Probability Puzzles with Obsolete Coins

Posted on by Denise Gaskins
jar of coins

I love math puzzles, and Henry Ernest Dudeney is the foremost puzzlemeister of all time.

Whenever I need a diversion from the pressing day-to-day busyness of life, I like to crack open one of his books. And get humbled. He stumps me as often as not, but I enjoy the challenge.

Today, I’ve got two of his somewhat-easier puzzles from Amusements in Mathematics, dealing with the probability of obsolete coins tossed or pulled from a bag.

Okay, so the penny isn’t obsolete quite yet, even though the US government quit making them. But the “penny” in these puzzles is the old British pence, which went out of date seemingly ages ago, along with all the other non-decimal coins that made old math puzzles so confusing.

Probability puzzles are great for middle school students because the arithmetic itself is simple. The challenge is in figuring out exactly what calculation to do.

Have fun playing math with your kids!

Continue reading Probability Puzzles with Obsolete Coins

Conversion Factors: How Old Are You in Nanoseconds?

Posted on by Denise Gaskins
birthday cupcake with sparkler

Homeschool Memories

[Based on a problem I made up for my co-op students, once upon a time…]

Conversion factors are special fractions that contain problem-solving information. Why are they called conversion factors?

  • “Conversion” means change, and conversion factors help you change the numbers and units in your problem.
  • “Factors” are things you multiply with. So to use a conversion factor, you will multiply it by something.

For instance, if I am driving an average of 60 mph on the highway, I can use that rate as a conversion factor. I may use the fraction:

Or I may flip it over to make:

It all depends on what problem I want to solve.

After driving two hours, how far have I gone?

But if I am planning to go 240 more miles, how much longer will it take?

Any rate can be used as a conversion factor. You can recognize them by their form: this per that. Miles per hour, dollars per gallon, cm per meter, and many, many more.

Of course, you will need to use the rate that is relevant to the problem you are trying to solve. If I were trying to figure out how far a tank of gas would take me, it wouldn’t be any help to know that an M1A1 Abrams tank would get about 1/3 mile per gallon. I won’t be driving one of those.

Continue reading Conversion Factors: How Old Are You in Nanoseconds?

This Puzzle Is Murder

Posted on by Denise Gaskins
cartoon detective

Do you sometimes mourn (in a small way) the loss of a favorite website? I still miss the Daily Set puzzle, which was part of my morning routine for years.

But lately, I’ve added a new teaser to wake up my brain for the day.

While Set was a visual-logic puzzle, this one is straightforward (though not simple) deduction. I think you’ll enjoy it.

Continue reading This Puzzle Is Murder

Tasty Treats from the Moscow Puzzles

Posted on by Denise Gaskins
basket of apples

“Problems stressing deduction rather than calculation have a special appeal and value. They teach you to analyze, and to seek unorthodox ways of solving a problem.”

—Boris Kordemsky

Today I’m sharing a few treats from The Moscow Puzzles by Boris Kordemsky, which mixes classic brainteasers and original stumpers.

Recreational math expert Martin Gardner called Kordemsky’s book “the outstanding puzzle collection in the history of Russian mathematics.”

Have fun playing logic with your kids!

Continue reading Tasty Treats from the Moscow Puzzles

Rescuing Cool Math for Older Kids

Posted on by Denise Gaskins
mother and teen daughter do homework together

Do you have math dreams for your children?

Here are some dreams shared the authors of Avoid Hard Work!

For our children, we dream that mathematics…

  • … makes sense.
  • … is more than just arithmetic.
  • … is joyous.
  • … makes them strong.
  • … is meaningful.
  • … is creative.
  • … is full of fascinating questions.
  • … opens up many paths to solutions.
  • … is friendly.
  • … solves big problems and makes the world better.
  • … is a powerful tool they can master.
  • … is beautiful.
  • … lets them learn in their own ways.
  • … is connected to their lives.
  • … asks “why” and not just “how.”
  • … opens the world.

Continue reading Rescuing Cool Math for Older Kids

Puzzle: The Eccentric Teacher

Posted on by Denise Gaskins
boy and girl ready to solve math puzzles

One of my favorite things as a teacher was to gather a group of children to play math together.

Call it a math club or math circle, the name didn’t matter, but the activity was always fun. We did non-schooly games and projects, and the kids enjoyed both the camaraderie and the experience of thinking hard in a stress-free setting.

If you’d like to pull together a math club/circle of your own, here are some tips.

Today’s puzzle involves an unusual teacher trying to collect students to participate in a group activity…

Continue reading Puzzle: The Eccentric Teacher

Are You Smarter than a 3rd-6th Grader?

Posted on by Denise Gaskins
girl raising hand in math class

Recently, I stumbled on an old blog post featuring Singapore Math problems, and it brought back memories.

Back when my children were young, the original Primary Math series from Singapore was one of my favorite math curricula. I tweaked our school program constantly, so none of my kids had the same education, but three of them spent a good part of their elementary years in those books.

And I followed the Math in Singapore 2007 blog for its single season of publication. The blog has gone the way of many others, preserved only in the Internet Archive.

In the post I re-discovered, Patsy Wang-Iverson was reporting on a week-long seminar organized by Celine Koh, who offered the following problems (adapted from school exams and study books) for teacher discussion.

How many can you solve?

Continue reading Are You Smarter than a 3rd-6th Grader?

Puzzle: Random Blocks

Posted on by Denise Gaskins
colorful wooden blocks

In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown below. How many of the 1-cm cubes do not have red paint on any face?

red cude cut into smaller blocks

Create Your Own Math

And then he challenges us as teachers:

  • Do you have any ideas for extending the problem?
  • If so, then jot them down.

Continue reading Puzzle: Random Blocks

Playing with Calendar Patterns

Posted on by Denise Gaskins
play math on any calendar

11 Years Ago This Month…

My book business had been on hiatus for nearly 15 years, as I focused on homeschooling five children. I posted on forums and blogged off and on, but the old books fell into (not entirely undeserved) oblivion.

Now my older kids were moving out into their adult lives, and I’d begun to think about publishing again. I dusted off the old manuscripts to see what could be salvaged and began my adventure of indie publishing.

And all the gurus agreed, every author needed an email newsletter.

Share a playful math activity every month? Sure I could do that!

So while I revised and edited the manuscript for Let’s Play Math, to be published in paperback that fall, I launched my first “Playful Math” email, with an idea that’s still fun all these years later: Play math on your calendar.

Continue reading Playing with Calendar Patterns