# Quotable: Focus on Being Silent

[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.

## 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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# Every Day Is Math Day

Happy 11/12/13, otherwise known as “tenty-one, tenty-two, tenty-three.”

Do your young children have trouble counting in the teens? Try making up Funny Numbers to help them! It’s a great habit to develop, because Funny Numbers will come in handy as mental math tools throughout their school math career.

If you’d like to make your own Happy Math Day post, check out the instructions here: Every Day Is Mathematics Day. And please share a link in the comments section below — I’d love to see what math holiday you invent!

Update: The numbers 11, 12, and 13 form an arithmetic progression. If that sounds too scary for your kids, check out Patrick’s bedtime math discussion Making Progress, Arithmetically.

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# 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.

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.

(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?

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# Talking Math with Your Kids

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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By Denise Gaskins

# 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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By Denise Gaskins

# PUFM 1.1 Counting

Photo by Iain Watson 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.

Many things in mathematics need to be understood relationally — that is, in relationship to other concepts. But some things just need to be memorized. How do you know which is which? A homeschooling friend pointed out that one thing children definitely need to memorize is the counting sequence from 1-100 and beyond. While there are some patterns that make counting easier, one does just have to memorize which “nonsense sounds” we have attached to each number.

Another sort-of counting that young students should master is subitizing — recognizing at a glance how many items are in a small group. Children do this instinctively, but we can help them develop the skill by playing subitizing games.

[Aside: In writing this blog post, I ran into some nostalgia. Back when we first did these PUFM lessons, my daughter Kitten was only a toddler. I wrote, “I’ve tried to do lots of counting with my youngest, who hasn’t quite gotten beyond, ‘…eleven, twelve, firteen, firteen, nineteen, seven,…’ The numbers tend to start appearing randomly after she gets past 10.” Ah, memories.]

By Denise Gaskins

# 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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# 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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# 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.

# 30+ Things to Do with a Hundred Chart

[Photo by geishaboy500.]

Are you looking for creative ways to help your children study math? Even without a workbook or teacher’s manual, your kids can learn a lot about numbers. Just spend an afternoon playing around with a hundred chart (also called a hundred board or hundred grid).

Here are a few ideas to get you started…

# How to Make Math Cards

Many of the games on this blog call for Math Cards. You do not need to look for these in stores or in your school supply catalog. Math cards are simply a modified deck of normal, poker-style playing cards. Remove all face cards and jokers from the deck, leaving the ace through ten of each suit. Or use a set of Rook cards, without the bird.

Using the ace as a one, this gives you four sets of numbers 1-10, and you will be ready to play your way to fluency in almost any arithmetical topic: addition, subtraction, multiplication, division, greater-than/less-than, fractions, negative numbers, and more.

## Card Holder for Young Hands

Little hands often have trouble holding more than a few cards at a time. Your child may enjoy making and using a card holder.

Save the plastic lids from two margarine tubs or similar containers. Place the lids together, top to top. Line up the edges, then staple them together, putting two or three staples near the center of the lids. Let your child decorate the card holder with stickers, if desired.

To use the card holder, slip playing cards between the two lids and fan them out. The lids will hold the cards upright, so the child can easily see them all.

Get 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.

# Elementary Problem Solving: The Early Years

[Rescued from my old blog. To read the entire series, click here: Elementary Problem Solving Series. Photo by Studio 757 via flickr.]

You can begin to teach your children algebraic thinking in preschool, if you treat algebra as a problem-solving game. Young children are masters at solving problems, at figuring things out. They constantly explore their world, piecing together the mystery of how things work. For preschool children, mathematical concepts are just part of life’s daily adventure. Their minds grapple with understanding the three-ness of three blocks or three fingers or one raisin plus two more raisins make three.

Wise homeschooling parents put those creative minds to work. They build a foundation for algebra with games that require the same problem-solving skills children need for abstract math: the ability to visualize a situation and to apply common sense.

# Number Bonds = Better Understanding

[Rescued from my old blog.]

A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.

Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing.