A frequently-asked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?”

The *Council of the Great City Schools* has published a handy 6-page pdf summary of second grade math concepts, with suggestions for how parents can support their children’s learning:

Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your children toward these grade-level goals by encouraging them to view mathematics as mental play. Don’t think of the standards as a “to do” list, but as your guide to an adventure of exploration. The key to learning math is to see it the mathematician’s way, as a game of playing with ideas.

The following are excerpts from the roadmap document (along with a couple of extra tips) and links to related posts from the past eight years of playing with math on this blog…

In grade two, students will extend their understanding of place value to the hundreds place. They will use this place value understanding to solve word problems, including those involving length and other units of measure. Students will continue to work on their addition and subtraction skills, quickly and accurately adding and subtracting numbers up through 20 and also working with numbers up through 100. They will also build a foundation for understanding fractions by working with shapes and geometry.

Activities in these areas will include:

- Quickly and accurately adding numbers together that total up to 20 or less or subtracting from numbers up through 20.

- Solving one- or two-step word problems by adding or subtracting numbers up through 100.

- Adding and subtracting three digit numbers.

- Measuring lengths of objects in standard units such as inches and centimeters.

- Solving addition and subtraction word problems involving length or money.

- Breaking up a rectangle into same-size squares, a step toward fractions.

- Dividing circles and rectangles into halves, thirds, fourths, or other basic fractions.

- Solving addition, subtraction, and comparison word problems using information presented in a bar graph.

- Writing equations to represent addition of equal numbers. An equation is a mathematical statement that uses numbers and symbols, such as 3 + 3 = 6.

*[Photo by geishaboy500 via Flickr (CC BY 2.0).]*

Tip: Second grade students should be intimately familiar with the numbers up to 100. Check out the many games and activities in 20+ Things to Do with a Hundred Chart.

- Play math games with your child. For example, “I’m thinking of a number. It has 6 tens, but only half that many hundreds. And it has as many ones as how old you are. What is the number?”

- You can also identify a target number and ask your child to either add or subtract to obtain that target number (use a target of 20 or less).

- Have your child explain the relationship between different numbers without counting. For example, 147 is 47 more than 100 and three less than 150. Ask your child to explain his or her thinking.

- Have your child create story problems to represent addition, subtraction, and comparisons. For example, “Keisha has 57 cents. She has 14 cents more than Karen has. How much money does Ryan have?”

- Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math.

- Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time.

*[Photo by Eden, Janine and Jim. (CC BY 2.0 via Flickr)]*

“The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful.

“In mathematics, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts and skills. This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.”

—

Council of the Great City Schools

Parent Roadmaps to the Common Core Standards- Mathematics

- For wonderful advice on how to support children’s mathematical intuition, browse Talking Math With Your Kids.

- For creative ways to build a love for mathematics, follow Moebius Noodles.

- For more activity ideas, check out Helping Your Child Learn Mathematics.

- For other grade-level math standards, see the rest of the Council of the Great City Schools’ parent roadmaps in mathematics. Also available in Spanish.

- For a more detailed list of second grade math topics, read the Common Core State Standards for grade 2 mathematics.

- And be sure to explore the many great ideas for early math on my Pinterest board: Playful Math for Preschool & Early Elementary.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

A frequently-asked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?”

The *Council of the Great City Schools* has published a handy 6-page pdf summary of first grade math concepts, with suggestions for how parents can support their children’s learning:

Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your children toward these grade-level goals by encouraging them to view mathematics as mental play. Don’t think of the standards as a “to do” list, but as your guide to an adventure of exploration. The key to learning math is to see it the mathematician’s way, as a game of playing with ideas.

The following are excerpts from the roadmap document, along with links to related posts from the past eight years of playing with math on this blog…

In grade one, students will work with whole numbers and place value — including grouping numbers into tens and ones as they learn to add and subtract up through 20. Students will also use charts, tables, and diagrams to solve problems.

Activities in these areas will include:

- Quickly and accurately adding numbers together that total up to 10 or less and subtracting from numbers up through 10.

- Understanding the rules of addition and subtraction (for example, 5+2=2+5).

- Solving word problems that involve adding or subtracting numbers up through 20.

- Understanding what the different digits mean in two-digit numbers (place value).

- Comparing two-digit numbers using the symbols > (more than), = (equal to) , and < (less than).

- Understanding the meaning of the equal sign (=) and determining if statements involving addition and subtraction are true or false (for example, which of the following statements are true? 3+3=6, 4+1=5+2).

- Measuring the lengths of objects using a shorter object as a unit of length.

- Putting objects in order from longest to shortest or shortest to longest.

- Organizing objects into categories and comparing the number of objects in different categories.

- Dividing circles and rectangles into halves and quarters.

Tip: Be sure to leave plenty of time for fun stuff, like this Land or Water? game.

- Look for everyday opportunities to have your child do mathematics. For example, if you open a carton of eggs and take out seven, ask, “How many are left in the carton?”

- Play math games with your child. For example, “I’m thinking of a number. When I add five to it, I get 11. What is the number?”

- Encourage your child to read and write numbers in different ways. For example, what are some ways that you can make the number 15? 15 can be 10+5, 7+8, 20-5, or 5+5+5. Ask your child to explain his or her thinking.

- Have your child create story problems to represent addition, subtraction, and comparisons. For example, “I have seven pennies. My brother has five pennies. How many pennies does he need to have the same number as I have?”

- Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math.

- Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time.

*[Photo by glenngould. (CC BY 2.0 via Flickr)]*

“The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful.

“In mathematics, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts and skills. This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.”

—

Council of the Great City Schools

Parent Roadmaps to the Common Core Standards- Mathematics

- For wonderful advice on how to support children’s mathematical intuition, browse Talking Math With Your Kids.

- For creative ways to build a love for mathematics, follow Moebius Noodles.

- For more activity ideas, check out Helping Your Child Learn Mathematics.

- For other grade-level math standards, see the rest of the Council of the Great City Schools’ parent roadmaps in mathematics. Also available in Spanish.

- For a more detailed list of first grade math topics, read the Common Core State Standards for grade 1 mathematics.

- And be sure to explore the many great ideas for early math on my Pinterest board: Playful Math for Preschool & Early Elementary.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s *Math Teachers at Play* (MTaP) math education blog carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at Triumphant Learning.

**Click to tweet about the carnival:**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

**Elementary Concepts:**As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!**Arithmetic/Pre-Algebra:**This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.**Beginning Algebra and Geometry:**Can you explain why we never divide by zero, how to bisect an angle, or what is wrong with distributing the square in the expression ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.**Advanced Math:**Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again, but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?**Mathematical Recreations:**What kind of math do you do, just for the fun of it?**About Teaching Math:**Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

We need more hosts! Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

A frequently-asked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?”

The *Council of the Great City Schools* has published a handy 6-page pdf summary of kindergarten math concepts, with suggestions for how parents can support their children’s learning:

Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your children toward these grade-level goals by encouraging them to view mathematics as mental play. Don’t think of the standards as a “to do” list, but as your guide to an adventure of exploration. The key to learning math is to see it the mathematician’s way, as a game of playing with ideas.

The following are excerpts from the roadmap document, along with links to related posts from the past eight years of playing with math on this blog…

In kindergarten, your child will focus primarily on two important areas. The first is learning numbers and what numbers represent. The second is addition and subtraction. Students will also learn to identify and work with shapes.

Activities in these areas include:

- Counting how many objects are in a group and comparing the quantities of two groups of objects.

- Comparing two numbers to identify which is greater or less than the other.

- Understanding addition as putting together and subtraction as taking away from.

- Adding and subtracting very small numbers quickly and accurately.

- Breaking up numbers less than or equal to 10 in more than one way (for example, 9=6+3, 9=5+4).

- For any number from 1 to 9, finding the missing quantity that is needed to reach 10.

- Representing addition and subtraction word problems using objects or by drawing pictures.

Tip: Cut a sheet of plain, white 4×8-foot bathroom paneling in sixths to make individual 24×32-inch white boards. Draw a large 10-frame to organize items for counting. Nine pencils need one more to make a complete set of ten.

- Use everyday objects to allow your child to count and group a collection of objects.

- Encourage your child to construct numbers in multiple ways. For example, what are some ways that you can make 10? Answers might include 5+5, 6+4, 8+2, etc. Have your child explain his or her thinking.

- Have your child create story problems to represent addition and subtraction of small numbers. For example, “Ann had eight balloons. Then she gave three away, so she only had five left.”

- Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math.

- Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time.

*[Photo by moyerphotos. (CC BY 2.0 via Flickr)]*

“The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful.

“In mathematics, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts and skills. This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.”

—

Council of the Great City Schools

Parent Roadmaps to the Common Core Standards- Mathematics

- For wonderful advice on how to support children’s mathematical intuition, browse Talking Math With Your Kids.

- For creative ways to build a love for mathematics, follow Moebius Noodles.

- For more activity ideas, check out Helping Your Child Learn Mathematics.

- For other grade-level math standards, see the rest of the Council of the Great City Schools’ parent roadmaps in mathematics. Also available in Spanish.

- For a more detailed list of kindergarten math topics, read the Common Core State Standards for kindergarten mathematics.

- And be sure to explore the many great ideas for early math on my Pinterest board: Playful Math for Preschool & Early Elementary.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

*[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.

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:

**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.

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.

- Kids Talk About Math
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

**Click to tweet: Share the carnival with your friends.**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Peggy Kaye gives parents more than fifty marvelous and effective ways to help their children learn math by doing just what kids love best: playing games.

- Daphne explains how it feels to think hard, from a child’s point of view: “You just listened, so then I could figure it out.”

- The answers to some math questions depend on how you define your terms, patterns, or ways of looking at the problem. Tabitha poses an interesting conundrum: Math in the Alphabet.

- Moaz invents a game for practicing basic addition and subtraction: Domino Number Bonds Game.

- Sadie Estrella’s niece tells how she knows fractions, because “Doubles are easy.” [TMWYK] Oranges.

- Maya struggles to grow into her growth mindset: “I don’t ever want to ask a question in math again!”

- Somwrita Sarkar’s son marvels at the idea of a million lollies plus one more: What is the biggest number?

[Back to top.]

[Back to Table of Contents.]

This fun collection of cartoony illustrations, games, and creative activities offers a common-sense approach to mathematics for those who are slightly terrified of numbers.

- My entry for this month’s carnival continues our gaming theme with Horseshoes: A Place Value Game for all ages.

- Maria Miller warns parents and teachers about the side-effects of a common practice: Should you use timed tests for math facts?

- Kelly shows how her family has fun with creative arithmetic in Math activity: The Counting Circle.

- I’ve enjoyed Julie’s posts on geometric doodling. Now her family is moving on to more “practical” geometry: Distance, Area, Volume Activities for Kids and Measuring Distance, Area and Volume.

- It’s not enough for kids to memorize and follow the steps of a math calculation. Tina Cardone shares her plan for building her students’ Number Sense, Logic, and Perseverance.

- Rodi Steinig’s math club students explore a variety of puzzles in Martin Gardner #3: Maze of Minotaur and Scrambled Boxtops.

[Back to top.]

[Back to Table of Contents.]

This collection of puzzles, games and activities is designed to stimulate and challenge people of all ages. Many of the puzzles have a long history, while others are original. Includes hints and solutions.

- Lisa Winer presents a mathemagic trick that gets her students’ attention every year in 1089 Math Magic Trick (and more). Can your kids explain why it works?

- Megan Schmidt challenges her algebra students with a deceptively non-algebraic-looking puzzle: The Un-Puzzle.

- Jennifer Wilson’s students tackle the big question of math, “How can we be sure?”, by proving conjectures about their Origami Regular Octagons.

- Cassie Cooper’s students rave over a lesson about the distance and midpoint formulas: Road Trip Across the USA.

- John Golden shares a wealth of wonderful “for cheap or free” resources for Algebra and Geometry in Such a Thing as Free.

[Back to top.]

[Back to Table of Contents.]

These mathematical recreations of paradoxes and paper folding, Moebius variations and mnemonics, both ancient and modern, will delight and perplex while demonstrating principles of logic, probability, geometry, and more.

- Kalid Azad looks at a problem from several perspectives to gain Intuition For The Law Of Sines.

- Shireen Dadmehr creates a game-like review lesson: Trig Identity Match Up Activity.

- John Chase presents his candy-corny Halloween worksheet for Calculus Students.

- “How can we count the ways?” is a more advanced question than most people realize. Egan Chernoff shares a video of one class working on Around the World (A Counting Problem Sequel).

- Keith Devlin tackles another counting problem and finds a huge difference between the (expected) abstract model and real world experience: Let’s Get Real About Math Word Problems.

- What does it mean to be “normal,” at least approximately? Bob Lochel’s students wrestle with the tricky problem of Assessing Normality in AP Stats.

- Having trouble convincing your students that
*correlation*doesn’t actually correlate with*causation*? Explore the fun at Tyler Vigen’s Spurious Correlations.

- Most of these are beyond the scope of this carnival, but advanced students may want to check out William Wu’s Undergraduate Level Math Book Recommendations for Self-Study.

- And don’t miss the 115th Carnival of Mathematics.

[Back to top.]

[Back to Table of Contents.]

Entertaining diversions for players of all ages in which only pencil and paper are needed: old favorites and less familiar games. I can’t believe Dover let this wonderful book go out of print!

- Shecky Riemann pays tribute to a giant on whose shoulders we all stand: A Martin Gardner Sunday.

- Colm Mulcahy presents a collection of Five Martin Gardner eye-openers involving squares and cubes.

- Alex Bellos asks Can you solve Martin Gardner’s best mathematical puzzles?

- Mike Lawler & son tackle the question, “Could the Koch snowflake (another treat from Gardner’s Mathematical Games column) grow tall enough to reach infinity?” Another example of why I love teaching math to my kids.

- Gary Antonick is also Remembering Martin Gardner on this week of his 100th birthday. Likewise the BBC: Martin Gardner, puzzle master extraordinaire. And Pi Guy collects more tribute articles in 100 Years of Martin Gardner.

- Finally, Michael Lugo links to A list of fifteen books that make up Gardner’s “canon.” For a taste of the treasures they contain, check out Gardner’s own retrospective:A Quarter Century of Recreational Mathematics.

[Back to top.]

[Back to Table of Contents.]

Math, history, art, and world cultures come together in this delightful book for kids. More than 70 games, puzzles, and projects encourage kids to hone their math skills.

- Frustrated with the Common Core Standards? Check out Prof. Triangleman’s Abbreviated List of Standards for Mathematical Practice — 25% or more fewer standards, all the flavor! (Original post from Christopher Danielson here.)

- Brian Stockus shares a simple but amazingly effective teaching tip in Numberless Word Problems.

- Tracy Zager seeks out strategies to answer the question, “How do we teach students to read math problems for understanding in a way that will yield empowered students who expect math to make sense?”

- John Golden asks his elementary ed students think about What’s a Problem? Fun post, and the “gotcha!” in the area investigation made me laugh.

- Dan Meyer reminds us that there’s educational gold in working on “fake world” math problems: Real Work v. Real World. But then Ben Orlin points out several Scenes from the “Real World” Where Math is Useful.

- Seth Godin talked about what it means to be Good at Math, and launched a mini-storm of responses:
- David Coffey points out how our mathematical worldview (see Skemp on Understanding) affects education, then challenges his readers to give a better answer to the question, “Whose fault is it that you aren’t good at math?“
- Patrick Honner steps up to defend the teachers, asking “Did No One Care About Seth Godin?“
- And Mike Lawler offers a potpourri of resources for anyone who really does want to have a better experience with math: Responding to David Coffey’s challenge.

[Back to top.]

[Back to Table of Contents.]

Book images are from Amazon.com, and if you click on a cover, the links take you to that book’s Amazon page, where you can read reviews and other details (and where I earn a small affiliate commission if you actually buy the book). But all of these books should be available through your public library or via inter-library loan.

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 **November 24-28:** MTaP 80 at Triumphant Learning. 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 more volunteers. 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!

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

]]>

I first saw place value games on the old PBS Square One TV show (video below). Many teachers have posted versions of the game online, but Snugglenumber by Anna Weltman is by far the cutest variation. Anna kindly gave me permission to use the game in my upcoming *Math You Can Play* book series, and I added the following variation:

**Math Concepts:** place value, strategic thinking.

**Players:** two or more.

**Equipment:** one deck of playing cards, or a double deck for more than three players.

Separate out the cards numbered ace (one) through nine, plus cards to represent the digit zero. We use the queens (Q is round enough for pretend), but you could also use the tens and just count them as zero.

Shuffle well and deal eleven cards to each player. Arrange your cards in the snugglenumber pattern shown here, one card per blank line, to form numbers that come as close to each target number as you can get it.

**Score according to horseshoes rules:**

- Three points for each
*ringer*, or exact hit on the target. - One point for each number that is six or less away from the target.
- If none of the players land in the scoring range for a target number, then score one point for the number closest to that target.

For a quick game, whoever scores the most points wins. Or follow tradition and play additional rounds until one player gets 21 points (40 for championship games) — and you have to win by at least two points over your closest opponent’s score.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

*[Photo by Olga Berrios via flickr.]*

Do you have a favorite blog post about math activities, games, lessons, or hands-on fun? The *Math Teachers at Play* (MTaP) math education blog carnival would love to feature your article!

We welcome math topics from preschool through the first year of calculus. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.

[Note: Sometimes the automated Google form refuses to load in my browser. If you have trouble, leave a link to your entry in the comments below.] - Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is Monday, October 20*. The carnival will be posted soon afterwards at — well, we don’t have a host for this month yet. Would you like to volunteer?

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

Have you ever heard of *Math Storytelling Day*? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

Check out these posts for more information:

- Happy Math Storytelling Day
- Math Storytelling Day resources
- Moebius Noodles: Math Storytelling Day archive

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

- Did they choose the pattern to keep their customers from getting bored while they were … occupied?
- Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?
- If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?
- And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?
- What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

Have you and your children created any mathematical stories this year? I’d love to hear them! Please share your links in the comments section below.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

*Math Teachers at Play* is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the September edition is now posted at *1001 Math Problems* blog. What a fun list of math posts to browse!

Welcome to the 78th edition of the Math Teachers At Play math education blog carnival, which I am thrilled to be hosting this month in celebration of my soon-to-be-released book, Camp Logic. What is the blog carnival? It is a monthly snapshot of some interesting recent ideas and activities posted by math education bloggers all over the internet.

By tradition, I begin with a fun fact about the number 78:

Seventy-eight is the 12th triangle number, which means that it is the sum of the integers from 1 to 12. Therefore, it is also the total number of gifts given on the last day in the song “The Twelve Days of Christmas!” …

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

The monthly *Math Teachers at Play* (MTaP) math education blog carnival is almost here. If you’ve written a blog post about math, we’d love to have you join us! Each of us can help others learn, so in a sense we are all teachers.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up to first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at 1001 Math Problems blog.

Help! I can’t keep the carnival going on my own. Would you volunteer to host the MTaP math education blog carnival some month this year? Hosting the carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

I’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better:

I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now.

I do hate sums. There is no greater mistake than to call arithmetic an

exactscience. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive.For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.

Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

Try the experiment, and if you do not find it as I say, you are a mere sciolist*, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

Of course I find myself not appreciated as an accountant. Mrs. Wakefield made me give up the book to [my daughter] Rose and her governess (who are here), and was quite satisfied with the work of those inferior intellects.

— Maria Price La Touche

The Letters of A Noble Woman

London: George Allen & Sons, 1908

***sciolist:** (archaic) A person who pretends to be knowledgeable and well informed. From late Latin *sciolus *(diminutive of Latin *scius *‘knowing’, from *scire *‘know’) + *-ist.*

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

*Math Teachers at Play* is a traveling collection of math tidbits — games, lesson ideas, and more — from around the Internet. It moves around from month to month, and the August edition is now posted at *Math = Love* blog. What a fun list of math posts to browse!

Welcome to the 77th edition of the Math Teachers at Play Blog Carnival! I’m super excited to be hosting this carnival because I’ve been reading it for years! Yes, I am that crazy person who started reading math teacher blogs as a high school junior. I think you are going to enjoy going through the submissions. I know I found several new-to-me blogs to add to my RSS reader! …

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our *Math Teachers at Play* (MTaP) math education blog carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is this Friday*. The carnival will be posted next week at Math = Love.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Last month’s Math Teachers at Play #76
- Carnival of Mathematics

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

How in the world can ^{1}/_{5} be the same as ^{1}/_{10}? Or ^{1}/_{80} be the same as one whole thing? Such nonsense!

No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.

Here’s the problem:

*How can you divide eight sausages evenly among five people?*

Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.

I saw five things worth remembering when you talk math with your kids:

- How patiently the man waited, giving the boys time to think. After more than a quarter century of teaching, I still have trouble with that.

- How the boys looked away, moved their fingers, grimaced, and mumbled — all signs of hard thought.

- How the boys alternated between speaking and thinking. While they were speaking, their thought couldn’t advance very far. Then the other boy, the one who had been quiet, would make the next connection — but as he tried to explain his thought, he would get to a point where he was stuck. And then the first boy, who had been thinking, could speak up and take the next step.

- How important the quiet time was for each boy, as they were struggling to understand what the other person had said and to consolidate that with their own ideas.

- How the following quote from W. W. Sawyer could have been written just for this video clip:

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.

I also noticed that the intuitive method of counting the boys invented at first was the same way Egyptian fractions worked. In Egyptian, the exact, correct answer would have been written as a mixed number:

**1 ^{1}/_{2} ^{1}/_{10}**

Cool!

And finally, I noticed how wonderfully many “ones” the boys used to make their fractions: one sausage, one half-sausage, one plate of sausages, and one “bit” of sausage. Each of these was used as the unit at least once during the discussion.

Which brings one more video to mind:

For more about the many meanings of one, see the questions and activities at this TED-Ed video page. For tips on talking math with your kids, please see Christopher Danielson’s blog. And for more on Egyptian fractions, read The Secret of Egyptian Fractions featuring the resourceful Alexandria Jones.

Share your ideas in the comment section below. How would YOU have divided the sausages? Did you ask your kids? What did they say? I wonder how many different ways can we think of to do it….

Many thanks to Tracy Johnston Zager (@TracyZager) who shared the sausage math video on Twitter.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

]]>

I missed out on the adventures at Twitter Math Camp, but I’m having a great time working through the blog posts about it. I prefer it this way — slow reading is more my speed. Chris at *A Sea of Math* posted a wonderful game based on one of the TMC workshops. Here is my variation.

**Math concepts:** comparing fractions, equivalent fractions, benchmark numbers, strategic thinking.

**Players:** two to four.

**Equipment:** two players need one deck of math cards, three or four players need a double deck.

Deal five cards to each player. Set the remainder of the deck face down in the middle of the table as a draw pile.

You will play six rounds:

- Closest to zero
- Closest to 1/4
- Closest to 1/3
- Closest to 1/2
- Closest to one
- Closest to two

In each round, players choose two cards from their hand to make a fraction that is as close as possible (but not equal) to the target number. Draw two cards to replenish your hand.

The player whose fraction is closest to the target collects all the cards played in that round. If there is a tie for closest fraction, the winners split the cards as evenly as they can, leaving any remaining cards on the table as a bonus for the winner of the next round.

After the last round, whoever has collected the most cards wins the game.

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

- Princess in the Dungeon Game
- Multiplication Models Card Game
- Quiz: Those Frustrating Fractions
- Egyptian Math: Fractions
- Subtracting Mixed Numbers: A Cry for Help

]]>