley fold” and solid lines show a “mountain fold.” This map was folded in half horizontally, then vertically, then vertically again.
Question: Each of the maps below was folded in four steps – in half each time. Which of the maps is an “impossible map”?
Thursday, October 13, 2022
Prime Time!
A new song!
Welcome to Prime Time Building Supply! Imagine a store that sells prime numbers. We sell classics like 2, 3, 5, or 7. We also sell the elegant and understated 1009. With our prime numbers, you can build composite numbers of any size!
The song: Prime Time
Wednesday, October 5, 2022
Gauss’ Trick
I am happy to announce the launch of a new project. This is the first in a series of musical math videos. Please enjoy and share this song about the mathematician Gauss as a little boy and his trick for adding the numbers from 1 to 100.
Musical video: https://youtu.be/XlGsUlIEdYc
Companion video explanation of Gauss' method: https://youtu.be/fTluDWc1vA
Tuesday, March 15, 2022
Lattice Polygons, Part 2
Lattice polygons are polygons are formed by connecting dots on square dot paper. (On a coordinate graph, the coordinates of the vertices are integers.).
The lattice polygon below is a rectangle whose dimensions are 2 units by 4 units. Its area is 8 square units.
(1) Can you make a small change to the rectangle so that the area of the new polygon is 6 square units? There are lots of ways to do this.
Thursday, March 10, 2022
Same Sum Circles, Part 2
Sunday, January 30, 2022
The Sock Problem #2
Silas reaches into his sock drawer in the dark, and he wants to make sure that he grabs a matching pair. The drawer has 3 identical blue socks, 2 orange, 1 red, 1 purple, and 1 green sock.
Question: How many socks must Silas grab to ensure that he has at least one matching pair?
PLAYFUL MATH BLOG CARNIVAL #163
BLOG CARNIVAL #163....LET'S GO! Fun fact: The number 163 is prime, which we can prove simply by showing that it is not divisible by 2, 3...

The scales below are balanced. Each scale is a different puzzle. For each scale, start by taking off as many blocks as you can from each si...