640px-Horseshoes_game

Horseshoes: A Place Value Game

[Feature photo above by Johnmack161 via Wikimedia Commons (CC BY 2.5).]

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:

Horseshoes

snugglenumber

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, so that the number on each line comes as close to the 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.

But Who’s Counting?


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Natural Math Multiplication Course

NaturalMathMultiplication

This April, the creative people at Moebius Noodles are inviting parents, teachers, playgroup hosts, and math circle leaders to join an open online course about multiplication. My preschool-2nd grade homeschool math group is eager to start!

Each week there will be five activities to help kids learn multiplication by exploring patterns and structure, with adaptations for ages 2-12.

The course starts April 6 and runs for four weeks.

Preliminary Syllabus

Week 1: Introduction.
What is multiplication? Hidden dangers and precursors of math difficulties. From open play to patterns: make your own math. 60 ways to stay creative in math. Our mathematical worries and dreams.

Week 2: Inspired by calculus.
Tree fractals. Substitution fractals. Multiplication towers. Doubling and halving games. Zoom and powers of the Universe.

Week 3: Inspired by algebra.
Factorization diagrams. Mirror books and snowflakes. Combination and chimeras. Spirolaterals and Waldorf stars: drafting by the numbers. MathLexicon.

Week 4: Times tables.
Coloring the monster table. Scavenger hunt: multiplication models and intrinsic facts. Cuisenaire, Montessori, and other arrays. The hidden and exotic patterns. Healthy memorizing.

Sounds like lots of fun!


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Quotable: Focus on Being Silent

Children Reading Pratham Books and Akshara[Photo by Pratham Books via flickr (CC BY 2.0).]

I discovered this gem in my blog reading today. One of the secrets of great teaching:

Audrey seemed, for once, at a loss for words. She was thinking about the question.

I try to stay focused on being silent after I ask young children questions, even semi-serious accidental ones. Unlike most adults, they actually take time to think about their answers and that often means waiting for a response, at least if you want an honest answer.

If you’re only looking for the “right” answer, it’s fairly easy to gently badger a child into it, but I’m not interested in doing that.

Thomas Hobson
Thank You For Teaching Me

Learn Math by Asking Questions

The best way for children to build mathematical fluency is through conversation. For more ideas on discussion-based math, check out these posts:

And be sure to follow Christopher Danielson’s Talking Math with Your Kids blog!


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Land or Water 2

Maze Game: Land or Water?

This was a fun activity from Moebius Noodles for our PK-1st grade Homeschool Math in the Park group. The children take turns making a maze and setting a dinosaur inside. Then the other dinosaurs (parents or siblings) try to guess whether their friend is on the land or in the water.

Draw the maze

Player #1

(1) First, draw a big circle on the white board. This is your lake.

(2) With a finger or a bit of cloth, erase a small section of the circle to create the opening for your maze.

(3) Starting at one edge of the opening, draw a random squiggle inside the circle. Make your squiggle end at the other edge of the opening.

Looks like Land

(4) Set your dinosaur anywhere inside the maze.

Player #2

(1) Now it’s your turn to guess. Is the dinosaur standing on the land? Is it swimming in the water?

(2) How will you figure out if you guessed right?

(3) Check by jumping across the lines of the maze. Each jump takes you across a boundary: Splash! (Into the water.) Thump! (Back on the land.) Splash! Thump! … Until you reach the dinosaur inside.

(4) Or go to the maze entrance and walk your dinosaur along the path. Can you find your way?

land or water


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Related posts on Let’s Play Math! blog:

Talking Math with Your Kids

Danielson-Talking Math

Christopher Danielson, one of my favorite math bloggers, has a new book out that is perfect for parents of preschool and elementary-age children:

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.

You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.

In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.

The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.

— Christopher Danielson
Talking Math with Your Kids


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Related posts on Let’s Play Math! blog:

Youth Sports Baseball Camp

Quotable: Learning the Math Facts

feature photo above by USAG- Humphreys via flickr (CC BY 2.0)

During off-times, at a long stoplight or in grocery store line, when the kids are restless and ready to argue for the sake of argument, I invite them to play the numbers game.

“Can you tell me how to get to twelve?”

My five year old begins, “You could take two fives and add a two.”

“Take sixty and divide it into five parts,” my nearly-seven year old says.

“You could do two tens and then take away a five and a three,” my younger son adds.

Eventually we run out of options and they begin naming numbers. It’s a simple game that builds up computational fluency, flexible thinking and number sense. I never say, “Can you tell me the transitive properties of numbers?” However, they are understanding that they can play with numbers.

photo by Mike Baird via flickr

photo by Mike Baird via flickr

I didn’t learn the rules of baseball by filling out a packet on baseball facts. Nobody held out a flash card where, in isolation, I recited someone else’s definition of the Infield Fly Rule. I didn’t memorize the rules of balls, strikes, and how to get someone out through a catechism of recitation.

Instead, I played baseball.

John Spencer
Memorizing Math Facts

Conversational Math

The best way for children to build mathematical fluency is through conversation. For more ideas on discussion-based math, check out these posts:

Learning the Math Facts

For more help with learning and practicing the basic arithmetic facts, try these tips and math games:


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Quotable: The Adventure of Learning Math

Math mascot Moby Snoodles

As for mathematics itself, it’s one of the most adventurous endeavors a young child can experience. Mathematics is exotic, even bizarre. It is surprising and unpredictable. And it can be more exciting, scary and dangerous than sailing the high seas!

But most parents and educators don’t present math this way. They just want the children to develop their mathematical skills rather than going for something more nebulous, like the mathematical state of mind.

Children marvel as snowflakes magically become fractals, inviting explorations of infinity, symmetry and recursion. Cookies offer gameplay in combinatorics and calculus. Paint chips come in beautiful gradients, and floor tiles form tessellations. Bedtime routines turn into children’s first algorithms. Cooking, then mashing potatoes (and not the other way around!) humorously introduces commutative property. Noticing and exploring math becomes a lot more interesting, even addictive.

Unlike simplistic math that quickly becomes boring, these deep experiences remain fresh, because they grow together with children’s and parents’ understanding of mathematics.

— Maria Droujkova and Yelena McManaman
Adventurous Math For the Playground Set (Scientific American online)


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Hundred Chart Idea #28: Hang It on the Wall

Math is beautiful when it communicates an abstract idea clearly and provides new insight. Yelena’s hundred chart poster does just that:

[From the Moebius Noodles blog]

Check out my newest home decor item, a hundred chart. The amount of work I put into it, I consider getting it framed to be proudly displayed in the living room. The thing is monumental in several ways:

1. It is monumentally different from my usual approach to choosing math aids. My rule is if it takes me more than 5 minutes to prepare a math manipulative, I skip it and find another way.

2. It is monumentally time-consuming to create from scratch all by yourself.

3. It is monumentally fun to show to a child.

— Yelena McManaman
Moebius Noodles

Now she’s provided a fantastic set of free hundred chart printables:

Thanks, Yelena!

Share Your Ideas

It began with a humble list of seven things in the first (now out of print) edition of my book about teaching home school math. Over the years I added new ideas, and online friends contributed, too, so the list grew to become one of the most popular posts on my blog:

Can you think of anything else we might do with a hundred chart? Add your ideas in the Comments section below, and I’ll add the best ones to our master list.


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Build Mathematical Skills by Delaying Arithmetic, Part 2

To my fellow homeschoolers,

Most young children are not developmentally ready to master abstract, pencil-and-paper rules for manipulating numbers. But they are eager to learn about and explore the world of ideas. Numbers, patterns, and shapes are part of life all around us. As parent-teachers, we have many ways to feed our children’s voracious mental appetites without resorting to workbooks.

To delay formal arithmetic does not mean that we avoid mathematical topics — only that we delay math fact drill and the memorization of procedures. Notice the wide variety of mathematics Benezet’s children explored through books and through their own life experiences:

Grade I

There is no formal instruction in arithmetic. In connection with the use of readers, and as the need for it arises, the children are taught to recognize and read numbers up to 100. This instruction is not concentrated into any particular period or time but comes in incidentally in connection with assignments of the reading lesson or with reference to certain pages of the text.

Meanwhile, the children are given a basic idea of comparison and estimate thru [sic] the understanding of such contrasting words as: more, less; many. few; higher, lower; taller, shorter; earlier, later; narrower, wider; smaller, larger; etc.

As soon as it is practicable the children are taught to keep count of the date upon the calendar. Holidays and birthdays, both of members of the class and their friends and relatives, are noted.

— L. P. Benezet
The Teaching of Arithmetic II: The Story of an experiment

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Build Mathematical Skills by Delaying Arithmetic, Part 1

To my fellow homeschoolers,

It’s counter-intuitive, but true: Our children will do better in math if we delay teaching them formal arithmetic skills. In the early years, we need to focus on conversation and reasoning — talking to them about numbers, bugs, patterns, cooking, shapes, dinosaurs, logic, science, gardening, knights, princesses, and whatever else they are interested in.

In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite – my new Three R’s. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language.

— L. P. Benezet
The Teaching of Arithmetic I: The Story of an experiment

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How Crazy Can You Make It?

And here is yet more fun from Education Unboxed. This type of page was always one of my my favorites in Miquon Math.

Update:

Handmade “How Crazy…?” worksheets are wonderful, but if you want something a tad more polished, I created a printable. The first page has a sample number, and the second is blank so that you can fill in any target:

Add an extra degree of freedom: students can fill in the blanks with equivalent and non-equivalent expressions. Draw lines anchoring the ones that are equivalent to the target number, but leave the non-answers floating in space.

How CRAZY Can You Make It


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PUFM 1.4 Subtraction

Photo by Martin Thomas via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

When adding, we combine two addends to get a sum. For subtraction we are given the sum and one addend and must find the “missing addend”.

— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers

Notice that subtraction is not defined independently of addition. It must be taught along with addition, as an inverse (or mirror-image) operation. The basic question of subtraction is, “What would I have to add to this number, to get that number?”

Inverse operations are a very fundamental idea in mathematics. The inverse of any math operation is whatever will get you back to where you started. In order to fully understand a math operation, you must understand its inverse.

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Addition Games with Cuisenaire Rods

Education Unboxed has posted some playful addition games for young learners. If your browser has as much trouble displaying Vimeo content as mine does, I’ve included the direct links:

Six is Having a Party! – Math Facts with Cuisenaire Rods

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PUFM 1.3 Addition

Photo by Luis Argerich via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.

The basic idea of addition is that we are combining similar things. Once again, we meet the counting models from lesson 1.1: sets, measurement, and the numberline. As homeschooling parents, we need to keep our eyes open for a chance to use all of these models — to point them out in the “real world” or to weave them into oral story problems — so our children gain a well-rounded understanding of math.

Addition arises in the set model when we combine two sets, and in the measurement model when we combine objects and measure their total length, weight, etc.

One can also model addition as “steps on the number line”. In this number line model the two summands play different roles: the first specifies our starting point and the second specifies how many steps to take.

— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers

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Family

Tell Me a (Math) Story

feature photo above by Keoni Cabral via flickr (CC BY 2.0)

My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?

As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”

The fastest way to a child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.

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Do You Teach Math to Young Children?

Sue VanHattum is trying to convince the publishers that this excellent book would reach a wider audience if they made it available at a lower price. What do you think?

As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even “work” at all? Should we push them, or just let them be?

There are no correct answers to these questions, and Zvonkin deals with them in classic math-circle style: He doesn’t ask and then answer a question, but shows us a problem — be it mathematical or pedagogical — and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.

This book is not a guidebook. It does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. On the other hand, if you are interested in running a math circle, or homeschooling children, you will find this book to be an invaluable, inspiring resource. It’s not a “how to” manual as much as a “this happened” journal. … Just about every page contains a really clever teaching idea, a cool math problem, and an inspiring and funny story.

— Paul Zeitz
Introduction to Math from Three to Seven


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Counting Rope

Easy-to-Make Counting Rope

This is wonderful! I am definitely not a crafts-person, but I can’t wait to make some of these. If I can just find my daughter’s pony beads….

Hat Tip

From Cindy at love2learn2day, who got the idea from a math conference workshop by Kim Sutton.

Krista at the LivingMathForum wrote, “We’ve used these for several years. My son even made a bunch of them a few years ago and sold them at a homeschool resource fair. We always have one in most of our board games to help younger children add up their die rolls. I find them relaxing for some reason, just moving the beads along the cord, and my son will sometimes sit and listen to me reading, etc., and just manipulate the beads.”


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Moebius Noodles Photo Game

Hooray! Moebius Noodles tipped the bucket. Thank you to everyone who chipped in!

Now the Fun Begins

The first Moebius Noodles game is a celebration of the Möbius strip. To play:

  1. Post a photo with a Möbius strip anywhere online.
  2. Notify Maria: droujkova@gmail.com. She’ll add your picture to her Moebius Noodles slide show, with a link to your site, blog or Twitter.

And for dinner tonight, try Möbius Marinara!


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Support Moebius Noodles, Update

Would you love to introduce your preschoolers to the mind-stretching wonder of math? Check out Moebius Noodles, an open community of mathematical resources for parents and educators of young children.

Moebius Noodles activities and games use stuff you already have around the house to explore symmetry, fractals, functions, transformations, topology, and more, in a way that is accessible to babies and toddlers (and their parents!) and easily adapted to include older siblings.

Even a small donation will help this amazing project get off the ground — and Maria is offering a variety of “secret rewards” (like free books, or a secret-message game designed especially for your child) to those who chip in now.


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Have Little Ones? Try Moebius Noodles!

Moebius Noodles Fundraiser Badge

Would you like to do math with your babies and toddlers — real math, not just counting and simple shapes — but don’t know how? For the last few years, Maria Droujkova has been teaching parents to do advanced, fun math with young children. I had the chance to lurk on a discussion group this summer and thoroughly enjoyed it. Now she is taking the next step — and you are invited to join in the fun!

The Moebius Noodles project includes:

  • Cool math concepts.
    Symmetry, fractals, coordinate planes, functions, transformations, topology, and more.
  • Math that grows with your child.
    Games and activities are adaptable to a wide range of ages, from babies to teens.
  • Math your child owns.
    Plenty of variations and suggestions to help kids bring math into their own worlds.
  • Active and open support group.
    A community of parents who share stories and photos, discuss examples, modify games, and ask and answer questions.
  • Math therapy for parents.
    For those who feared and disliked math in school, this project offers a second chance as you experience the math-rich world around you through playing with your child.

Maria is offering a variety of “Secret Rewards” (including free copies of the Moebius Noodles book) to those who chip in toward the project. Check out her Moebius Noodles blog post for more information.


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Freebie of the Day: The Arithmetic Primer

Homeschool Freebie of the Day is offering a pdf math guidebook for grades 1-2. This is not a workbook, but offers suggestions for how to weave oral math discussions with young children into your daily life.


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Arithmetic Village Books

Thanks to the generosity of author Kimberly Moore, I am giving away a complete set of the beautiful Arithmetic Village picture books. You can read the first book free online.

When you think of math do you think of a light-hearted fairy tale?

No? Then come and meet some of the delightful characters who live in Arithmetic Village.

Polly Plus collects jewels slowly and methodically, Linus Minus is carefree and loses his. Tina Times and King David Divide… well you’ll see.

The first book offers the overview of the math concepts. These are then demonstrated through the lives of each character. The books are designed to be supported by a manipulative kit [homemade: see video below] with 100 jewels, 10 golden bags, and a treasure chest…

— Kimberly Moore
Proposal: Arithmetic Village

My fantasy-loving daughter Kitten would have been thrilled with this math program when she was little, just as this 6yo girl was. But it’s not just for girls — here is a thorough review by a homeschool mom of two boys.

Visit the Arithmetic Village website to read more about the books and explore the activity pages (links under each topic in the main page menu). Or check out Kim’s YouTube videos for activity ideas.

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World Maths Day 2011: Register Now


Update: World Maths Day for 2011 is over. Congratulations to the 5.3 million registered students from 218 countries, who answered a grand total of 428,598,214 problems correctly. Wow!


It’s time to register for World Maths Day, which will take place on March 1, 2011. Last year, more than two million students from 235 countries combined to correctly answer 479,732,631 World Maths Day questions.

Would you like to help break the record this year? Don’t delay:

  • Registrations close February 28!

About World Maths Day

  • Play with students from schools all around the world. Individuals and homeschoolers are welcome, too.
  • The competition is designed for ages 4-18 and all ability levels. Teachers, parents and media can also register and play.
  • It’s simple to register and participate. Start practicing as soon as you register.
  • And best of all, it’s absolutely free.

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Review: Math Mammoth

When Maria of Homeschool Math Blog asked if I would review her Math Mammoth curriculum, I jumped at the chance. I’ve always enjoyed her blog posts, and I liked the worksheets I had seen on her website. (Maria gives away more than 300 pages absolutely free!)

She sent me her then-new 4th grade worktexts, and Kitten and I dug in.

Well, that was longer ago than I care to admit. But of course, it takes quite a bit of daily use before one can be absolutely sure of one’s opinion about a homeschool program — or at least, it does for me. Too many times a homeschool resource will look great in the catalog, and we’ll start it with high hopes only to bog down in the day-to-day grind and abandon it after a few weeks or months. So I wanted to give Math Mammoth a thorough workout before I wrote this review.

And all excuses aside, I really am a pro at crastinating. . .

My aim is to help parents and teachers teach math so our children and students can really understand what is going on. I’ve strived to explain the concepts so that both the teacher and the student can “get it” by reading the explanations in the books.

— Maria Miller
author of Math Mammoth worktexts
and Homeschool Math Blog

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Free Elementary Math Books

EverydayNumberStories

Today’s Homeschool Freebie is an elementary math textbook from 1915:

The book covers the basic arithmetic from addition and subtraction to simple multiplication and division, with quite a bit of measuring and fraction work, too. The concepts are taught through stories, and then the teacher is to give the student plenty of hands-on experience with measurements. Each lesson concludes with a page of practice problems.

If you miss the daily freebie, you may still be able to get the book through Google (but I’m not sure this works if you are outside the United States):

States by the Numbers

All week long, CurrClick is offering a free “Make It Real Learning” math workbook:

The States by the Numbers series features 4th-6th grade “math adventures” about your favorite states (the freebie is Wisconsin). The workbook covers place values, rounding, estimation, fractions and percentages using data from the Census Bureau’s 2008 Statistical Abstract of the United States. The workbook includes basic instruction and 80 practice problems, plus several “What’s the big idea?” journal pages which ask learners to reflect on the things they’ve learned. You may want to let your students use a calculator, since real data often means large, unwieldy numbers.


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math problems for girls by woodleywonderworks

Mental Math: Addition

[Photo by woodleywonderworks.]

The question came from a homeschool forum, though I’ve reworded it to avoid plagiarism:

My student is just starting first grade, but I’ve been looking ahead and wondering: How will we do big addition problems without using pencil and paper? I think it must have something to do with number bonds. For instance, how would you solve a problem like 27 + 35 mentally?

The purpose of number bonds is that students will be comfortable taking numbers apart and putting them back together in their heads. As they learn to work with numbers this way, students grow in understanding — some call it “number sense” — and develop a confidence about math that I often find lacking in children who simply follow the steps of an algorithm.

["Algorithm" means a set of instructions for doing something, like a recipe. In this case, it means the standard, pencil and paper method for adding numbers: Write one number above the other, then start by adding the ones column and work towards the higher place values, carrying or "renaming" as needed.]

For the calculation you mention, I can think of three ways to take the numbers apart and put them back together. You can choose whichever method you like, or perhaps you might come up with another one yourself…

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Cute Math Facts for Visual Thinkers

numberwalk[Photo by angela7dreams.]

A forum friend posted about her daughter’s adventure in learning the math facts:

She loves stories and drawing, so I came up with the “Math Friends” book. She made a little book, and we talked about different numbers that are buddies.

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More Free Math Resources


[Photo by One Laptop Per Child.]

Once again, I am adding to my Free (Mostly) Math Resources page. Here are a handful of helpful websites for teaching math…

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writing

Writing to Learn Math II

[Photo by Andy Hay.]

In addition to all the funny Google searches, I get plenty of normal inquiries about math topics. People come here looking for help with fractions, word problems, and math club activities — no surprise, those — but I would never have predicted the popularity of the search topic “writing in math class.”

Last year, I compiled a variety of math journal resources, but I’ve found many more since then, especially for older (high school and college) students. So if you’re looking for new ways to get your math students writing…

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