Tag Archives: All ages

Math Teachers at Play #85

[Feature photo by Tomruen via Wikimedia Commons.]

MTaP-85

Do you enjoy math? I hope so! If not, browsing the articles linked in this post just may change your mind.

Welcome to the 85th edition of the Math Teachers At Play math education blog carnival‌—‌a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

By tradition, we start the carnival with a short puzzle or activity. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Let the mathematical fun begin!

TRY THIS PUZZLE

centered-triangular-numbers

In honor of our 85th edition, I present: the centered triangular numbers.

You can build centered triangles with stones in a sandbox, or with any small manipulative that won’t roll away. Like all figurate numbers, the centered triangles start with the number one: a single stone. Imagine this as a triangle with a stone at each corner and sides of length zero.

Around this, you build the next triangle, which has 2 stones on each side. The sides are one unit long. Four stones in all, so the second centered triangular number is 4.

Then build a 3-stones-per-side triangle centered around that. Each new side is 2 units long, and we’ve used a total of 10 stones so far. The third centered triangular number is ten.

Keep building triangles centered around each other, each with one more stone per side. Each triangle’s sides are one unit longer than the sides of the triangle just inside it.

  • 85 is a centered triangular number. How many triangles will you need to use up 85 stones? (Don’t forget to count the first stone as a triangle.)
  • Can you find a pattern in the numbers?
  • What other centered polygon shapes can you build?
  • High school students: Can you find an equation to fit the pattern?



TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

And since I’ve been in a bookish mood lately, each section includes a link to one of my favorite under-appreciated (5 reviews or fewer) math book. The covers link to Amazon.com, where I get a few cent’s commission if you actually buy something‌—‌but you should be able to borrow all these books through your local library or library loan system.

Math Teachers at Play #85: a smorgasbord of great ideas for learning, teaching, and playing around with math. http://ctt.ec/8N2Br+

Click to tweet: Math Teachers at Play #85: a smorgasbord of great ideas for learning, teaching, and playing around with math.


EARLY LEARNING ACTIVITIES

Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers by Alexander Zvonkinmath3-7

This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s‌—‌what he tried, what worked, what failed, but most important, what the kids experienced.

  • Thomas Hobson (@TheTeacherTom) slows down to model “safe and proper woodworking procedures” while the children keep track‌—‌debating, frequently recounting, always rearranging, stacking, building, making patterns.

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ELEMENTARY EXPLORATION AND MIDDLE SCHOOL MASTERY

More Math Games & Activities from Around the World by Claudia Zaslavskymoremathgames

Math, history, art, and world cultures come together in this delightful book for kids, even for those who find traditional math lessons boring. More than 70 games, puzzles, and projects encourage kids to hone their math skills as they calculate, measure, and solve problems.

  • Julie (@jmommymom) and family read the math fairy tale book The Man Who Counted: A Collection of Mathematical Adventures and try their hand at the Four 4s challenge.
  • Spencer Olmsted’s class is on fire with math patterns. “It’s a wonderful thing to connect a physical model, the ordered pairs that describe it, and a graph‌—‌it’s practically poetry.”

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ADVENTURES IN BASIC ALGEBRA & GEOMETRY

Mathematical Cavalcade by Brian Boltmathcavalcade

This collection of puzzles, games and activities is designed to stimulate and challenge people of all ages who enjoy puzzles with a mathematical flavor. The second part of the book contains a commentary giving hints and solutions.

  • Stephen Cavadino (@srcav) says, “I love it when my student talk maths well, and this post looks at an interesting discussion my year 9s had on perimeter.”
  • Tina Cardone (@crstn85) gets a seasonal reminder that extended wait time and letting kids ask us for help rather than continuing the conversation as soon as they have responded really does work.

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ADVANCED MATHEMATICAL ENDEAVORS

A Decade of the Berkeley Math Circle: The American Experience by Zvezdelina Stankova, Tom Rikeberkeleymath

A wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik’s cube and abstract algebra… Also features 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions.

  • Dan MacKinnon (@mathrecreation) uses The Geometer’s Sketchpad to construct patterns through iteration. Working through how to build iterations helps teach basic principles of geometric construction as well as more advanced ideas (self similarity, limits).
  • Bob Lochel (@bobloch) develops a new perspective on imaginary numbers. “The bulbs have gone off. I GET this now! What I appreciate most here is that we don’t need to wait until deep into algebra 2 to think about the imaginary unit.”
  • Have you ever wondered where Euler’s Formula comes from? See how arithmetic, geometry, trigonometry, and calculus dance together on the complex plane to create mathematical beauty.

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PUZZLING RECREATIONS

The Universe in a Handkerchief: Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays by Martin Gardneruniversehandkerchief

Puzzles and paradoxes from Lewis Carroll, the author of Alice in Wonderland, whose interests ranged from inventing new games like Arithmetical Croquet to important problems in symbolic logic and propositional calculus. Written by Carroll expert and well-known mathematics author Martin Gardner.

  • Mario Livio (@Mario_Livio) leads NOVA viewers on a mathematical mystery tour‌—‌an exploration of math’s astonishing power across the centuries. Is math a human invention or the discovery of the language of the universe?

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TEACHING TIPS

Common Core Math For Parents For Dummies by Christopher Danielsoncommon core math

Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math.

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LOOKING AHEAD

And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of May 25-29 at ZenoMath. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival information page.

We need volunteers for the fall semester. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


Math Game: Thirty-One

Math Concepts: addition to thirty-one, thinking ahead.
Players: best for two.
Equipment: one deck of math cards.

How to Play

Lay out the ace to six of each suit in a row, face up and not overlapping, one suit above another. You will have one column of four aces, a column of four twos, and so on‌—‌six columns in all.

The first player flips a card upside down and says its number value. Players alternate, each time turning down one card, mentally adding its value to the running total, and saying the new sum out loud. The player who exactly reaches thirty-one, or who forces the next player to go over that sum, wins the game.

31-Game

Variation

For a shorter game, use only the ace to four of each suit. Play to a target sum of twenty-two.

History (and a Puzzle)

Thirty-One comes from British mathematician Henry Dudeney’s classic book, The Canterbury Puzzles. According to Dudeney, “This is a game that used to be (and may be to this day, for aught I know) a favourite means of swindling employed by card-sharpers at racecourses and in railway carriages.”

Dudeney challenges his readers to find a rule by which a player can always win: “Now, the question is, in order to win, should you turn down the first card, or courteously request your opponent to do so? And how should you conduct your play?”


Dudeney, H. E. The Canterbury Puzzles, Thomas Nelson and Sons, 1919 (originally published 1907); available at Project Gutenberg or the Internet Archive.
http://www.gutenberg.org/ebooks/27635
https://archive.org/details/canterburypuzzle00dudeuoft


Addition-Games600x800

This post is an excerpt from my book Addition & Subtraction: Math Games for Elementary Students, coming this spring to bookstores all over the Internet.


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


April 2015 Math Calendar

Feature photo above by Kelly Sikkema via Flickr (CC BY 2.0).

AprilMathCalendar

Six years ago, my homeschool co-op classes had fun creating this April calendar to hand out at our end-of-semester party. Looking at my regular calendar today, I noticed that April this year starts on Wednesday, just like it did back then. I wonder when’s the next time that will happen?

A math calendar is not as easy to read as a traditional calendar — it is more like a puzzle. The expression in each square simplifies to that day’s date, so your family can treat each day like a mini-review quiz: “Do you remember how to calculate this?”

The calendar my students made is appropriate for middle school and beyond, but you can make a math calendar with puzzles for any age or skill level. Better yet, encourage the kids to make puzzles of their own.

How to Use the Math Calendar

At home:
Post the calendar on your refrigerator. Use each math puzzle as a daily review “mini-quiz” for your children (or yourself).

In the classroom:
Post today’s calculation on the board as a warm-up puzzle. Encourage your students to make up “Today is…” puzzles of their own.

As a puzzle:
Cut the calendar squares apart, then challenge your students to arrange them in ascending (or descending) order.

Help Us Make the Next Math Calendar

If you like, you may use the following worksheet:

Submission details here: Kids’ Project — More Math Calendars?


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


2015 Mathematics Game

[Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both (CC BY 2.0) via Flickr.]

2015YearGame

Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!

For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.

Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2015 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.

  • You must use all four digits. You may not use any other numbers.
  • Solutions that keep the year digits in 2-0-1-5 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
  • You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

  • You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
  • You MAY NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.

Click here to continue reading.

Limited Time: Christmas Card Game

12 Days of Christmas card game

12 Days of Christmas is a card game designed by Dr. Gord Hamilton of Math Pickle. It’s designed for 2-8 players, ages 8+, to be played in 20-30 minutes. Simple enough for the whole family to play, yet strategic enough for the game geeks in the family to enjoy along with everyone else. To order, check out the Kickstarter:

But don’t delay! The Kickstarter project ends Christmas Day.


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


December Advent Math from Nrich

[Feature photo (above) by Austin Kirk via Flickr (CC BY 2.0).]

Click on the pictures below to explore a mathy Advent Calendar with a new game, activity, or challenge puzzle for each day during the run-up to Christmas. Enjoy!

Advent Calendar 2014 – Primary

adventprimary

Advent Calendar 2014 – Secondary

adventsecondary


Tabletop Academy PressGet monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.


Math Teachers at Play #79

79

[Feature photo above by Jimmie, and “79” image (right) by Steve Bowbrick via flickr (CC BY 2.0).]

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 79th edition of the Math Teachers At Play (MTaP) math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle, game, or trivia tidbits. If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Since I’ve been spending all my free time working on my upcoming Math You Can Play book series, I’m in the mood for games. So I found a few games featuring prime and nonprime numbers [which category is #79 — do you know?], and I’ll sprinkle some of my best-loved math game books throughout the carnival.

TRY THESE NUMBER GAMES

Students can explore prime and non-prime numbers with two free classroom favorites: The Factor Game (pdf lesson download) or Tax Collector. For $15-20 you can buy a downloadable file of the beautiful, colorful, mathematical board game Prime Climb. Or try the following game by retired Canadian math professor Jerry Ameis:

Factor Finding Game

FactorFindingGame

Math Concepts: multiples, factors, composites, and primes.
Players: only two.
Equipment: pair of 6-sided dice, 10 squares each of two different colors construction paper, and the game board (click the image to print it, or copy by hand).

On your turn, roll the dice and make a 2-digit number. Use one of your colored squares to mark a position on the game board. You can only mark one square per turn.

  • If your 2-digit number is prime, cover a PRIME square.
  • If any of the numbers showing are factors of your 2-digit number, cover one of them.
  • BUT if there’s no square available that matches your number, you lose your turn.

The first player to get three squares in a row (horizontal/vertical/diagonal) wins. Or for a harder challenge, try for four in a row.

Hat tips: Jimmie Lanley.



TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

Tweet: Math Teachers at Play #76: a smorgasbord of great ideas for learning, teaching, and playing around with math. http://ctt.ec/fU9Z2+

Click to tweet: Share the carnival with your friends.
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