Professor Povey’s Perplexing Problems

Check out this new puzzle book for upper-level high school students & adults:

Professor Povey picture

Thomas Povey is a Professor of Engineering Science at the University of Oxford, where he researches jet-engine and rocket technology. In his new book Professor Povey’s Perplexing Problems, he shares his favorite idiosyncratic stumpers from pre-university maths and physics.

These problems “should test your ability to grapple with the unfamiliar,” Povey writes. “You will learn to tease new problems apart, and apply things you already know in ways you had never considered. You have all the tools you need, but you should see what amazing things you can do with them.”

Can You Solve This?

Alex Bellos shared one of Professor Povey’s puzzles in The Guardian. Can you figure it out?

Professor Povey cover

The book starts off with geometry, but most of the chapters focus on various topics from physics. Some of the puzzles are accessible through applied common sense, but for many of them, it helps to have taken an algebra-based (high school level) physics course.

Kitten is just finishing up her physics textbook, and she still has one more year of homeschooling. I’m hoping to work several of these puzzles into our schedule this year. It should be great fun!

Spoiler

If like me you’re a bit rusty on your physics, don’t worry. Each answer is thoroughly explained—‌in fact, it takes a bit of discipline to close the book and try your hand at each problem before reading on. I wish they’d put the solutions in the back rather than in the main text, to make it easier to browse the problems without reading spoilers.

Speaking of which, here’s the answer to the video puzzle above…

Math Calendars for Middle and High School Students

High school math teacher Chris Rime posted three wonderful review calendars for middle and high school students on his blog.

The links at Chris’s blog will let you download editable Word docx files. If you’re cautious about internet links and prefer PDF, here you go:

algebra-1-september-2015
Chris writes:

There are no explicit instructions about process being more important than the answer on these, so you’ll need to stress that in class.

I remind students that everyone already knows the answer to each of the questions, and that one of the things we’re practicing is explaining our reasoning…

Enjoy!

And if anyone else has a math review calendar to share, for any grade level, please add your link in the comment section below.

Playful Math Snacks for August: Logic Puzzles

The August “Let’s Play Math” newsletter went out last week to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on logic puzzles for all ages, including a newly-discovered deleted scene from Harry Potter and the Sorcerer’s Stone. What fun!

If you missed this month’s edition, no worries—‌here are some great puzzles from the Let’s Play Math blog archive:

The Centauri Logic Challenge

Sign Up Today

If you missed this month’s edition, no worries — there will be more playful math snacks coming soon. Click the link below to sign up today!

And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

New Hundred Chart Game: Odd-Even-Prime Race

Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.

Here is the newest entry, a variation on #10, the “Race to 100” game:

(11.5) Play “Odd-‌Even-‌Prime Race.″ Roll two dice. If your token is starting on an odd number, move that many spaces forward. From an even number (except 2), move backward — but never lower than the first square. If you are starting on a prime number (including 2), you may choose to either add or multiply the dice and move that many spaces forward. The first person to reach or pass 100 wins the game.
[Hat tip: Ali Adams in a comment on another post.]

And here’s a question for your students:

  • If you’re sitting on a prime number, wouldn’t you always want to multiply the dice to move farther up the board? Doesn’t multiplying always make the number bigger?

 
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“New Hundred Chart Game: Odd-Even-Prime Race” copyright © 2015 by Denise Gaskins. Image at the top of the post copyright © geishaboy500 (CC BY 2.0).

Math Teachers at Play #89 via Mrs. E Teaches Math

Math Teachers at Play89From elementary addition to polar coordinates in high school — and all sorts of games, activities, and investigations in between — there’s plenty of fun to be had at this month’s math education carnival. Mrs. E has collected more than twenty great blog posts for us to enjoy:

“Welcome to the 89th edition of Math Teachers at Play (MTaP) Blog Carnival! MTaP is a monthly blog carnival with a collection of tips, games, and activities for teachers of students of all ages…”

Click here to read the whole post at Mrs. E Teaches Math.

Math with Many Right Answers

The discussion matters more than the final answer.
The discussion matters more than the final answer.

One of the most persistent math myths in popular culture is the idea that mathematics is primarily about getting right answers.

The truth is, the answer doesn’t matter that much in math. What really matters is how you explain that answer. An answer is “right” if the explanation makes sense.

And if you don’t give an explanation, then you really aren’t doing mathematics at all.

Try This Number Puzzle

Here is a short sequence of numbers. Can you figure out the rule and fill in the next three blanks?

2, 3, 5, 7, ___, ___, ___, …

Remember, what’s important is not which numbers you pick, but rather how you explain your answer.

Possibility 1

Perhaps the sequence is the prime numbers?

2, 3, 5, 7, 11, 13, 17, …

The prime numbers make a wonderful sequence, though it isn’t the one I was thinking of.

Continue reading Math with Many Right Answers

Math(s) Teachers at Play #88 via mathematicsandcoding

From elementary to high school, manipulatives to Minecraft, there’s plenty of fun to be had at this month’s math education blog carnival:

Enjoy!
MTAP88

“So, here is issue 88 of the Math(s) Teachers at Play blog carnival. This acts as a round up of some cool blog posts that have been published since issue 87 over at cavmaths. As usual people have submitted entries, which I will supplement with some posts that I have really enjoyed reading in the last few weeks…”

Click here to read the blog carnival post at mathematicsandcoding.


[Feature photo (top) by Pratham Books, 88 cards photo by Bailey Weaver, both via Flickr (CC BY 2.0).]

Noticing Fractions in a Sidewalk

fraction-circle

My daughters didn’t want to admit to knowing me, when I stopped to take a picture of the sidewalk along a back street during our trip to Jeju. But aren’t those some wonderful fractions?

What do you see? What do you wonder?

Here is one of the relationships I noticed in the outer ring:

\frac{4 \frac {2}{2}}{20} = \frac {1}{4}

sidewalk

And this one’s a little trickier:

\frac{1 \frac {1}{2}}{12} = \frac {1}{8}

Can you find it in the picture?

Each square of the sidewalk is made from four smaller tiles, about 25 cm square, cut from lava rock. Some of the sidewalk tiles are cut from mostly-smooth rock, some bubbly, and some half-n-half.

I wonder how far we could go before we had to repeat a circle pattern?

Continue reading Noticing Fractions in a Sidewalk