Writing to Learn Math: When students learn to visualize shapes, designs, and patterns, it makes them better at math.
Do you want your children to develop the ability to reason creatively and figure out things on their own?
Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.
In this game, players practice multiplication facts and use strategic planning as they build 2-D shapes to block their opponent.
Many parents remember struggling to learn math. We hope to provide a better experience for our children.
And one of the best ways for children to enjoy learning is through hands-on play.
Math Concepts: multiplication, area, 2-D shapes.
Players: two players.
Equipment: square graph paper (lined or dotty).
This game offers a fun twist on the old classic Battleship. Can you discover your opponent’s secret shape before they find yours?
Many parents remember struggling to learn math. We hope to provide a better experience for our children.
And one of the best ways for children to enjoy learning is through hands-on play.
Math Concepts: coordinate graphing (first quadrant), simple linear equations, irregular polygons.
Players: two players or two teams.
Equipment: printed gameboard or square grid paper for each player, pencils, ruler or other straightedge.
No peeking! This post is for those of you who have given the trisection proof a good workout on your own.
If you have a question about the proof or a solution you would like to share, please post a comment here.
But if you haven’t yet worked at the puzzle, go back and give it a try.
When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.
One of the great unsolved problems of antiquity was to trisect any angle, to cut it into thirds with only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass.
Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator.
One “cheat” that works is to fold your paper.
I will show you how it works, and your job is to show why.
Thursday is Pythagorean Triple Day, one of the rarest math holidays.
The numbers of Thursday’s date: 7/24/25 or 24/7/25, fit the pattern of the Pythagorean Theorem: 7 squared + 24 squared = 25 squared.
Any three numbers that fit the a2 + b2 = c2 pattern form a Pythagorean Triple.
We were eclectic homeschoolers back in the Dark Ages before there was an internet. Our primary curriculum was the public library.
As we went along, I noticed how many of our homeschooling friends felt uncomfortable with math, and even hated or feared the subject.
Math anxiety runs rampant in Western culture. By one researcher’s estimate, more than 90% of adults experience some level of math anxiety — that is, discomfort, avoidance, and even emotional pain when faced with a math calculation.
So I became a sort of “math evangelist” in the homeschooling community, spreading the news that we can find beauty and fun even in math.
On May 5, we celebrate one of the rarest math holidays: Square Root Day, 5/5/25.
Here are a few ideas for playing math with squares and roots.
Five is the square root of twenty-five, which means it is the number we can “square” (multiply times itself) to get 25.
The root is the base number from which the square grows. In physical terms, it is the side of the square.
Imagine a straight segment of length 5, perhaps a stick or a piece of chalk. Now lay that segment down and slide it sideways for a distance equal to its length. Drag the stick across sand, or pull the chalk across paper or a slate.
Notice how this sideways motion transforms the one-dimensional length into a two-dimensional shape, a square.
The area of this shape is the square of its root: 5 × 5 = 25.
What do you think would happen if you could drag the square through a third dimension, or drag that resulting shape through a fourth dimension?
How many shapes do you suppose might grow from that original root of 5?
Are your students doing anything special for Pi Day?
Back when we were homeschooling, my kids and I always felt stir-crazy after two months with no significant break. We needed a day off — and what better way could we spend it than to play math all afternoon?
I love any excuse to celebrate math!
Pi Day is March 14. If you write dates in the month/date format, then 3/14 at 1:59 is about as close as the calendar can get to 3.14159etc.
(Otherwise, you can celebrate Pi Approximation Day on July 22, or 22/7.)
Unfortunately, most of the activities on teacher blogs and Pinterest focus on the pi/pie wordplay or on memorizing the digits. With a bit of digging, however, I found a few puzzles that let us sink our metaphorical teeth into real mathematical meat.
In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same.
Every circle you can imagine is the exact image of every other circle there is.
This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand upright, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters.
What makes a circle so special and beautiful? Any child will tell you, what makes a circle is its roundness. Perfectly smooth and plump, but not too fat.
The definition of a circle is “all the points at a certain distance from the center.” Can you see why this definition forces absolute symmetry, with no pointy sides or bumped-out curves?
One way to express that perfect roundness in numbers is to compare it to the distance across. How many times would you have to walk back and forth across the middle of the circle to make the same distance as one trip around?
The ratio is the same for every circle, no matter which direction you walk.
That’s pi!
For all ages:
Sarah Carter created this fun variation on the classic Four 4s puzzle for Pi Day:
Using only the digits 3, 1, 4 once in each calculation, how many numbers can you make?
You can use any math you know: add, subtract, multiply, square roots, factorials, etc. You can concatenate the digits, putting them together to make a two-digit or three-digit number.
For older students:
1. Imagine the Earth as a perfect sphere with a long rope tightly wrapped around the equator. Then increase the length of the rope by 10 feet, and magically lift it off the Earth to float above the equator. Will an ant be able to squeeze under the rope without touching it? What about a cat? A person?
2. If you ride a bicycle over a puddle of water, the wheels will leave wet marks on the road. Obviously, each wheel leaves a periodic pattern. How the two patterns are related? Do they overlap? Does their relative position depend on the length of the puddle? The bicycle? The size of the wheels?
3. Draw a semicircle. Along its diameter draw smaller semicircles (not necessarily the same size) that touch each other. Because there are no spaces in between, the sum of the diameters of the small semicircles must equal the diameter of the large one. What about their perimeter, the sum of their arc lengths?
4. Choose any smallish number N. How can you cut a circular shape into N parts of equal area with lines of equal lengths, using only a straight-edge and compass? Hint: The lines don’t have to be straight.
[Solutions at Alexander Bogomolny’s Pi Page. Scroll down to “Extras.”]
It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.
— Edward Titchmarsh
Here are a few pi-related links you may find interesting:
Or for pure silliness:
Have fun playing math with your kids!
Publication Day!
Prealgebra & Geometry: Math Games for Middle School hits the online bookstores today.
You can prepare your children for high school math by playing with positive and negative integers, number properties, mixed operations, algebraic functions, coordinate geometry, and more. Prealgebra & Geometry features 41 kid-tested games, offering a variety of challenges for students in 4–9th grades and beyond.
A true understanding of mathematics requires more than the ability to memorize procedures. This book helps your children learn to think mathematically, giving them a strong foundation for future learning.
And don’t worry if you’ve forgotten all the math you learned in school. I’ve included plenty of definitions and explanations throughout the book. It’s like having a painless math refresher course as you play.
Denise Gaskins' Let's Play Math 