Math Resources

I have been meaning to do a post on all of the different math activities and things that we have been doing and none of them seem to warrant their own post, so let's have a math smorgasbord and look at everything briefly.  We really love math at our home.  :)

As a follow-up to my soroban post, this is the primary thing we are doing now.  I told my mom how cool I think the soroban abacus is and she showed me a neat homeschooling site called thehevproject.com, which has short and sweet abacus training videos with 15-problem worksheets after each lesson.  There are only 33 lessons, but that's plenty to get our feet in the door so that's where we are starting.  I'm looking forward to telling you more about this website in an upcoming post.  When I saw the abacus in the video, we went ahead and bought two Japanese Soroban Wood Abacus from Amazon (one for each of my older kids), got on hev's monthly plan, and today Peter finished lesson 10.  Helen will start next week.  So far so good.

Last Christmas we were working on multiplication.  We bought the flashcards and played games on www.multiplication.com.  Helen really liked the stories but Peter never really engaged with it.  Now we're doing soroban, but when we get back to learning our tables, I'm going to really dig into this site.

Thanks to the advertisements, I noticed www.bigbrainz.com.  We downloaded the demo and Peter BEGGED me for the full version.  We got the 3-month subscription for Christmas and they really loved it.  The catch for us was that I played the game with the kids and told them the answers.  That's just where we were at.  I told my 5-year-old the answer like this, "eleven times six is sixty-six", and he would have to type it in.  My 3-year-old got to hear "sixty-six", and my 2-year-old got to hear "six, six".  I passed the biggest bosses for them all.  They all had fun, and all of them became very good at typing numbers quickly.  It was a great approach except that it backfired a little because after they had each won that way, none of them wanted to play the game anymore, so we let our subscription laps.  Maybe we'll come back to it.  My personal thought:  it's very much like a video game, and I have mixed feelings on docking kids as much for falling off a a machine as they do for missing a problem.  The graphics were fun.  I had fun playing it.  I never mastered my 12 times tables past 5 until I played the game myself.  Now I'm sharp as a pin with all my multiplication facts up to 12.  Ta-da.  It worked for me!  Maybe not the best thing for the early learning crowd unless you alter the game like I did.  Then again, maybe your EL kids are sharper than mine.

The kids seem to be benefiting a lot from our family subscription to more.starfall.com.  There are some really cute math songs and games there.

I would love to spend some time exploring http://wholemovement.com/.  I am amazed at what can be created and and learned by simply folding circles.

The kids love Mr. Numbers on YouTube, and again, when we get to our times tables, I'm going to dig deep into http://www.patternplaymath.com/.  I like the idea of using more than one approach to teaching, and I love what he has done.  His materials are very affordable too.

Before I got into Soroban, I printed out Ray's new primary arithmetic for young learners.  (Thanks to nee1 on BrilldKids for pointing this out!).  There are 89 lessons with between 15-30 problems each.  They seem like good practice questions, so if money is tight and you want a step-by-step approach, this will do the trick.  I still plan on making sure that ink wasn't wasted.  I think a child who completes this book will be ready to advance to Saxon 5/4.  :)

Speaking of Saxon, my plan is to use it as soon as my kids are ready for Saxon 5/4.  Did you know that Saxon himself didn't write Saxon books for the earlier grades?  Well, he didn't.  The company that ended up with the rights to his books did so they could make more money, and the general consensus I'm getting is that they aren't as good.  My father-in-law didn't like the 1st grade material when he used it at a private school.  I don't want to use it for the early grades.  I want something more hands on.  Like the soroban!  But after reading and following this thread, and then reading Robert Levy's reviews of Saxon math on Amazon.com, I am quite sold on using it for the upper grades.  I'm on track to begin Saxon 5/4 in about a year.  I think I could do it sooner, but I really want to focus on abacus training and developing mental math skills.  My plan is to finish the hevproject lessons, then do Ray's book with the aid of the soroban, supplementing with other sources as wanted, then the "in a nutshell" 3rd grade math on hevproject, and on to Saxon 5/4.  I've got a plan, and I LOVE having a step-by-step, know-what's-next plan.
Edit:  They say that to start Saxon 5/4, all a child needs to know is how to add and subtract two-digit numbers, and your multiplication up to 10.  Young children who know this information do well in Saxon 5/4, and it is thorough for other math topics.  Saxon designed 5/4 to be his beginning math book, and as such, it is comprehensive.  Starting 6-year-olds with the 5/4 book is not uncommon in the BrillKids community for this reason.  I promise I'm not a draconian drill-to-kill mom.  My kids actually really enjoy math, but I wouldn't call them a math whiz.  What I am suggesting, what I am using, is an accelerated math path.  Saxon is very good for this.  For more information, read the thread I referenced.  :)

For the younger kids.

Once upon a time, when I had but one baby, I read Glenn Doman's "How to teach your baby math."  Then I did something crazy.  I bought $40-ish worth of materials and painstakingly made my own math-dot cards.  I was crazy.  And stupid.  Shortly after finishing I found a site where I could have just printed them out instead of using stickers.  Really?  All that time down the drain.  :'(  You think I'm joking?  It was such a pain to check to double check to make sure each card had exactly as many dots as I thought it did.  I placed thousands of dot stickers.  Stupid.  Don't do that. Technology means you don't have to, there's plenty of free resources out there.  Check this article out for more information on Doman's math dot program.

I have a hard time trying to make the sale when it comes to BrillKids Little Math program.  Why?  Because I know it doesn't always work.  Little Reader and Little Musician are simply amazing, and I have perfect confidence that they will work so I freely endorse them.  Little Math, I'm not so confident about.  Certainly there are cases where Doman's dot program has worked remarkably well, such as here, but youtube isn't littered with success stories like it is with babies reading.  One theory as to why this isn't the case is because parents can't reinforce it when away from the learning materials.  We can say, "Look, that sign says stop", and read cereal boxes to them, but we can't say "Hey, look at those 46 sheep in that field", or "Hey, you spilled 53 cheerios on the floor."  Maybe that's part of it.  I am convinced that using Little Math with my young children has been beneficial for my children, and that all early exposure to learning has its benefits.  Nothing is wasted.  But it's a hard sell.  I don't think I would have purchased it without my deep understanding of Doman's work, of how babies' brains develop, and how my kids don't have to demonstrate the ability to quantisize big numbers for the program to be successful.  So there you have it.  If you want to be sold on BrillKids' Little Math program, read Glenn Doman's math book and know that Little Math does all of the work for you, all you have to do is push play and there are cute icons that flash for you and keep track of everything.  If you read Doman's book and want that for your child, get Little Math.  That's it.  I'm not going to try to sell it any more than this paragraph.  Someday soon maybe my baby will demonstrate that she's a math whiz and I'll change my tune, but in the meantime I'm content to say that we have Little Math and we faithfully use it.  It's very well done.

TweedleWink also incorporates the math dots into their lessons.  We bought the whole package and we really love it- full review coming soon.  :)  Also, Your Baby/Child Can Discover incorporates math in an engaging way that we really love.  These programs aren't "sit down and do math" videos, but they are part of our overall math enrichment, so I share them here.

Math Games and Activities is an awesome book I stumbled upon and we've used it a lot.  Fun with tangrams also stemmed from this book.

A friend in my local homeschooling group shared this.  It's so cool.  Math is beautiful.  I made a printout for this and we've played with it with clear glass pebbles.  They place them, for example, on numbers divisible by 3, and it's a self-correcting activity because it makes a pattern.
http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
And here's a blog post with a few ideas on how to use it:
http://mathinyourfeet.blogspot.com/2012/11/new-math-game-factor-dominoes.html
She references this blog, which has a higher quality image for a print-out:
http://mike-naylor.blogspot.com/2012/11/factor-visualization.html

We play with pattern blocks a lot.  It's mostly free-play, but we do have some pictures they can place the pieces on.  There are some awesome teaching ideas for pattern blocks on this channel:  https://www.youtube.com/user/erloakland/videos.

https://www.khanacademy.org/ is awesome.

Products I would get in a heart-beat with a dream budget:  Math-U-See (we only have manipulatives and a decimal street poster, not the actual lesson books and videos), Mathtacular, Touchmath, Rightstart Math, and I definitely plan on getting Hands on Equations.

Phew!  I hope there's some gold nuggets in this article for you.  :)

Math and the Japanese Soroban

Lately I have been doing a lot of research on how to teach math while in fact doing very little math with my children.  :(  That's going to change soon as I have chosen a course.  We're going to learn and practice math with an ancient calculator.  One that, the more they use and practice with, the faster they become at mental math, and the less dependent they will be on the tool.  It's the abacus!  But not just any abacus, the soroban.  Take a look at where practice will take you:

And here's a YouTube play-list that will teach you how to use it:

Baby Math by marthazen

I first learned about the Soroban a couple of years ago when Timberdoodle started carrying Aba-Conundrums (Currently sold out, so this link is to Amazon).  Aba-Conundrums includes a soroban and some puzzles, but the book does not train a child to calculate with a calculator.  But the abacus itself has appealing colors and large beads, so I'm thinking about getting this one.

Ultimately it was "Teaching My Toddler"'s excellent post that led me to look into soroban training again.  Her blog post is HIGHLY recommended- she's the one doing this stuff, I'm just dreaming of starting soon.  :)

http://teachingmytoddlers.blogspot.com/2013/03/learning-soroban-japanese-abacus.html

She purchased her abacus here- a teacher demonstration one is great for early learners because of the large size:

Tomoe Soroban

Once you have mastered addition and subtraction (this is something Mommy can work on too- how exciting to start learning with my kids), you can move on to multiplication and division.

And once you can calculate quickly with the abacus, you can develop your mental imaging to do calculations without the abacus- the more you use a calculator, them more you don't have to!  So I come full circle, from the demonstration in the first video to this website that tells more about Anzan- the mental abacus you develop and henceforth can carry in your brain.  Thank you, Japan!  (and thank you, UK, for the information and printables on this site.)  It's a small world after all.  :)

http://www.sorobancymru.co.uk/index.html

Counting Game

From the family archives comes my son's first counting video.  I credit the idea for the game from Siegfried Engelmann's "Give your Child a Superior Mind".

My husband and I taught our son this "game" by playing it with each other at every meal.  Our son thought that it was so-o-o cool, and before long he was playing with us.  Soon after, he was counting to ten independently.

Learning to count set the foundation for learning his numbers, but by itself, it was simply recitation.  Even now, a year later, he only really knows his numbers up to four.  He recognizes the numerals and math-u-see blocks up to ten, but cannot properly identify more than four objects.  This counting game was his first introduction to math.  Counting books were more enjoyable to him, and the foundation was set.

It was also his first memorization exercise.  Repetition is all it takes to teach younger children recitation.  Recently our son learned the Pledge of Allegiance from hearing it every day in our devotionals.

Just food for thought.

Adapting Math-U-See for the pre-primer crowd

I had a friend who recently introduced Math-U-See to me, with the recommendation that children learn their numbers and numerals up to nine before beginning.  This was good advice.  As I poured through the Introduction to Mathematics book (now replaced by the Primer) and became excited about the program, I realize that they need this foundation before being ready to begin the formal program.

Therefore, my goal is to teach my three-year-old his numbers up to nine.  As I contemplated how to get him there, I decided that the answer is quite simply to play with the Math-U-See blocks with my children.

 In the beginning, I referred to the blocks by their number and color.  "Will you please hand me the orange two block?"  After a couple of weeks, I just started asking for the number, and if he was confused, I would clarify by telling him a color.  In a way this is teaching him to associate numbers with colored blocks, but this information is being used in the real world too.  In the month that we started playing with the blocks, he has gone from understanding two to understanding four.  If I give him three raisins and his sister four, he will complain using real numbers.  Although he knows that the violet block is "six", he still doesn't recognize six objects in a different context.   But understanding six in any context is pretty good for a three-year-old, and further understanding will come with practice.

Building Walls

This activity has even worked with my 22-month old.  I will choose a larger block, like nine or ten, to build a wall on.  Then I will place a slightly smaller numbered block and ask my children which block I need to finish the row.  My son is often involved in his own building project, and will shout out "three".  My daughter is more excited to help me, and grabs me a pink block.  She recognizes the missing space up to three, but struggles with four or more.  Since she does not even say her numbers yet, I think this is a great start.  My son can do it with all of the blocks now.  He reached this mastery by building his own walls.  We build ten walls, nine walls, eight walls, and so on.  My daughter prefers to make her own six walls, because violet is so pretty.

Unit Puzzles

I made these puzzles to teach quantity and numeral recognition.  Procedure?  Give the child a handful of unit blocks, tell them the name of the puzzle that they are doing, and let them place the blocks on the cards.  They are willing enough to do these puzzles if all I give them are unit blocks, but if the rest of the blocks are within reach, they won't touch these.  I only occasionally pull these out, but I have had good results.  Those familiar with the Math-U-See program will recognize this format, I have simply repurposed it for my younger children.  You need Math-U-See blocks to do these puzzles, but if anyone is interested, feel free to print these out and use them.

0-4 pdf

5-9 pdf

We love Math-U-See, and we haven't even started yet!  In the future, we will be purchasing more blocks, and using their full curriculum.  It is amazing to me that these manipulatives can be used from the pre-primer stage all the way through algebra.  Playing with blocks is fun = Math is fun!

Decimal Street

Recently we have started using the Math-U-See curriculum in our home, adapting it for our pre-primer children.  One of the highlights of the program is making a poster of a placed called "decimal street" to teach place value.  Looking for ideas, I found The Daniel Academy's lapbook.  I really liked the idea of using Cars characters to make the street more appealing.

For our edition, green units go to Mater's tow yard (mater is green!), tens go to Sally's hotel, and the hundreds get to go to Lightning McQueen's castle.  Sweet!  The Sheriff is there to make sure that none of these places become too crowded.  Only nine units can be in Mater's tow yard at one time, for example.  If there are ten, then they trade up to become a ten block and can go to Sally's hotel.  The helicopter is there because he's just cool that way.  Un-pictured are the numeral cards that can be placed on the respective squares to say how many blocks there are (or should be) in the different places.

My children (namely my son) love to use their trucks to load the different blocks.  If a tornado stirs things up, it's the truck that puts every block back in it's place.  "Mommy!  The semi-truck is taking the tens to Sally's hotel!"  Getting to play with the math-u-see blocks is their reward for finishing the rest of their school.

I have been amazed at how my son has picked up on the idea of place value with this poster, because he still doesn't understand his numbers yet beyond four.  Four-hundred and forty-four makes perfect sense to him, but five is still a little hard for him to grasp beyond knowing that that's how many fingers he has on his hand.  Playing with the blocks every day is helping him learn his numbers too.

Chess for preschoolers

"Checkmate in two moves" says my son after an engaging match.

Then I wake up.  The truth is, my three-year-old son does not even have the attention span to play Candyland.  Before he was two, he knew his basic colors inside and out, and so when he was 2 1/2, we gave him Candyland for Christmas.  He thought that the board was cute, and that the little gingerbread men were fun toys, but we ended up putting it away.  Even now, his version of the game is to walk the gingerbread men down the path and to talk to all of the characters as they journey to the king.  We managed to play half of a real game once, then he threw the pieces all over the floor and said "The end!"  Fair enough, we put it away.

There is something that I heard Susan Wise Bauer say 10 years ago at a homeschooling conference that means more to me today than ever before.  She said: "There is an intellectual maturity than can be given to children through a superb education, and then there is a social maturity that only happens when they've gone around the sun a few times."  I find myself thinking these words all of the time.  What was my goal in presenting Candyland to my son in the first place?  He already knew his colors.  Sitting down to play a game like that requires a certain social maturity that he just doesn't have yet.  Next year I'll probably be rolling my eyes at this article because it will be all that he'll want to play.

So why chess?

When my son was a baby, I saved this article from the Mothering magazine and decided that I would introduce chess to my children when they were three.  That was before I had heard of Doman or any of the other early programs.  Studies have shown (that's vague, I know, I'm not going find you a study for this post, sorry!) Ahem!  Studies have shown that children who play chess do better in math and science, and overall academically than their peers who don't play chess.  I believe it.  My family loves chess, and my children are often exposed to it when we visit them.

Going back to the social vs intellectual maturity idea, what can you teach a preschooler?  What are they intellectually ready to handle?  I've put it to the test with my son and here is why I have found:

1.                  They are old enough to learn how to respect the pieces.  When he would throw the pieces all over the floor, we immediately put them away, even though he still wanted to play with them.  He doesn't throw them around anymore.

2.                  They can learn the names of the pieces.  He knows them.  Even my 22-month old knows the difference between a pawn and a horsie.

3.                  They can learn how the different pieces move.  This has been our biggest breakthrough.  He knows how about half of the pieces move, and he thinks that it's funny that they can only move certain ways.  How silly!  Moving on with his version of the game…

4.                  They can learn that only one piece can occupy a square at a time.  This was actually a tricky thing that had to be learned.  Pictured is how my daughter set up the board, you can see that she doesn't quite understand this yet.  My son does.

5.                  They can appreciate the beauty of the pieces and the board.  This is the number one thing that makes them request the game again and again, I think.  The pieces are beautiful.  The board has intriguing spatial patterns.  They want to learn.

6.                  They can even learn how to set the board up.  We're working on this, but he now knows where the pawns go, and that the rooks go in the corners.

Where do we go from here?  As soon as he can play Candyland, I will introduce him to Lincolnshire chess (referred to in the Mothering article as "The Pawn Game").  When he can play Candyland, he will have mastered the art of taking turns, he will understand that somebody wins and somebody doesn't, and he will have the patience to see the game to the end.  Here is a video showing how to play Lincolnshire chess.



As a side note, Frank Ho from math and chess shares a kinesthetic way of teaching how the different pieces move.  I can't wait to try it!

Fun with tangrams

I have recently rediscovered and been enchanted by tangrams.  What an amazing discovery!  They have a fascinating history, and so many uses, from story telling, understanding area, puzzle solving, and more.  I stumbled across a fantastic book, Math games and Activities.  It has several tangram worksheets like the one I cut out and laminated on construction paper below.

My husband had a hard plastic tangram from high school that we played with, but it was very slippery on the lamination, and as I thought about what else I could use, I discovered that the foam sheets that I had purchased from the dollar store were the perfect size!  I traced a tangram on all six colors, and cut them out to make a very attractive set.  I also cut out all of the exercises in the book, as well as a double-sided set of puzzles that I found here.  These made an excellent Christmas present for our extended family.

I am amazed at how versatile tangram activities are.  Some of the puzzles have challenged me, and yet my daughter who is not yet two has been able to do outlined puzzles.

There are a lot of creative ways that I have seen tangrams used, such as for breakfast, on felt, or in a homemade book format (scroll down to see this one).  Have fun!

Math pond

Making a math pond was a simple project that has become one of my son's favorite activities. I used the vast resources of the internet to find simple drawings I liked and then edited them on photoshop to print out these ponds on blue paper. I then found free coloring pictures for the ducks, the fishes, and the frogs, and printed them on colored paper. For the fishes and frogs, I trimmed construction paper to make it fit in our printer. This is so much cheaper and easier than printing in color.

The Duck Pond

I initially made the math pond for ducks during a week when I was focusing on the color yellow. There are two songs I used for the ducks, as I placed the corresponding number in the ponds.Five Yellow Ducks
One yellow duck went out to play
Out in the farmer’s pond one day.
He had such enormous fun
That he called for another yellow duck to come.
Two yellow ducks went out to play
(etc., ending with "They had such enormous fun
That they played until the day was done")



The other song I use goes like this:Five Little Ducks
Five little ducks went out to play,
Over the hill and far away,
But when old mother duck said "quack, quack, quack",
Four little ducks came-a-waddling back.
Four little ducks went out to play (etc.)
...
But when old mother duck said "quack, quack, quack"
No little ducks came-a-waddling back.
But when old father duck said "QUACK, QUACK, QUACK!"
Five little ducks came-a-waddling back.

The Fishing Pond

The next week we were learning about orange, so I made orange fishes to add to our math pond game. Elsewhere on this site I have mentioned that I love my laminator, which I have made several bits of intelligence cards with. It is also perfect for projects like this, as having laminated fish is better for the endurance of this toy, especially if it is used often. You could also use clear contact paper, or even clear boxing tape and have similar durability. I cut the fishes out, laminated them, then cut them out again to create a water-proof seal, which has really turned out to be handy a couple of times. Then I taped paper-clips to the back for some real fishing.

My fishing pole was made with an oak dowel I bought at home depot. (I had bought it to help Helen grasp it as part of the "physically superb" program, but it wasn’t very practical for me and I never used it. The fishing pole has been a much better use!) I taped a piece of ribbon to the pole, and then used a lot of tape to safely secure a strong magnet to the other end. Voila! A fishing pole.

I will set up the ponds with the corresponding number of fish (I only did different animals in this picture for illustration purposes, I only do one animal at a time) and let the consistent set-up of the numbers do the teaching. With my son, I just focus on having fun. Making it a "joyous" activity. I am sure I could have found cute songs or rhymes for the fishing pond, but Peter loves it as it is, so I let myself off easy this time.

The Frog Pond

You guessed it, this was for green week. When I introduced the frogs, Peter was very excited and ran to get his fishing pole. I taped paper clips to the frogs too. He loves fishing for frogs more than the fish. Go figure. Here's a variation of a famous song for the frogs:Five Little Speckled Frogs
One little speckled frog
Sits on a speckled log,
Eating the most delicious bugs, YUM YUM!
He jumped into the pool,
Where it was nice and cool,
See, there is one speckled frog.
Two little speckled frogs (etc.)

I could have gone on to make purple snails or octopi, red crabs, or blue sea serpents for the math pond, but I didn't. That will perhaps be a project when Helen gets older…
Here is a website with more Math Pond Activities.