If you teach children in the primary grades, you’ll enjoy this new series from the wonderful Steve Wyborney. Every day for the rest of the school year, Steve will post a new estimation or number sense resource for grades K–8 (or any age!) at his blog:
“This is my way of providing support and encouragement – as well as bringing math joy to your classroom… I’m going to stick with you all year long.”
—Steve Wyborney
“Mathematics, besides being beautiful and useful, is fun. I hope [my book] brings mathematical joy to many.”
—Bernardo Recamán, The Bogotá Puzzles
Dover Publications occasionally posts free samples from some of their wonderful collection of books. This month’s sampler includes several puzzles from The Bogotá Puzzles by Bernardo Recamán.
Inspired by such illustrious collections as The Canterbury Puzzles, The Moscow Puzzles, and The Tokyo Puzzles. Colombian mathematician and professor Bernardo Recamán assembled these 80 brainteasers, word problems, sudoku-style challenges, and other math-based diversions while living and working in Bogotá.
Enjoy!
If you’d like to receive future Dover Sampler emails, you can sign up here.
THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).
It’s back-to-school time here in the States. And that means it’s time for the Kenken Classroom Newsletter. Yay for math puzzles!
KenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence.
Free via email every Friday during the school year.
What a great way to prepare your children for success in math!
Sign up anytime:
Here is a math problem in honor of one of our family’s favorite movies…
Han Solo was doing much-needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?
Stop and think about how you would solve it before reading further.
New Year’s Day
Now is the accepted time to make your regular annual good resolutions. Next week you can begin paving hell with them as usual.
Yesterday, everybody smoked his last cigar, took his last drink, and swore his last oath. Today, we are a pious and exemplary community. Thirty days from now, we shall have cast our reformation to the winds and gone to cutting our ancient shortcomings considerably shorter than ever. We shall also reflect pleasantly upon how we did the same old thing last year about this time.
However, go in, community. New Year’s is a harmless annual institution, of no particular use to anybody save as a scapegoat for promiscuous drunks, and friendly calls, and humbug resolutions, and we wish you to enjoy it with a looseness suited to the greatness of the occasion.
— Mark Twain
Letter to Virginia City Territorial Enterprise, Jan. 1863
quoted in Early Tales & Sketches, Vol. 1: 1851-1864 (affiliate link)
If you’d like to enjoy a mathematical New Year’s Resolution, may I recommend Evelyn Lamb’s Math Reading Challenge? I haven’t decided if I’m going to follow along, but it does look like fun.
Meanwhile, I do resolve to challenge myself with more math puzzles this year. Would you like to join me?
Here’s a great way to start: with the 2020 Mathematics Game!
If you haven’t seen the meme going around, this is a palindrome week because the dates (written American style and with the year shortened to ’19) are the same when reversed.
Here’s a math puzzle for palindrome week — or any time you want to play with math:
What do you think: Will all numbers eventually turn into palindromes?
You can find all sorts of hundred charts on my Free Math Printable Files page.
Read about the history of palindromes on Nrich Math’s Palindromes page.
Find out more about the Palindromic Number Conjecture in Mark Chubb’s article An Unsolved Problem your Students Should Attempt.
Or play with Manan Shah’s advanced palindromic number questions.
KenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence.
Free via email every Friday during the school year.
What a great way to prepare your children for success in math!
Sign up anytime:
Click Here for KenKen Classroom Newsletter
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Place the numbers from 1 to 6 into each row and column. None of the numbers may repeat in any row or column. Within the black “cages,” the numbers must add, subtract, multiply, or divide to give the answer shown.
Did you know that numbers can be polite? In math, a polite number is any number we can write as the sum of two or more consecutive positive whole numbers.
(Consecutive means numbers that come one right after another in the counting sequence.)
For example, five is a polite number, because we can write it as the sum of two consecutive numbers:
5 = 2 + 3
Nine is a doubly polite number, because we can write it two ways:
9 = 4 + 5
9 = 2 + 3 + 4
And fifteen is an amazingly polite number. We can write fifteen as the sum of consecutive numbers in three ways:
15 = 7 + 8
15 = 4 + 5 + 6
15 = 1 + 2 + 3 + 4 + 5
How many other polite numbers can you find?
Are all numbers polite?
Or can you find an impolite number?
Can you make a collection of polite and impolite numbers? Find as many as you can.
How many different ways can you write each polite number as a sum of consecutive numbers?
What do you notice about your collection of polite and impolite numbers?
Can you think of a way to organize your collection so you can look for patterns?
Make a conjecture about polite or impolite numbers. A conjecture is a statement that you think might be true.
For example, you might make a conjecture that “All odd numbers are…” — How would you finish that sentence?
Make another conjecture.
And another.
Can you make at least five conjectures about polite and impolite numbers?
What is your favorite conjecture? Does thinking about it make you wonder about numbers?
Can you think of any way to test your conjectures, to know whether they will always be true or not?
This is how mathematics works. Mathematicians play with numbers, shapes, or ideas and explore how those relate to other ideas.
After collecting a set of interesting things, they think about ways to organize them, so they can look for patterns and connections. They make conjectures and try to imagine ways to test them.
And mathematicians compare their ideas with each other. In real life, math is a very social game.
So play with polite and impolite numbers. Compare your conjectures with a friend.
Share your ideas in the comments section below.
And check out the list of student conjectures at the Ramblings of a Math Mom blog.
CREDITS: Numbers photo (top) by James Cridland via Flickr (CC BY 2.0). I first saw this activity at Dave Marain’s Math Notations blog, and it’s also available as a cute printable Nrich poster. For a detailed analysis, check out Wai Yan Pong’s “Sums of Consecutive Integers” article.
Happy 2019! Have you set any goals for the year?
My goals are to continue playing with math (1) in my homeschool co–op classes and (2) on this blog — and (3) hopefully to publish a couple of new books as well.
My favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
Use the digits in the year 2019 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find.
Let’s resolve to have fun with math this year. Ben has posted a preview of 2018’s mathematical holidays. Iva offers plenty of cool ways to think about the number 2018. And Patrick proposes a new mathematical conjecture.
But my favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.
Use the digits in the year 2018 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
Denise Gaskins' Let's Play Math 