Honestly, I don't know whether logic really fits as a math skill or not, but I tend to lump most thinking skill / problem solving / logic activities together and call them math.  One of the things I've included on our problem solving days, even before my children could read, is the logic matrix. 

Here's an example from Mr. Meyers site.  He has a few more here.

My children have developed much critical thinking from this type of activity.  I'd like to share some of my resources thus far for really great logic matrixes.

Beginners:

Primarily Bears from AIMS  (this is a great source for other fun "thinking" math with manipulatives - mostly bears counters)

EdHelper

Older:

Mind Benders

http://schools.portnet.k12.ny.us/~mayerweb/Logic3rd/Web/wmatrixlogic.htm

http://scifiles.larc.nasa.gov/text/educators/activities/2000_2001/worksheets/logic_problems.html

My children love the challenge of the logic matrix.  They also love that they seemingly don't have to do "real" math when I plop these in front of them.  (If they only knew!) 

I just wanted to share what a hit this math activity was last week. 

Using the information sheets that the website provides, the kids had to fill out a chart to show how many presidents have come from which states.  Then, they used graph paper to create a bar graph to show the information from the chart.  Fun activity!

I'm trying to keep up with my promise to show you what some of our unconventional math lessons look like around here.  Today I want to share how I plan a math lesson around a piece of literature.  It's really very easy!

Like most everything I do, I grab a pencil and a pad of paper before I do anything else because I'm always writing notes.  If I don't write something down as it pops in my head, it's usually gone - never to return again! 

So with pen and paper in hand, I grab a math book and quickly read through it.  I jot down math concepts and activity ideas that jump out at me.  The more you do it, the easier ideas start jumping out at you, I promise.  Sometimes, I'll only write a couple of ideas - which means one day's worth of lessons is all we'll do before that book goes back on the shelf (or back to the library.)  If a lot of ideas are written, I might plan a few days worth of lessons around the book. 

If NOTHING pops out at me, but I really like the book, I'll do one of two things:

1.  We'll just read the book together for fun - no math strings attached.

2.  I'll do a quick google search to see if any good lessons are floating around in cyberspace just waiting for me to grab.

This week we read Sir Cumference and the Isle of Immeter.  I found a worksheet in my geometry folder that sent Mahayla on a hunt through the house measuring the perimeter, area and volume of various objects. 

Caleb and I pulled out the one-inch tiles and measured the perimeter and area of things around the school room.  After a while, he tried his hand at measuring the length and width of the objects with the tiles, then multiplying the numbers to find the area.  Finally, he had to use a ruler to find the perimeter and area of many things.

Not only did this simple little lesson create excitement, but it allowed the kids to practice measurement, perimeter, area, volume, mental addition & multiplication and more complex math formulas such as 2l + 2w=p, l x w=a and l x w x h=v.  I could've done the same sort of teaching from the textbook, but I'm rather sure this lesson will stick a little better! 

A couple weeks ago, I forced gave the moms at co-op the opportunity to try their hands at this process and they were VERY GOOD at it!!  Here is a great list of math ideas they came up with on many various math titles.  The activities are in no particular order - some will be appropriate for little ones, while others will be appropriate for jr. high.  I just asked the moms to pick a book and try to think of ideas that would be good for their own children. 

The cute math clip art came from Philip Martin.

After the last couple of living math posts, I promised to share some of our non-textbook lessons.  Here are some of the fun things we've been doing/have planned to do this winter on our living math days.  My hope is to encourage you that....

1.) Living math really is thoughtful, meaningful math.

2.) Living math isn't hard to implement at all. 

Here are a few of our January/February activities with links...

This Grab the Candy Game allows the kids to practice coordinate graphing and record keeping.  Valentine Battleship is another version of a coordinate graphing game.

How Many Different Ways Can You Make the Word Snow? is a quick activity to encourage problem solving and critical thinking.  This Heart Paths sheet is similar, but requires an extra "rule" to make the kiddos think a bit harder.

These Candy Heart Patterns are a little harder than they first seem.  I gave these to my 5th grader as "fun filler" and she realized half-way through that she hadn't thought the pattern through completely! 

Glyphs are pictures children make based on a legend or key of codes.  Not only does it reinforce problem solving, critical thinking and organization skills, but mapping as well.  Here's a link to the Snowman Glyph activity we used.

These Symmetrical Heart Masks reinforced the concept of symmetry, as well as creativity. 

This President's Day activity is going to require charting and creating a graph.

Even this worksheet of Valentine Word Problems is a fun, seasonal way to change the pace from a textbook.

There are a few more activities we've done or have planned to do, but I'll let you find them for yourself at MathWire - an awesome site for living math ideas!

When the activities are quick, I'll do several in one day.

As for living literature, we've checked out this series of books from the library to go along with our Medieval Unit.  Some of them are better than the others, but they'll go along well with our unit.

Sir Cumference and the First Roundtable: A Math Adventure

Sir Cumference and the Sword in the Cone: A Math Adventure

Sir Cumference and the Great Knight of Angleland

Sir Cumference and the Dragon of Pi

Sir Cumference and the Isle of Immeter

I'd love to hear about your living math learning!  If you share on your blog, please let me know so I can come visit!  Happy math times!

Wow, it seems like my Living Math post struck a nerve.  Are there that many math-haters out there?  :)  I think more questions have come in regarding the idea of living math than just about anything else I've ever written.  One person asked a question that pretty much encompasses all the other questions, so I'll use hers and try to post something that makes sense.  I'll be happy to continue answering questions if you think of any more.

I hated math when I wad a kid.  Hated it.  It didn't make much sense to me, I had a hard time memorizing facts, and my teacher's didn't spend much time helping me to understand.  I used to nearly have anxiety attacks in middle school when the teacher put this sort of problem on the board.  "If a train from NY is traveling 60 mph......"  You probably didn't care much for those problems either, did you?  :)

I remember my poor Dad spending countless hours trying to teach the concept of fractions to me in third grade, only to have every lesson end in tears and me leaving the table saying, "I just don't get it!"  Surprisingly, I made very good grades in spite of the disdain for math.  And even though I hated every minute of it, I survived. 

Fast forward to my early twenties when I started teaching.  What was one of the subjects I had to teach?  Math!  But, I wasn't afraid.  I could handle elementary math, couldn't I?  Imagine my surprise (and my Dad's) when math actually became one of my favorite subjects to teach!!  You see, I had learned to teach with manipulatives, something my teachers had never given me.  What a difference it made!  I was finally able to understand fractions AND I was able to teach someone else to understand them!  Wow!

So, needless to say, I'm a big believer in teaching math with manipulatives.  There's a connection made in the brain that allows children (and adults) to "see" math and to understand the why's of math rules.  I believe teaching math with manipulatives is a key element to making math a living subject. And just why would math need to be a living subject?  The same reason we try to make history or science living subjects - because "living" subjects draw people in.  They give a relevance to learning that means more than facts on paper.  They make heart and mind connections so that we hopefully love what we're learning.  And they give whole pictures of a topic so the "pieces" fit together better.

Besides manipulatives, what else makes math living?  A Charlotte Mason education certainly includes good books, right?  Math can include living books, too!   There is so much wonderful math literature out there!  I've started a  small library for myself (some of which I pictured below),  but most of the books we've used have been easy to find at our library.  Below are three websites that list many titles you might like to check out. 

List of living math books

Penny Gardner's List of Living Math Literature

Living Math Books Sorted By Mathmatical Concept

Including literature during a math lesson is very easy.  I wrote a post not too long ago about using One Grain of Rice for a lesson in doubling numbers.  Some other very simple ideas would be...

*Reading The Doorbell Rang then using manipulatives to make fair shares.

*Reading How Big is a Foot and comparing measurments based on your feet and your child's feet.  Then talking about the necessity of a standard unit of measurement.

*Reading Alexander, Who Used to be Rich Last Sunday then working on a skill like money subtraction with real coins.

The ideas are endless, but well worth the thought  because your children will thrive on such exciting activities.  The greatest part is that you probably don't have to really work that hard.  Doing a Google search on "(name of book) activities" will most likely place activity ideas right in front of you.  Here are some great websites to get you started.

Mathwire Literature Connections

Winter Math Activities - great ideas, with a couple tied to literature

NCTM Ideas

Linda's Learning Links

Math and Literature Idea Bank from Math Cats

Finally, another way to make math living for your children is to give them real tasks to do.  Let them be part of budgeting, coupons, planning the garden plot, balancing the checkbook, deciding how much grass seed to buy, recipe conversions, bill paying, measuring air in the tires..............As my children get older, I give them just a bit more responsibilty with real-life tasks in hopes that they will be fully able to do them on their own before leaving my house.  They appreciate being included and I reap the benefit of capable helpers!

Am I advocating never opening a math workbook or never working on math drills.  Absolutely not.  My philosophy is "varied learning makes for well-rounded kids".  I'm simply suggesting that math doesn't have to be boring and it doesn't have to come from a workbook.  I have friends who worry about skipping lessons in the math workbook, so they might add living lessons to the hour of math the workbook requires.  Please promise me that if you plan to try some living math, you'll tear up that day's worksheet and pitch it in the garbage.  (Gasp - it really is okay to throw workbook pages away.  I promise.)  Living math won't be nearly as exciting if it's on top of "regular" lessons.   ;)

May you and your children find math to be exciting and worthwhile!  I would love to hear some of your favorite math books and how you used them in your homeschool!! 

Have you ever read One Grain of Rice by Demi?  Good book!  We read it again the other day and my 5th grader did some fun math activities to go along with the story. 

I found the activities and worksheets at this site. 

After reading the story, Mahayla had to chart the number of grains of rice the raja gave away.  Since the numbers became huge, I let her use a calculator.

Next, she had to determine how many cups of rice were given away on a few of the days, as well as the weight of the rice and number of people it would feed.

Fun math, real-world type stuff, and lots of computation!  Who could ask for more?  :)

Talk about a fun week of math learning!  Here are a couple of the activities my children did during our week of m&m math fun.  Overall, we covered estimation, sorting, counting, adding, word problems, pictographs, bar graphs, comparison graphs, pie graphs, graphs made in a spreadsheet program, fractions, fair shares (division), mean/median/mode, decimals and percentages.  I'd say that was enough math to rival any textbook curriculum for a week!

http://www.col-ed.org/cur/math/math26.txt

            graphing and probability

http://score.kings.k12.ca.us/lessons/mandm.html

            estimating, sorting, counting, graphing, plotting, fractions, percentage, and calculating mean, median, mode

http://faculty.roosevelt.edu/donovan/documents/M%20&%20M%20Math%20Intermediate_files/M%20&%20M%20Math%20Intermediate.htm

            predicting, classifying, graphing, percentages

http://ofcn.org/cyber.serv/academy/ace/math/cecmath/cecmath013.html

            averages with m&m cookies

http://www.lessonplanspage.com/MathEstimationClassification.htm

            easy estimation and classification

http://www.atozteacherstuff.com/pdf.htm?m&mschart.pdf

            printable m&m graph

http://www.create.cett.msstate.edu/create/classroom/lplan_view.asp?articleID=98

            collect, graph, record and interpret data to create a bar graph on the computer

http://www.learnnc.org/lessons/KarenWalker5232002614

            estimate, sort, graph and add with printable charts near the bottom

http://www.beaconlearningcenter.com/Lessons/2622.htm

            fractions, decimals and percentage

http://www.mms.com/us/fungames/

            official m&m website

http://www.ciese.org/math/activities/candycircles/index.html

            mean, median and mode

http://42explore.com/choclat.htm

            many, many chocolate related activities and links

I've got a fun math activity for you!  It's important to me that my children not only know how to read graphs, but know how to create them as well.  Mahayla is a pro at gathering information and creating her own graphs on paper.  Caleb is just beginning, though, so I wanted him to make a "concrete"  graph to be sure he understands all the parts and why they are where they are. 

Here's how the lesson went......We decided on a topic - animals.  He decided to gather data from 40 people by asking what their favorite animal is.  He then came up with a list of several animals he would let them choose from.  Then, he wrote the animal's names on a piece of paper and tallied the "votes" as they were given to him.

Next, he wrote each animal's name on a notecard and placed the cards along the floor.  He knew he needed numbers going up the side  to show how many people liked each animal.  He used 1" tiles to show the results from the 40 people he interviewed.  And finally, he wrote a title card calling his graph, "Favorite Animals".  :)

Next time, he'll be ready to create a graph on paper.  He knows the "parts" because he had to make them and manipulate them.  It's a strong visual that won't soon be forgotten.

Mahayla just wanted to be part of the action!  I asked her to create a line graph showing a week's worth of data from her peak meter numbers.  The doctor will be so impressed with this picture when we include it in her file during the next visit!  He asked her to keep a chart.  Little did he know that we would take him this seriously.  LOL

If you've been around me long enough, you know I'm not much on doing one curriculum exclusively.  You can read all my "excuses" in previous posts.  Truth be told, though, there are so many good and fun things out there, that I can't bear to pass up many of them!  Hence, the reason I do a workbook math curriculum two to three days a week and jump around the other days.

I just posted about my "plan" for Mahayla from Kindergarten up to now, the 5th grade.  In that post, I mentioned that I would try to give you some ideas for the "other math" that I use.  So, here goes. 

Most workbook curriculums I've come across simply don't cover enough, if any, logic, real-life problem solving, hands-on problem solving, graph making, multi-step thinking and other what I call "meaty" work.  Over the years, I've collected many resources here and there that have these types of thinking skills activities in them.  I've also tried to bookmark good math sites, too.  As I run across something I want to do during the school year, I copy it and put it in a folder so I'm not searching at the last minute for a math activity to do on our days off from workbooks.

Some days, the activities will be short, so we'll do several of them (logic matrix activities like those found in Mind Benders are an example.)  Some times, we may work on one activity for a few days because it's so involved (like our candy math days that I'll talk about below.)

Four things to know:

1.  These are supplemental activities, so I DO NOT try to work through every activity in every resource!! 

2.  I try to find activities that are going to add to their math experience, not repeat what they already know.  In other words, if their math workbook program has drilled them to death on subtraction with borrowing, I'm not going to find some cutsie seasonal worksheet that drills them on subtraction with borrowing.  Now, I might find a thought-provoking activity where subtraction with borrowing is necessary to solving the problem. 

3.  I usually work through these sorts of activities with them.  They are challenging and often require more than one step.  I'm sure to be there guiding so frustration doesn't set in. 

4.  Please don't try to go out and aquire everything I'll mention.  I've picked these things up over many years and rarely ever spent more than a $1.00 or $2.00 on anything.  I've also run across the websites over years.  Trying to buy, search through or use everything I'll mention WILL throw you into overload!!  More than anything, I'm hoping to give you examples of what I add to our math curriculum and where I find it.

Logic 

*I love the Mind Benders books from The Critical Thinking Company.

*AIMS has a fun early logic book called Primarily Bears. 

*Logic Posters, Problems and Puzzles

*Puzzlers Paradise

Problem Solving - (includes pretty much everything else like real-life math, creating graphs, etc.)

*Problem Play and Problem Parade 

*Venn Perplexors

*Meeting Math Standards With Favorite Picture Books

*Menu Math

*Munchie Math

*Thinking Skills

Fun Individual Activities To Print From The Internet

*A Taste of Fractions

*Symmetrical Design

*M & M Math

*More M & M Math  (all M & M activities could be done with a variety of foods - Skittles, candy hearts, trail mix, gummy bears, life savers.......)

*Christmas Math

*Valentine Math

*Birthday Math

Internet Resources

*NC Math

*Math Lab

*Math Magic

*Literature For Learning Math Concepts

*Literature & Money Lessons

*NCTM Activities

*Auntie Math

*Menu Math

Online Activities

*Math Playground

*Math Cats

*The Golf of Mexico

*Online Manipulatives

*Rainforest Maths

My children are always so excited on our "problem solving" days.  I hope your children will enjoy a little spicing up of their math time, too!

Some background first.....When Mahayla was in Kindergarten, we started with Horizons Math.  We continued with Horizons through 3rd grade, but used it loosely.  What I mean by that is I usually only bought one of the two workbooks and never bought the Teacher's Guide.  Two or three days a week, we would do one workbook page from Horizons and one workbook page from Miquon.  The other two days I would pull from logic books, problem solving books, NC Math or we'd do real-life sorts of things.  (I'll post very soon on my math resources.)

Last year (her 4th grade year), we switched to Saxon 5/4.  I loved that it was "self-teaching" and I could go over the lesson with her and then leave her to work on the problems without much help.  She, on the other hand, hated it.  She didn't like copying work from the book to her paper.  She didn't like all the problems - mental math, new lessons problems, practice problems, fact sheets.  So, I backed off.  She only had to do mental math, the new lesson problems and 1/2 of the practice problems.  And this only two or three days a week because we were still doing "other math" the rest of the week.

Even though she liked this plan better, math was still such a struggle.  I can't count the number of tears.  I can't tell you how many times Principal Daddy had to be called upon.  I can't tell you how frustrated I became day after day of fussing with her about doing the Saxon work.

Fast forward to yesterday.  Since we only finished about half of Saxon 5/4 (because of adding other math each week), I wanted to see if she needed to finish the 5/4 book or if she was ready to move on to 6/5.  I printed out the Placement Test and let her go for it.  No help.  Would you know that little stinker easily surpassed the 5/4 book, the 6/5 book and almost made it past the 7/6 book??? 

So here's what I told her (as she's laughing at her accomplishment.)  THIS year, I'm keeping a brick by me during math time.  If she dares to complain once about how hard math is, I'm throwing the brick at her!  (Just kidding!)  Seriously, though, NO COMPLAINING ALLOWED!  I've decided to keep with my plans of Saxon 6/5 instead of moving her up.  One reason, I already have it!  ($$$)  Another reason, I see lots in the book that we've never covered that I'd hate to skip.  And finally, I plan to stick to my schedule of Saxon two or three times a week, so 6/5 makes more sense.

My point in all this?  Aren't you glad I'm getting to the point?  Two of the biggest questions I'm asked are, "Aren't you afraid of not finishing a workbook?" and "How do you know you're covering everything your child needs if you use so many different materials?"  I've always said, the proof's in the pudding.  Here's a prime example.  Workbook companies don't know YOUR kids.  Workbook companies also don't KNOW everything.  Workbook companies can't possibly cover EVERYTHING either.  You know what your kids need.  You know how they learn best.  You know what their interests are.  You know how much of one type of learning they can handle before they explode.  You have mommy's intuition.  You have the Holy Spirit leading you in decisions.  (Hopefully, if not, I hope you'll email me and ask how!) 

Are your kiddos getting bored with the same old math day after day? Do they whine and complain about math? Are you looking for a fun way to keep the math skills sharp this summer? Are you looking for a great way to boost those logical thinking skills? I have an answer - Play Games! Card Games. Board Games. Mental Games. Paper and Pencil Games. Whatever you find, I promise your children will do their math with smiles on their faces. Unless their sore losers, but that’s another post! :)

Here are a few ideas to get you started. I betcha most of the games we have came from yard sales or Goodwill. Keep your eyes open this summer! Please add your favorite math games in a comment!!

SET

Mastermind

Battleship

Life

Monopoly

Backgammom

‘Smath

Money Matters For Kids

Sequence

Connect Four

Yahtzee

Hive Alive

Guess Who?

SkipBo

Dutch Blitz

Uno

Perfection

War

Rummy

Hearts

Dominoes

River Crossing

Block To Block

I also want to put a plug in for math computer games. I don’t let my kids have too much computer game time, but there are all sorts of really great free math game sites that are worth a half-hour here and there on those 95 degree days in the summer. (If I knew how to copy my favorites list for you I would, but there are too many math sites to list here. Do a search and you’ll find some great ones!)

Related Tags: math, games, homeschool, fun