Monday Math Freebie - A Twist on the Dot Game

While searching for resources for teaching scientific notation I came across a middle school version of the dot game where students were required to simplify exponents and record numbers in scientific notation. I loved this idea and wrote to the author asking if I could adapt his idea for the elementary classroom. My thanks to Kevin Koch for giving me permission to create these resources! Here's what I've come up with so far.

In this version of the dot game, students draw line segments and form boxes as usual. When they complete a box, they earn one point. However, if they complete a box with a picture, they must solve some type of problem (write the number, name the fraction, etc.). Answering correctly earns a player extra points. Once all the boxes have been made, players total their scores. The player with the highest score is the winner.

I made two versions to start. One game is for young students on identifying numbers. The other is for older students and is on naming and writing fractions in simplest form. Here's what they look like.

Download What's That Number? Dots and Boxes.

 

 Download Fraction Dots and Boxes.

I hope you get a chance to use these in your home or classroom. Please let me know if you try these and how you like them! 

Thinking Beyond Big

Even though I've been thinking about nanotechnology and things that are very small lately, I'm also pondering something at the opposite end of the spectrum. Actually, it's not a thing, but an idea.

What do you know about infinity? While teaching about fractions and decimals I often talk about the density property of numbers, or the idea that there always exists another real number between any two given real numbers. For example, can you name a number between 1 and 2? How about 1.5? Can you now name a number between 1 and 1.5? Sure you can! Let's pick 1.4. Can you name a number between 1.4 and 1.5? No matter what numbers you pick, you can always name a number between them, and you can do this forever.

Can numbers be infinitely big and/or infinitely small? Are there different sets of infinite numbers? These are great questions, and the just the very sort I want kids to ponder as they think about numbers and our system of numeration.

Here are two videos I like that nicely capture these questions and ideas.

Thinking Small

When the Virginia Standards of Learning for Science were revised in 2010, nanotechnology was added to the content of the 3rd and 5th grade study of matter. Here's how it reads.

Nanotechnology is the study of materials at the molecular (atomic) scale. Items at this scale are so small they are no longer visible with the naked eye. Nanotechnology has shown that the behavior and properties of some substances at the nanoscale (a nanometer is one-billionth of a meter) contradict how they behave and what their properties are at the visible scale.

In 5th grade they include the above information and add the following sentence.

Many products on the market today are already benefiting from nanotechnology such as sunscreens, scratch-resistant coatings, and medical procedures.

Since elementary school students are just grappling with our number system and how it's constructed, understanding the math of the nanoscale (negative exponents!) can be difficult. One of the best ways to approach this topic is to make comparisons that kids will understand. This UC-SD-TV program is one of my favorite resources on nanoscience.

If you want to play around a bit with the nanoscale, check out this McREL site.

Finally, if you are looking for some teaching resources, check out my Pinterest board on nanotechnology.

Making Cartesian Divers

If you have an interest in math and science and don't subscribe to the AIMS blog, Math & Science Sandbox, you should! They post all kinds of ideas for teaching math and science, as well as a bunch of challenging problems to solve.

Back in May they posted this terrific video on making Cartesian divers.

Check out the Interesting Science Objects post to download a PDF about Cartesian divers.

History and Biography in Math and THE BOY WHO LOVE MATH

I've just finished teaching a course for teachers called Improving Elementary Math. As I think about what I might do differently next time and finally put away all my books and manipulatives, I find myself wondering how I might do more with biography in the elementary math classroom.

AIMS has long published a series of books on Historical Connections in Mathematics (3 volumes for the middle and high school audience). They also publish the series Mathematicians are People, Too (2 volumes for the middle school range, grades 5-9). Although the focus of these books is on the mathematicians and their stories, the mathematics are touched upon and explained in simple terms.

• Mathematicians featured in Mathematicians are People, Too, Volume One include: Thales, Pythagoras, Archimedes, Hypatia, Napier, Galileo, Pascal, Newton, Euler, Lagrange, Germain, Gauss, Galois, Noether, and Ramanujan.
• Mathematicians featured in Mathematicians are People, Too, Volume Two include: Euclid, Omar Khayyam, Fibonacci, Cardano, Descartes, Fermat, Agnesi, Banneker, Babbage, Somerville, Abel, Lovelace, Kovalevsky, Einstein, and Polya.

I don't have any answers yet, though I have quite a few biographies in my library.

Right now I'm quite fond of the book THE BOY WHO LOVED MATH: THE IMPROBABLE LIFE OF PAUL ERDOS, written by Deborah Heiligman and illustrated by LeUyen Pham. It begins this way:

There once was a boy who loved math. He grew up to be 1 of the greatest mathematicians who ever lived. And it all started with a big problem . . . 

Heiligman takes readers through his early years, his life at home with Fraulein, his foray into school (which didn't last long), and his fascination for numbers.

When Paul was 10 "He fell in love with prime numbers." On a double-page spread featuring a Sieve of Eratosthenes on one side and an introduction to prime numbers on the other, readers learn a lot of math while learning about Paul. As Paul asked questions about numbers, so too can readers. Here's an excerpt.

Paul had a lot of questions about Prime Numbers.
Do they go on forever?
Is there a pattern to them?
Why is it that the higher up you go, the farther apart the prime numbers are?
Paul loved to think about prime numbers.

Paul did go to high school, and by the time he was 20, was already well-known around the world for his math. He lived unconventionally, traveling the world and staying with mathematicians, working problems with them, and living a very mathematical life.

There is an author's note in the back, describing her research and expanding on some of the stories in the book, as well as sharing bits that were not included in the text. There is also a lengthy note from the illustrator that describes many of the images and their meaning while outlining how math is included in the illustrations.

I think all kids would enjoy this story, but if I were still teaching young kids today, I'd slip it to the child who felt he/she didn't fit in, or the one with an unbounded love for a subject that other kids just didn't understand. Surely they'd be as inspired as I was by Uncle Paul's story.

After writing this I realized this was a perfect post for Nonfiction Monday. Head on over to Abby the Librarian for more on nonfiction this week.