Have a Mathematical Thanksgiving Dinner

With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

Optimal Potatoes

Green Bean Matherole

Borromean Onion Rings

Thanksgiving Turduckenen-duckenen

And for Dessert

May I suggest some of Don Cohen’s Infinite Cake?

Click here for cake

CREDITS: “Thankful” photo (top) by Pro Church Media via Unsplash.com. Food videos by mathemusician/doodler Vi Hart.

Discern Patterns

I’m almost done rewriting the Standards for Mathematical Practice into student-friendly language.

They say mathematics is the science of patterns. So here’s…

Math Tip #7: Discern Patterns.

  • Look for patterns in numbers, shapes, and algebra equations.
  • Notice how numbers can break apart to make a calculation easier.
  • Number patterns morph into algebra rules.
  • Adapt math situations to make the structure clear. (For example, by adding new lines to a geometry diagram.)
  • Step back from a situation to see it from a new perspective.
  • Try to find simpler patterns within complex equations or diagrams.
  • Not all patterns continue forever. Test your patterns. Can you trust them?

Continue reading Discern Patterns

Exciting New Homeschool Math Program

Homeschooling friends, check out this new homeschool math program that’s fun, rigorous, and engaging — a delightful, hands-on course that helps parents (and their children) understand math.

Introduction to Cuisenaire Rod Structures Course

I had the privilege of previewing this class as Sonya and Lacy put it together. I highly recommend it to anyone who struggles with math, or who wants to take a non-traditional approach.

By focusing on making sense of number relationships, and by teaching algebra before arithmetic, this course provides a stress-free path to rich mathematical mastery.

And for all they provide, including weekly live workshops and a slew of printable math journal pages that prompt deep thinking, the price is a steal!

Continue reading Exciting New Homeschool Math Program

Say What You Mean

Continuing my project of rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP6…

Math Tip #6: Say What You Mean.

  • Words can be tricky, so watch your language.
  • Label drawings and graphs to make them clear.
  • If you use a variable, tell what it means.
  • Care about definitions and units.
  • Pay attention to rules (like the order of operations).
  • Use symbols properly (like the equal sign).
  • Understand precision. Never copy down all the digits on a calculator.

Continue reading Say What You Mean

Math as a Verb

Here’s the full quote:

I like to play games. Almost any type of game.

I also like to play math.

If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

—John Golden
Yes, Playing Around

CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

Master Your Tools

As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP5…

Math Tip #5: Master Your Tools.

  • Collect problem-solving tools.
  • Practice until you can use them with confidence.
  • Classic math tools: pencil and paper, ruler, protractor, compass.
  • Modern tools: calculator, spreadsheet, computer software, online resources.
  • Physical items: dice, counters, special math manipulatives.
  • Tools for organizing data: graphs, charts, lists, diagrams.
  • Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.

Continue reading Master Your Tools

FAQ: Playful Math for Older Students

My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

Here are a few ideas to get your older children playing with math…

Continue reading FAQ: Playful Math for Older Students

Look Beneath the Surface

So, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s the fourth installment…

Math Tip #4: Look Beneath the Surface.

  • Notice the math behind everyday life.
  • Examine a complex situation. Ignore the parts that aren’t relevant.
  • Pay attention to the big picture, but don’t lose track of the details.
  • Make assumptions that simplify the problem.
  • Express the essential truth using numbers, shapes, or equations.
  • Test how well your model reflects the real world.
  • Draw conclusions. Explain how your solution relates to the original situation.

Continue reading Look Beneath the Surface

The Value of Puzzles

I love puzzles. Don’t you?

Here are several examples of river-crossing puzzles you and your kids can try. They date back at least to the time of Alcuin, the famous scholar from the court of Charlemagne.

I wish someone would write a whole math curriculum devoted entirely to puzzles.

W.W. Sawyer on the Value of Puzzles

Master teacher W.W. Sawyer didn’t write a curriculum, but he often used puzzles in the classroom.

“It is quite possible to use simultaneous equations as an introduction to algebra. Within a single lesson, pupils who previously did not know what x meant can come not merely to see what simultaneous equtions are, but to have some competence in solving them.

“No rules need to be learnt; the work proceeds on a basis of common sense.

“The problems the pupils solve in such a first lesson will not be of any practical value. They will be in the nature of puzzles.

“Fortunately, nature has so arranged things that until the age of twelve years or so, children are more interested in puzzles than in realistic problems.”

—W. W. Sawyer, Vision in Elementary Mathematics

Then he gives this example:

“A man has two sons. The sons are twins; they are the same height. If we add the man’s height to the height of one son, we get 10 feet. The total height of the man and the two sons is 14 feet. What are the heights of the man and his sons?”

Try This at Home

Not only can children solve puzzles like this, but even better — they can make up story puzzles of their own. You could spend a whole week or more making up silly height puzzles for each other to solve. By the time you were done, your kids would have a great introduction to algebra!

Maybe I never grew up. Because I still prefer puzzles over “real world” math problems.

What are your favorite kinds of puzzles? Please share in the comments section.

CREDITS: “Boat puzzles” comic from xkcd.com.
[THE FINE PRINT: I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]